Diss. ETH Nr. 15652
EARTHQUAKE SOURCE PARAMETERS IN THE ALPINE-MEDITERRANEAN REGION FROM SURFACE WAVE ANALYSIS
A dissertation submitted to the
Swiss Federal Institute of Technology
Dissertation for the degree of
Doctor of Natural Sciences
Dipl. Natw. ETH
Born on June 30, 1973
Citizen of Stabio - TI, Switzerland
Accepted on the recommendation of
Prof. Dr. Domenico Giardini, examiner
Dr. Jochen Braunmiller, co-examiner
Dr. Urs Kradolfer, co-examiner
Prof. Dr. Torsten Dahm, co-examiner
In this thesis, I present two methods to retrieve earthquake source parameters from regional surface wave data for moment magnitude Mw > 4.3 earthquakes. The first method involves fast and fully automatic moment tensor (MT) computation. Automatization includes near real-time earthquake alert screening, data collection from near-real time accessible broad-band stations at regional distances ( < 20o), MT computation, solution quality assessment and dissemination. The routine is triggered by events with magnitude M > 4.7 in the European-Mediterranean region. MTs are computed using long period data with PREM synthetics. I tested various long period pass bands to evaluate the influence of location accuracy and of simple 1D synthetics on MT retrieval. The best fixed period band for the entire region is currently 50 - 100 s, because relatively few stations are near-real time accessible and often the quickly available locations are of low precision. To assess solution quality, the automatic results are compared with the independent, manually derived Swiss regional moment tensor catalog. Solutions are divided into three qualities. Near real-time application from April 2000 to April 2002 resulted in 38 quality A, with well resolved Mw, depth and focal mechanism, 21 B, with well resolved Mw and 28 unreliable quality C solutions. For Mw > 5.5 we consistently obtained A solutions. Between Mw = 4.5 - 5.5 we obtained quality A and B. In a second step, I significantly improved MT retrieval relative to the standard routine by selecting different period bands for each station and component. The band width depends on the epicentral distance and on the signal-to-noise ratio of each period within each seismogram component. For events in the eastern Mediterranean Sea and the near East, the shortest period used is 50 s. For events in Europe, the short period cut-off varies from 35 s for close stations to 50 s for distant stations. Only periods that exceed a signal-to-noise ratio Rm are actually used. The use of shorter periods and removal of noisy data leads to an improvement of solution quality for 4.3 < Mw < 4.7 earthquakes. For events between May 2002 and September 2003 the new routine provided 20% more quality A solutions than the standard routine. Successful analysis of more smaller earthquakes with the new routine suggests to lower the currently implemented trigger magnitude from M > 4.7 to about M > 4.3.
The second method retrieves seismic moment Mo directly from surface wave amplitudes recorded at regional distances. The amplitude-moment relation is derived from digital broad-band data of 18 earthquakes (3.9 < Mw < 5.1) in and near Switzerland with independent Mo values. The amplitudes were measured at empirically determined, distance varying, reference periods T. For amplitudes measured at T, the distance attenuation term of the surface wave magnitude relation S() = log(A/T)max + 1.66log is independent of distance. Mo is then defined by logMo = S() + 14.90 assuming 1:1 scaling of log Mo - MS, which is true for MS 7.2 in continental areas. Uncertainties of ±0.30 for the 14.90-constant correspond to a factor of 2Mo uncertainty, which was verified with independent data. This relation allows fast, direct Mo determination which can be applied to any earthquake. Re-calibration of the 14.90-constant, however, is probably required for other tectonic regions. I applied the amplitude-Mo relation to determine Mo of 25 stronger 20th century events in Switzerland from analog data. The data recorded by early instrumental seismographs were collected from several European observatories. Amplitudes were measured from scans at large magnification and corrected for differences between T and the actual measurement period. The resulting magnitudes range from Mw = 4.6 to 5.8. The Mw = 5.8 1946 event in the Valais was the largest 20th century earthquake. Magnitude uncertainties for the early-instrumental events are on the order of 0.4 units. The Mo estimates were then used for the up-date of the Earthquake Catalog of Switzerland to calibrate an intensity-Mo relationship for pre-instrumental data. Accurate intensity-Mo relations are fundamental for improved seismic hazard evaluations in regions characterized by moderate seismicity and by long recurrence times of larger events.
In questo lavoro sono presentati due metodi, i quali, utilizzando onde di superficie, permettono di determinare i parametri della sorgente di terremoti regionali con magnitudine Mw > 4.3. Il primo calcola velocemente ed in maniera completamente automatica il tensore momento. Il processo di automatizzazione include l’analisi delle localizzazioni automatiche provenienti da diverse agenzie, la richiesta dei dati in tempo reale da stazioni a banda larga situate a distanza regionale ( < 20o), il calcolo del tensore momento, la deteminazione dell’affidabilita della soluzione e la sua pubblicazione (sul web e via e-mail). La procedura analizza ogni evento dichiarato con magnitudine M > 4.7 e localizzato in Europea e nell’ area mediterranea. I tensori momento sono calcolati usando dati reali a lungo periodo e librerie di sismogrammi sintetici calcolati con modello PREM. Sono stati testati diversi intervalli di periodo, focalizzando l’analisi sulla stabilitá delle soluzioni in base alla precisione della localizzazione usata ed ai sismogrammi sintetici calcolati per un semplice modello 1D. La bassa affidabilità delle localizzazioni disponibili e l’ancora scarsa disponibilità di dati a banda larga in tempo reale evidenziano che l’intervallo compreso tra i 50 ed i 100 secondi risulta essere il più adatto per l’analisi dei terremoti nell’intera area europea e mediterranea. Il confronto dei risultati con un catalogo indipendent di soluzioni tensore momento ha permesso di stabilire le regole generali per determinare l’affidabilità delle soluzioni così ottenute. Quest’ultime sono state quindi divise in tre gruppi: soluzioni di ’tipo A’, con momento sismico Mo, profondità e meccanismo focale affidabili; soluzioni di ’tipo B’, con il solo valore di Mo affidabile ed infine, soluzioni di ’tipo C’, per cui nessuno dei tre parametri elencati può essere considerato affidabile. Durante il periodo compreso tra l’aprile 2000 e l’aprile 2002, la procedura ha ottenuto 28 soluzioni di tipo A, 21 di tipo B e 28 di tipo C. Per eventi con Mw > 5.5 generalmente si sono ottenute soluzioni di tipo A, mentre per eventi con Mw = 4.5 - 5.5 si sono ottenuti soluzioni di tipo A e B. In seguito la procedura è stata significativamente migliorata selezionando l’intervallo dei periodi in base alla distanza e al rapporto tra il segnale ed il rumore contenuto nei sismogrammi. Pertanto, eventi nel Mediterraneo orientale e nel vicino oriente sono stati analizzati con periodi compresi tra 50 e 100 secondi, mentre, quelli verificatisi in Europa, con il periodo più corto che varia tra i 35 s per le stazioni più vicine ed i 50 s per quelle più lontane. Inoltre sono stati utilizzati solo i periodi il cui segnale supera un determinato rapporto tra segnale e rumore, Rm. L’utilizzo di periodi più corti e la rimozione di sismogrammi contenenti rumore permettono un significativo miglioramento soprattutto per eventi con magnitudine 4.3 < Mw < 4.7. L’analisi di eventi occorsi tra il maggio 2002 ed il settembre 2003 con la nuova procedura ha prodotto 66 soluzioni con qualità A, migliorando del 20% le prestazioni rispetto alla prima procedura. L’efficacia della nuova procedura suggerisce di spostare la magnitudine di soglia da M > 4.7 verso M > 4.3.
Con il secondo metodo è possibile calcolare il momento sismico Mo direttamente dall’ampiezza delle onde di superficie. La relazione tra l’ampiezza ed il momento sismico è stata derivata utilizzando dati digitali di 18 terremoti (3.9 < Mw < 5.1) occorsi recentemente in Svizzera e nelle zone limitrofe, per i quali esistono stime indipendenti del momento sismico ottenute tramite inversione del tensore momento. L’ampiezza delle onde di superficie à stata misurata con periodi di riferimento T dipendenti dalla distanza e determinati empiricamente, cosicché il termine dell’attenuazione della magnitudine delle onde di superficie S() = log(A/T)max + 1.66log non varia più rispetto alla distanza tra stazione ed evento. Assumendo un rapporto di 1:1 per l’espressione log Mo - MS, considerata valida per terremoti continentali con magnitudine MS 7.2, il momento sismico è di conseguenza definito dalla relazione logMo = S() + 14.90. L’incertezza di ±0.30 della costante 14.90 porta ad un fattore di incertezza di 2Mo, verificato con dati indipendenti. Questa relazione permette di ottenere velocemente una stima di Mo per terremoti recenti ed è applicabile in ogni regione dopo aver ricalibrato la costante. L’applicazione a sismogrammi registrati su strumenti meccanici ed elettromeccanici, raccolti in vari osservatori europei ha permesso di determinare il momento sismico di 25 terremoti verificatisi in Svizzera e nelle zone limitrofe durante il 20o secolo. Attraverso l’ingrandimento digitale delle immagini dei sismogrammi si è potuta effettuare una precisa lettura dell’ampiezza e del periodo. Questo è stato successivamente corretto rispetto il periodo di riferimento T. Le magnitudini Mw ottenute risultano comprese tra 4.6 e 5.8, quest’ultima per il più forte terremoto avvenuto in Svizzera (1946, Vallese). L’incertezza della magnitudine determinata con questi strumenti è di circa 0.4. I valori di Mo ottenuti hanno permesso la calibrazione tra l’intensità ed il momento sismico per gli eventi pre-strumentali, utile all’aggiornamento del catalogo dei terremoti in Svizzera (ECOS). Precise relazioni tra in momento sismico e l’intensità sono fondamentali per ottenere stime affidabili del l’azzardo sismico in regioni a sismicità moderata e con lunghi tempi di ricorrenza.
In this thesis I present two methods to retrieve earthquakes source parameters (seismic moment Mo, depth and focal mechanism) for moderate to strong earthquakes from regional surface waves. The first method, described in chapters 3 and 4, performs fully automatic and near-real time waveform inversion for the seismic moment tensor. The primary motivation is to provide rapid magnitude and depth estimates after strong and potentially damaging events to assist disaster relief agencies’ response efforts. The second method, described in chapter 5, retrieves Mo from surface wave amplitudes and can be applied to digital broad band seismograms or to early-instrumental analog seismograms. Here, this method is applied to derive Mo from 20th century analog data, that are crucial for long term seismic hazard studies in areas characterized by low and moderate seismicity.
Fast intervention of disaster relief agencies needs accurate Mo and depth estimates within a short time after a potentially destructive event. In the European-Mediterranean area seismicity is mainly located in the eastern Mediterranean Sea (Figure 1.1), where several destructive earthquakes (e.g. the Mw = 7.6 August 17, 1999 Izmit event) occurred during the last years. In Europe and in the central and western Mediterranean Sea seismicity is lower, but strong destructive earthquakes are not rare (e.g. the Mw = 6.0 September 6, 2002 Molise, the Mw = 7.0 May 21, 2003 Northern Algeria and the Mw = 6.4 February 24, 2004 Morocco earthquakes). When such an earthquake occurs, tele-communications in and around the epicentral area are often interrupted. Magnitude and depth estimates, that are crucial for damage evaluation, can then be estimated only using far-field seismological data. Moment tensor (MT) analysis is particularly well suited because MT inversion prevents underestimation of the magnitude compared to the standard location techniques, since moment tensor derived seismic moment of large events does not saturate (Kanamori, 1977).
Fast size and depth estimates are also important after moderate events that do not cause serious damages, but are widely felt. Thanks to the world-wide-web, people search for information immediately after a felt earthquake. In Europe even after a moderate event, a large number of people want to be quickly informed about its magnitude and its consequences. For this reason the press, police and civil protection agencies need fast and precise information about location, size and depth of the earthquake. An example is the recent Mw = 4.5 February 23, 2004 Rigney eastern France event, that was felt over the western part of Switzerland. Within minutes the Swiss Seismological Service got swamped with calls from concerned people and press, and the web-server was heavily accessed.
Quick moment tensor solutions are routinely provided by several groups at a global scale but only for large events (Mw > 5.5). These solutions are disseminated only after revision by a seismologist. Moment tensor solutions for moderate (Mw > 4.8) events in the European-Mediterranean region are now provided by the Swiss Seismological Service, the Italian INGV and the Spanish IGN. Such solutions are computed manually and only for the more relevant earthquakes the moment tensor is available within hours after event origin time, while other earthquakes are analyzed with a delay of weeks to months. The routine presented here computes fully automatic moment tensors from earthquake alert detection, to data collection, moment tensor inversion, solution assessment and finally solution dissemination (via e-mail and web). Computing fully automatic, near-real time moment tensors for a moderate event (4.5 < Mw < 5.0) requires near-real time access to dense networks of broadband and high dynamic range seismometer at regional distance ( < 20o). Significant technological improvements and infrastructure investments during the last few years in the European-Mediterranean area allowed the development and implementation of the procedure described here.
The seismic moment tensor provides not only size and depth estimates to alert disaster relief agencies. Earthquake focal mechanisms, that can be obtained from the seismic moment tensor, provides indispensable information for seismotectonic studies, e.g. for stress field estimation in Switzerland (Kastrup et al., 2004). The strain rate tensor, that can be computed from the moment tensor, combined with GPS measurements and geological data can then be used to infer deformation fields of the crust, e.g. for deformation fields in the eastern Mediterranean See (Jenny et al., 2004). Seismic hazard studies then need accurate magnitude and depth estimates. The automatic routine presented here, will over time result in a complete moment tensor catalog that includes also moderate events, which are significant for regions of low and moderate seismicity.
The Swiss Seismological Service evaluates the seismic hazard in Switzerland. Accurate seismic hazard maps are indispensable for defining building codes in densely populated and industrialized regions or nuclear power plant construction requirements. An example is the Basel area, where strong destructive earthquakes have occurred in the past (e.g. the Mw = 6.9 1356 event, which is the largest event known in Europe north of the Alps) and where numerous chemical plants are operating. To evaluate seismic hazard for such areas with long term recurrent seismicity, requires a complete earthquake catalog covering long time periods.
The Swiss Seismological Service recently completed a comprehensive up-date of the earthquake catalog of Switzerland and surrounding regions (Fäh et al., 2003). The catalog expresses the size of all events using moment magnitude (Mw). The largest part of the catalog includes pre-instrumental events where only epicentral intensities are available. For these events, the epicentral intensities were linked to the seismic moment using a epicentral intensity - seismic moment relation that was inferred using earthquakes with both epicentral intensity and seismic moment available. To enlarge this data-set, also the major 20th century events that occurred within or near Switzerland were used. Seismic moment determination of these events constitutes the second large part of this thesis.
For these events, I collected analog seismograms from various observatories in Europe that were recorded on mechanical and electromagnetic seismographs for which the instrument response is well known and the instrument calibrations were available. Figure 1.2 shows an example of a Wiechert seismograph and one of its recordings. Because of the low quality of such records, a reliable digitization was not possible for most of the collected data-set and, thus, the moment tensor inversion technique could not be applied to derive Mo estimates for most of the events investigated. Nevertheless, accurate readings of amplitude and periods were possible. I thus developed a method to evaluate seismic moment (Mo) directly from surface wave amplitude. The method, developed using broad-band digital seismograms of recent events, was then applied to the early-instrumental seismograms of the 20th century major Swiss events.
A moment tensor can be decomposed into elementary tensors following two different approaches: a pure mathematical decomposition or a decomposition into source components with a physical meaning (e.g. double-couple, explosion, tension crack components, etc.). The decomposition into physical sources is not unique. The paper of Jost & Herrmann (1989) gives an excellent overview on the different decomposition methods that are generally applied in seismology. The MT decomposition performed in this thesis is described in the next paragraphs. Generally the MT can be decomposed uniquely into an isotropic and a deviatoric part. In order to derive a general formulation of the moment tensor decomposition, let mi be the eigenvalues corresponding to the orthogonal eigenvector ai = (aix,aiy,aiz)T of M pq. Using the orthogonality of the eigenvectors, we can write the principal axis transformation of M in reverse order as:
In this study the deviatoric part is decomposed into a double-couple component and a compensated linear vector dipole (CLVD) (Knopoff & Randall, 1970). Assuming |m3*|<|m 2*|<|m 1*| the deviatoric part can be rewritten as
The focal mechanism (strike, dip and slip) of the earthquake can be solved from the six elements of the seismic moment tensor:
The magnitude of an earthquake can be expressed in term of scalar seismic moment Mo that can be determined from the seismic moment tensor:
A more extensive and detailed description of the seismic moment tensor can be found in Jost & Herrmann (1989), Dahlen & Tromp (1998) and in Aki & Richards (2002). For details of the MT code see Giardini (1992).
We produce fast and automatic moment tensor solutions for all moderate to strong earthquakes in the European-Mediterranean region. The procedure automatically screens near real-time earthquake alerts provided by a large number of agencies. Each event with magnitude M > 4.7 triggers an automatic request for near real-time data at several national and international data centers. Moment tensor inversion is performed using complete regional long period (50 - 100 s) waveforms. Initially the data are inverted for a fixed depth to remove traces with a low signal-to-noise ratio. The remaining data are then inverted for several trial depths to find the best-fit depth. Solutions are produced within 90 minutes after an earthquake. We analyze the results for the April 2000 to April 2002 period to evaluate the performance of the procedure. For quality assessment, we compared the results with the independent Swiss regional moment tensor catalog (SRMT) and divided the 87 moment tensor solutions into three groups: 38 quality A with well-resolved Mw, depth and focal mechanism; 21 quality B with well-resolved Mw; and 28 unreliable quality C solutions. The non-homogeneous station and event distribution, varying noise level, and inaccurate earthquake locations affected solution quality. For larger events (Mw > 5.5) we consistently obtained quality A solutions. Between Mw = 4.5 - 5.5 we obtained quality A and B solutions. Solutions that pass empirical rules mimicking the a posteriori quality for our data set are automatically disseminated.
Quick and accurate source parameter determination (magnitude, depth and focal mechanism) provides important information for fast intervention in areas strongly damaged by large earthquakes. When compared to standard determination of earthquake location and magnitude, moment tensor inversion usually provides more accurate source parameters and particularly so for the size of large events, since their moment magnitudes Mw do not saturate (Kanamori, 1977). The recent increase in the number of near real-time accessible broadband stations in the European-Mediterranean region now allows automatic, near real-time moment tensor analysis monitoring strong events.
Accurate and quick moment tensor inversion is routinely performed on a global scale by the Harvard Centroid-Moment Tensor (CMT) project (Dziewonski et al., 1981; Dziewonski & Woodhouse, 1983), the United States Geological Survey (Sipkin, 1982, 1986) and the Earthquake Research Institute (ERI), Japan (Kawakatsu, 1995). These approaches use teleseismic data, limiting analysis to stronger earthquakes (Mw > 5.5). Analysis of smaller earthquakes requires data recorded at regional distances, which is becoming possible with the growing number of broadband seismic networks. Several groups in the United States (Dreger & Helmberger, 1993; Ritsema & Lay, 1993; Romanowicz et al., 1993; Náblek & Xia, 1995; Braunmiller et al., 1995; Thio & Kanamori, 1995; Dreger et al., 1995; Pasyanos et al., 1996) and Japan (Kubo et al., 2002), routinely invert for the seismic moment tensor using seismic data recorded at near regional distances ( < 10o).
In the European-Mediterranean region, event-station distances are generally larger ( > 10o) than in the western United States. However, several studies (Arvidsson & Ekstrom, 1998; Braunmiller, 1998) showed that source parameters of moderate events can be determined routinely with long period regional data (T > 30 - 40s) for larger event-station distances. The Swiss Seismological Service (Braunmiller et al., 2000, 2002) and the Italian Istituto Nazionale di Geofisica e Vulcanologia (INGV) (Pondrelli et al., 2002) now routinely produce moment tensor solutions in the European-Mediterranean area for moderate to strong earthquakes (Mw > 4.5), and smaller earthquakes (Mw > 3.0) in the Alpine area (Braunmiller et al., 2000, 2002). Small to moderate earthquakes in the western Mediterranean region are regularly processed by the Spanish Instituto Andaluz de Geofísica (Stich et al., 2003).
Here we test whether the current near real-time data availability and location accuracy are sufficient for automatic regional moment tensor retrieval using intermediate to long period surface waves (50 - 100 s). Our goal is to develop a robust procedure that provides fully automatic, fast and reliable solutions for moderate to strong earthquakes in the European-Mediterranean region.
Our automatic procedure consists of two main parts: first, moment tensor inversion for a detected earthquake and second, automatic quality assessment of the solution. We first describe the method and show the reliability of the automatic solutions. Then we present empirical rules for automatic quality assessment. Finally, we discuss source parameters (focal mechanism, depth and Mw) and investigate factors that affect solution quality.
Ultimately, we like to obtain a moment tensor within a few minutes after an event. This requires on-line data access to stations at close epicentral distances, currently unavailable for most of our study region. We anticipate that present waiting periods due to sparse networks and time delays for data acquisition will shorten considerably in the future.
Automatic moment tensor inversion consists of several steps (Figure 3.1). A few minutes after an event, an automatic earthquake alert (location, magnitude) is generally available, provided by the Swiss Seismological Service (SED) and other agencies linked to our institute. Automatic information coming from many agencies may include false alarms, but guarantees that we miss no significant event. We screen incoming information and any event in the European-Mediterranean area (22o < Lat < 68o,-25o < Long < 60o) with magnitude M > 4.7, independent of magnitude type [ML,mb,MS], starts the routine automatically.
We invert complete broadband waveforms recorded at regional epicentral distances ( < 20o); therefore, our data window is 30 minutes long. We wait an additional 20 minutes to assure data availability (Figure 3.1) before sending data requests to the AutoDRM (Kradolfer, 1996) of several international (ORFEUS, USGS) and national data centers (in Austria, Czech Republic, Germany, Israel, Norway, Switzerland) that provide near real-time broadband seismograms. The data centers automatically process these requests and usually within 20 minutes all available seismograms are received at our server to be stored and prepared for inversion. 70 minutes after event origin time, data acquisition is considered complete and the inversion starts, resulting in an automatic moment tensor solution within 90 minutes after an earthquake.
Between April 2000 and April 2002 only stations in central and northern Europe, Israel, the Caucasus region and Russia provided near real-time data (black triangles in Figure 3.2). Data availability and the response time of data centers varied. To ensure that we received a sufficient number of seismograms, we chose a relatively long waiting period before requesting data and starting the inversion. Stations in the western and central Mediterranean Sea, Turkey and eastern Europe (white triangles in Figure 3.2), became available during mid-2002 and are only shown to illustrate the evolving and improving station coverage.
The algorithm uses intermediate to long period three-component regional data. The inversion code, described in Giardini (1992), has already been applied to many earthquakes (Giardini, 1992; Giardini et al., 1993a,b; Sicilia, 1999). Synthetic seismograms are generated by normal mode summation (Woodhouse, 1988) computed for the PREM-Earth model (Dziewonski & Anderson, 1981) at different source depths and stored in libraries for quick access. The moment tensor is constrained to be deviatoric. We do not invert for the source centroid but compute time corrections by re-aligning data and synthetics (Giardini, 1992). Depth is retrieved by minimizing the normalized variance (defined as ratio of variance over data vector norm) for different trial depths.
The moment tensor inversion automatically starts 70 minutes after an event (Figure 3.1). The alert is the first available location, which is not necessarily the best epicenter estimate. 70 minutes after an event, several automatic and/or manual locations are usually available and we choose the a priori most accurate. We prefer a location from a network that surrounds the epicenter. When that is not available, we look for a manual location or one provided by an agency with a large aperture network.
The seismograms are bandpass filtered between 50 and 100 s period. A lowpass filter at 50 s applied to regional seismograms minimizes the effect of inaccurately known propagation paths and allows moment tensor retrieval of moderate sized earthquakes (Mw > 4.5) with a simple average 1D velocity model (Arvidsson & Ekstrom, 1998). We tested other filter parameters and report results in Section 3.5.2.
The automatic inversion consists of two main steps. First, the entire data set is inverted for a fixed depth (18 km) to remove traces with a low signal-to-noise ratio (high normalized variance > 0.8) and large re-alignment. From tests we found, that the choice of the fixed depth - 18 km or different depth - has little effect on the remaining data set and basically no effect on our results. The remaining traces are then inverted for several depths. The 50 - 100 s data have little depth resolution, because long period surface-wave excitation functions have little depth variation. Thus, we apply a limited number of depth-steps with increasing step width (10, 14, 18, 25, 31, 42, 55, 75, 100, 125, 150, 175 and 200 km) to find the best fitting depth. We use a minimum 10% variance increase to estimate depth uncertainty; our uncertainty range is simply defined by the trial depths that just exceed the 10% increase. We consider this uncertainty estimate conservative, since the waveform fit degrades visibly.
We started our procedure for automatic moment tensor inversion in April 2000. By April 2002, we obtained 87 moment tensor solutions (Figure 3.2, Table 3.1), mainly for events in the seismically active central-eastern Mediterranean region (Jackson & McKenzie, 1988).
We check the quality of the automatic moment tensors because solution accuracy depends on event location, location precision, station distribution and signal strength. First, we use an independent high-quality moment tensor catalog to quantify true quality. Second, to estimate solution quality automatically, we derive rules from solution parameters which reproduce overall true quality. These rules are applied automatically before disseminating solutions.
The Swiss automatic moment tensor (SAMT) catalog contains many moderate events not included in global catalogs, incomplete below Mw = 5.5 and with very few Mw < 5.0 events. Therefore, we compared our automatic solutions with those of the Swiss Seismological Service’s regional moment tensor (SRMT) catalog. The SRMT covers the European-Mediterranean area and is nearly complete down to mb = 4.5 (Braunmiller et al., 2002). SRMT solutions are derived with a more complete data set available weeks to months after an event than the data set used for SAMT analysis. SRMT solution quality is high based on comparison with other independent source parameter estimates available for selected events (Braunmiller et al., 2002). For a few events east of SRMT coverage (> 55oE), we compared our solutions with the Harvard catalog, or when not available, with magnitudes given by the USGS.
The true quality of a SAMT solution is estimated by comparing its focal mechanism, depth and Mw relative to the SRMT solution. We distinguish three quality levels: A has well-resolved mechanisms, depths and Mw, B has only well-resolved Mw, and C is unreliable. Figure 3.3 provides a sketch of the quality criteria described below.
The most stable focal mechanism parameters are the double couple part and the principal axes’ orientation. Moment tensor solutions for the same earthquake included in different catalogs may show differences in the non-double couple part (ratio of smallest to largest moment tensor eigenvalues following Dziewonski et al. (1981)). These differences are often introduced by an inaccurate source location (Zhang & Lay, 1990), differences in the station configuration (ílený & Vavryuk, 2002), inaccurate path-models (Henry et al., 2002; Fröhlich, 1994) and a poor resolution of Mr and Mr (Kuge & Lay, 1994). We therefore use mean axes’ difference |Ax|, defined as the average of the differences in principal axes’ orientation, to estimate the similarity between SAMT and SRMT focal mechanisms.
The mean difference |Ax| is zero for identical axes’ orientations. Interchanging two axes (for example changing a normal to a thrust or a left lateral to a right lateral mechanism) results in |Ax| = 60o. We thus require A quality solutions to have |Ax|< 30o; solutions with |Ax| > 30o are either B or C quality, depending on the magnitude difference (Figure 3.3). Figure 3.4 (top) shows the distribution of |Ax|. For quality A solutions the mean value of |Ax| is 18.8o ± 6.7o. Two solutions with |Ax|< 30o are not quality A, because one violates the depth (quality B) and one the magnitude criterion (quality C).
We also checked the focal parameter agreement between the SAMT and SRMT catalogs using the radiation pattern coefficient P (Kuge & Kawakatsu, 1993), a parameter describing the radiation pattern similarity of two mechanisms. Our median P = 0.85 for A quality solutions compares well with the median of P = 0.88 found by Helffrich (1997) who compared ERI, Harvard and USGS catalogs for shallow earthquakes (most SAMTs are for shallow earthquakes).
Because of the low-depth resolution and the discrete set of trial depths, we require that the difference |z| between SAMT depth range (best-fit depth plus uncertainty) and SRMT depth is < 10 km for an A quality solution. A similar scheme was proposed by Kubo et al. (2002) when comparing the Japanese regional NIED catalog with the Harvard-CMT and the Japanese Meteorological Agency (JMA) focal mechanism catalog. Differences |z| > 10 km result in B or C solutions (Figure 3.3). Figure 3.4 (middle) shows |z| for the three quality groups.
The difference between SAMT and SRMT Mw estimates must be < 0.2 units for an A or B quality solution (Mw = - 10.73 following Kanamori (1977)). A required difference |Mw|< 0.2 is consistent with Pasyanos et al. (1996), who found that automatic and revised regional MT solutions in northern California have Mw estimates that usually differ by less than 0.2 units even when the focal mechanism and depth estimates differ strongly. Mw depends mainly on the signal amplitude and is therefore the parameter easiest to resolve. One goal for our automatic procedure is to provide robust Mw values so that disaster relief agencies may quickly estimate possible earthquake damages. Damages are governed by the rupture process and local site effects; our Mw can only help to estimate whether no, local or widespread damages are expected. Therefore we accept an Mw estimate as accurate even when the focal mechanism and/or the depth exceed their A-quality threshold: these are our quality B solutions. |Mw| > 0.2 are quality C, irrespective of focal mechanism and depth (Figure 3.3). The distribution of |Mw| is shown in Figure 3.4 (bottom).
For our data we observe that SAMTs with |Ax|< 30o usually have |z|< 10 km and |Mw|< 0.2. Based on our rules, the 87 automatic moment tensors are divided into 38 quality A, 21 quality B and 28 quality C solutions.
The true quality can be verified only a posteriori. For automatic solution dissemination, we derive empirical rules, matching the a posteriori true qualities that can be implemented into the automatic procedure. The rules follow three principles: (1) applied to the whole data set, the rules should closely follow the true quality; (2) the rules should not overestimate quality: true quality B solutions should not be assigned Aa, and quality C should not be assigned Aa or Ba (we use the superscript a to denote assigned quality). We want to have high confidence that an automatic Aa solution is truly A; (3) the rules should be simple.
A combination of number of stations and components used (i.e., with good signal-to-noise ratio) provides a simple yet reasonably accurate measure to assess solution quality (Table 3.2). The empirical rules were defined based on the April 2000 to April 2002 data set and may be modified when, for example, station availability increases. Figure 3.5 shows that it is generally sufficient to use 2 or more components for each station to obtain quality A solutions even when only a few stations can be used. Using fewer stations and components results in lower quality solutions. Many solutions of earthquakes located in the larger Iran area result in quality B or C, because of the few stations available. For the southern Aegean Sea (34o < Lat. < 38.5o; 20o < Long. < 30o) we observe an interesting difference: we need more stations and components to obtain true quality A solutions (Figure 3.5). This exception is possibly due to large event-station distances (Figure 3.2).
In this section we focus on the geographical event distribution and factors that cause low true quality solutions. We also compare our Mw, depths and focal mechanisms results with the SRMT, the Harvard (CMT) and INGV (MEDNET) moment tensor results to illustrate their high consistency.
The distribution of the analyzed events (circles, Figure 3.2) reflects long-term seismicity (Jackson & McKenzie, 1988). The distribution of high quality solutions, however, is also affected by the station distribution (black triangles, Figure 3.2). Generally, analysis is hampered by long average event-station distances (Figure 3.6). Most data come from stations at distances > 7o with a peak around = 14o - 15o caused by high seismicity in the Aegean Sea and high station density in central Europe. Most high quality solutions are produced for earthquakes in the central-eastern Mediterranean region, where data from stations in central Europe, Israel, the Caucasus region and Russia provide good azimuthal coverage. In the western Mediterranean region, seismicity is relatively low and the inadequate station distribution resulted in a quality B solution for the one event analyzed. Station coverage for events in the Caspian Sea and Zagros mountain regions is also low and few of the frequent events have well-recovered source parameters. In central and northern Europe we obtained few high quality automatic solutions. Although a large number of stations is available, there, the lowpass filter at 50 s precludes moment tensor retrieval for the typically smaller (Mw < 4.5) events of this region.
Not all events triggered by our automatic procedure resulted in a moment tensor. Triggered events result in no-solution when either (1) no data are available, (2) the automatic alert is a false alarm, (3) the epicenter is strongly mislocated, (4) the true magnitude is far lower than the alert magnitude or when any of these cases combine. Case (4) caused most no-solution events due to the low trigger-threshold set for analysis (M > 4.7), that assures the processing of all stronger events. We let the procedure decide whether a solution can be produced or not. For a few smaller events, few traces containing only long-period noise were inverted, resulting in quality C solutions.
Earthquake size is the most stable source parameter and a few, good signal-to-noise seismograms generally constrain the seismic moment Mo. Figure 4.12 shows the high correlation of the automatic Mw estimates relative to SRMT, CMT and MEDNET Mw’s. Mean differences are very small, < 0.02 relative to SRMT and CMT, and lower than 0.1 unit relative to MEDNET, with standard deviations close to 0.1. The linear regressions (dashed lines in Figures 4.12) have slopes close to 1 and small intercepts, roughly consistent with a one-to-one relation between the magnitude estimates. We did not interpret small apparent differences because the data set is too small. Mean differences and regressions were determined for A and B quality solutions combined, because we did not see any significant systematic difference in the A and B quality Mw estimates (Figure 3.4 bottom).
Quality A solutions were obtained for earthquakes from Mw = 4.5 to Mw = 7.0. In general larger events (Mw > 5.5) result in quality A solutions (Figure 3.8), and earthquakes with Mw < 5.5 result in quality A or B. We obtained 3 quality B solutions for earthquakes with Mw > 5.5; in all cases the lower quality was caused by the inaccurate quick location used for the inversion. We repeated the inversion with the PDE-location. In two cases we obtained A quality solutions. One case stayed B quality, because of |Ax| = 31o, just outside the A quality criterion (|Ax|< 30o); the depth and magnitude differences both satisfied the A quality criteria. The number of MT solutions and the ratio of A/B solutions decrease for earthquakes with Mw < 5.0 due to lower signal strength and the large event-station distances (Figure 3.6).
Figure 3.9 illustrates the limitations of long-period (T > 50 s) analysis with respect to magnitude or signal strength. Variance increases with decreasing event size, effectively setting the lower limit for retrieving MT solutions to Mw 4.5. At such long periods signal strength at smaller magnitudes is just slightly above the noise level. We also observe that variance for quality B is higher than it is for A solutions.
Long period surface waves offer only limited depth resolution (Giardini, 1992). However, depth of quality A solutions agree very well with those in SRMT, CMT and MEDNET (Figure 3.10). The mean difference is always < 4 km with a standard deviation < 15 km. Our SAMT catalog contains only 3 deep earthquakes with quality A and we observe no significantly greater depth estimate differences for these events. Events with large depth difference (|z|> 20) are different events in each panel, reflecting the depth differences in the catalogs used for comparison. Note that quality A solutions for shallow and deep earthquakes are always correctly distinguished.
Figure 3.11 shows the focal mechanisms of the true quality A solutions together with the available SRMT, CMT and MEDNET solutions. Focal mechanisms show excellent agreement for all earthquakes: shallow, deep, weak and strong. Larger differences exist for only 3 CMT solutions (Nr. 20, 33, 36). These earthquakes are small (Mw = 5.0 - 5.1) for CMT analysis. Their CMTs have large non-double couple parts (0.316 < < 0.342) and large relative moment tensor uncertainties E (0.261 < E < 0.673) compared to the average values = 0.124 and E = 0.165 of all 19589 CMT solutions (1976 until November 2002). E is defined in Davis & Fröhlich (1995). Moment tensors with high and E have poorly constrained focal parameters (Fröhlich et al., 1997).
Our goal is to retrieve as many quality A solutions as possible, even for smaller earthquakes (4.5 < Mw < 5.0), while minimizing the number of quality C solutions. Solution quality depends on station distribution, location accuracy and the ability to correctly match phases in the seismograms. For the given station distribution (Figure 3.2), we performed two tests. First, we tried to find the optimum frequency band for analysis with the quickly available locations and data set used for near real-time processing. The frequency band needs to match phases - easy at longer periods - and contain good signal-to-noise seismograms - higher at shorter periods. We thus performed inversions for 5 selected period ranges (40 - 60, 45 - 80, 50 - 100, 60 - 125, and 70 - 140 s). In a second step, we repeated the same analysis with the more accurate PDE-locations to see whether location accuracy affects the choice of frequency band.
The number of quality A, B and C solutions changes strongly with different frequency bands (Figure 3.12, top left). The largest number of quality A solutions (and highest ratio of A/C solutions) is obtained with the 50 - 100 s band for the quickly available locations. Using the more accurate PDE-locations, the optimal period range shifts to lower periods of 45 - 80 s (Figure 3.12, bottom left). The reason for this shift is that mislocation introduces errors in the initial phase that are then mapped onto the moment tensor. The effect is smaller at longer periods (Patton & Aki, 1979) and the accuracy of the quick locations sets the optimum period range to 50 - 100 s. At longer periods (60 - 125, 70 - 140 s) the number of quality A and B solutions decreases for the quick and the PDE-locations because of weak signals for the smaller events. At these period ranges, only stronger earthquakes can be analyzed.
For shorter periods (40 - 60 s), the number of quality A solutions decreases strongly even for the PDE-locations. In most cases, quality A solutions at 45 - 80 s (or 50 - 100 s) become B at 40 - 60 s (Figure 3.12, bottom left). At periods below 50 s, surface waves become more sensitive to crustal thickness and average crustal velocity variations so that significant travel-time differences relative to PREM result (Larson & Ekström, 2001; Pasyanos et al., 2001). Unresolved near-source earth structure may also cause surface wave amplitude anomalies (van der Lee, 1998). Both phase and amplitude differences limit reliable moment tensor retrieval below 50 s period for our uneven station distribution and our average event-station distances of about 1500 km.
The frequency band chosen has little effect on the overall quality of the focal mechanism and depth estimates for quality A solutions. This also holds for the Mw estimates for A and B solutions measured relative to SRMT (Figure 3.12). The median values of the radiation pattern coefficient P are generally high, close to the value found by Helffrich (1997), and decrease only slightly for shorter periods. There is no significant change for the mean depth difference; all means are < 3 km with standard deviations < 15 km. Magnitude Mw differences for quality A and B solutions are close to 0.0 unit with standard deviation < 0.1.
From our tests, we deduce that the 50 - 100 s period range is the best average range with the quickly available locations for the entire European-Mediterranean region. It allows routine MT analysis for earthquakes down to Mw 4.5.
Two factors limit automatic retrieval of well-resolved MT for Mw > 4.5 earthquakes: location accuracy (Figure 3.12), usually lower for smaller events (Mw < 5.0) and the limited, inhomogeneous distribution of near real-time accessible stations (Figure 3.2).
Location accuracy is more important for shorter period analysis. Accurate quick locations are starting to become routinely available from the European-Mediterranean Seismological Center (EMSC). The EMSC merges automatic arrival-time picks from several European institutions, and the virtual network’s improved station coverage and aperture is capable of accurate automatic locations (Bossu et al., 2002). The locations we have received since June 2002 are of good quality.
The geographical distribution of near real-time accessible broadband stations is limited and inhomogeneous (Figure 3.2). In the context of the European MEREDIAN project (van Eck et al., 2001), the ORFEUS data center now has near real-time access to an increased (and still growing) number of broadband stations. Their distribution (white triangles, Figure 3.2) partially fills gaps like the western and central Mediterranean Sea, Turkey and eastern Europe. Northern Africa, however, lacks sufficient broadband instruments. For events since mid-2002, these data are available to us. Preliminary scanning of the results shows that the smaller epicentral distances overall and improved azimuthal coverage already increased the number of quality A relative to quality B and C solutions.
Better quick locations and a denser network (and the resulting reduced epicentral distances) also may speed up analysis and lower magnitude thresholds in the future. For closer epicentral distances, 15-minute seismograms contain the entire surface wave train. Reducing the seismogram length by 50% and assuming faster data accessibility, automatic solutions could then be obtained within 45 - 60 min after an event. At closer epicentral distances, signal strength is larger and relatively less perturbed by crustal and upper mantle heterogeneities. Combined with analysis at shorter periods, we would expect more reliable source parameter estimates for smaller events than possible now.
Although improved EMSC locations and additional data from ORFEUS started becoming available in mid-2002, we did not include these more recent events here. We wanted to have constant conditions - location and data access - for the entire period covered in this paper and therefore did not mix the two intervals.
We presented a fast and fully automatic procedure for moment tensor retrieval of moderate to strong (Mw > 4.5) earthquakes in the European-Mediterranean region using long-period (50 - 100 s) regional ( < 20o) seismograms. Automatic solutions are currently available within 90 minutes after an event. From April 2000 to April 2002, we obtained 87 moment tensor solutions that we grouped into three qualities based on main stress axes’ orientation, depth and Mw similarity with an independent, high quality moment tensor catalog. For 38 quality A solutions, magnitude, depth and focal mechanisms are well-resolved; 21 B solutions have well-resolved magnitude; 28 C solutions are not reliable. We derived simple empirical rules based on the number of stations and components used to predict the quality of a solution without a seismologist’s interference. Automatic quality Aa MTs are disseminated to EMSC (http://emsc-csem.org), quality Aa and Ba solutions are displayed on our web page (http://www.seismo.ethz.ch/mt), Aa and Ba solutions can be obtained via e-mail (contact first author for details).
In the near future, we foresee largely improved near real-time automatic waveform analysis capabilities and successful routine MT applications to smaller earthquakes (Mw 4.0) for most of the European-Mediterranean region. Many national networks are transitioning to BB stations with near real-time data transmission. Connecting these national data centers via internet will create a dense European-wide virtual network that could be used, for near real-time event detection, size determination and MT inversion in the European-Mediterranean region. We can realize this scenario by increasing both the number of BB stations, particularly where no or few stations currently exist, and near real-time open access to these data for the scientific community.
We thank Daniel Stich and an anonymous reviewer for their constructive comments. We thank Suzan van der Lee and Yuan Gao for providing modified moment tensor analysis codes. We appreciate discussions with Günter Bock about the topic, we will miss him. We thank Kathleen J. Jackson for enhancing the manuscript by correcting our grammar. Most figures were produced with GMT (Wessel & Smith, 1995). High quality near real-time broadband data were obtained from the following institutions and networks: GEOFON, Potsdam (Germany); Gräfenberg Seismological Observatory, Erlangen (Germany); Institute of Physics of the Earth, Masaryk University, Brno (Czech Republic); MEDNET, Istituto Nazionale di Geofisica e Vulcanologia, Roma (Italy); National Data Center, Soreq (Israel); Zentralanstalt für Meteorologie und Geodynamik, Wien (Austria); and the additional members of the MEREDIAN consortium and its lead agency ORFEUS, De Bilt (The Netherlands). Quick earthquake locations are send to us by EMSC (France); Geol. Survey B-W, Freiburg (Germany); GERESS array (Germany); GSR, Obninsk (Russia); IGN, Madrid (Spain); INGV, Rome (Italy); IPRG, Tel Aviv (Israel); LDG, Paris (France); NEIC (USGS); NIEP, Bucharest (Romania); SDAC, Hannover (Germany); (see http://www.seismo.ethz.ch/redpuma).
I present an improved automatic Frequency Adaptive Regional Moment Tensor (FARMT) routine. FARMT computes moment tensors (MT) of events with magnitude down to Mw 4.3 in the European - Mediterranean area using complete surface wave seismograms recorded at regional distances ( < 20o). Two features lead to significant improvements of FARMT compared to the original standard routine (SR) for 4.3 < Mw < 4.7 events. First, the short-period cut-off at each station depends on station-event distance. Second, FARMT performs a signal-to-noise analysis to remove noisy traces and period-bands that do not exceed a minimum signal-to-noise ratio Rm. Tests performed to asses the short period cut-off and Rm for automatic FARMT indicate that the short period cut-off for events in the eastern Mediterranean Sea and the near East is 50 s. Events in Europe can be analyzed with a distance-variable short period cut-off ranging from 35 s for the closest to 50 s for distant stations. Values of Rm = 1 - 5 lead to well resolved mechanisms and use more seismograms for inversion than the standard method. The automatic FARMT uses Rm = 2, since it assures usage of seismograms with weak, often nodal signal, and reduces the number of iterations by about 20% to reach the final MT. For the May 2002 to September 2003 data-set, the automatic FARMT resulted in 66 solutions with well determined MT, which is a 20% increase relative to SR.
Since April 2000, the Swiss Seismological Service (SED) computes real-time and fully automatic moment tensor (MT) solutions for Mw > 4.5 earthquakes in the European-Mediterranean area (Bernardi et al., 2004). Moment tensors are computed using 50 - 100 s period surface waves recorded at regional distances ( < 20o). For stronger events (M w > 5.5) the complete moment tensor (seismic moment Mo, depth and focal mechanism) is generally well resolved. For 4.5 < Mw < 5.5 events, Mo is generally well resolved while depth and focal mechanism resolution decreases with decreasing event size. Goal of this work is to improve the results for 4.5 < Mw < 5.5 events and to extend automatic analysis to even smaller events.
Fast and reliable MT analysis for moderate events in densely populated areas like central Europe is becoming a necessity for the seismological community to provide rapid information to the public. An example is the recent Mw = 4.5 February 23, 2004 Rigney, eastern France, event, that was felt over the entire western part of Switzerland. Within minutes the press and a large number of concerned people called the SED or connected to the SED’s web-page looking for information about the event. In addition to rapid information, efficient automatic MT analysis for Mw >~126' 4.5 events will relatively quickly lead to a MT catalog, even in areas with low seismicity, like most of the European - Mediterranean region that is indispensable for seismic hazard and seismotectonic studies.
The current routine - called standard routine (SR) here - satisfactorily analyzes only few events with Mw 4.8, because analysis is performed at a fixed period band of 50 - 100 s. The 50 - 100 s interval is the best single period interval for automatic MT computation in European and Mediterranean region (Bernardi et al., 2004), considering the sparse set of near-real time accessible stations, the limited accuracy of quick locations, and the complicated tectonic setting.
However, since 2002 the number of near-real time data has significantly increased in the European - Mediterranean region. Many of these stations are part of the Virtual European Broadband Seismograph Network (van Eck et al., 2004) and data can be collected in near-real time from the ORFEUS data-center. Accuracy of quick automatic locations for M > 4.5 events has significantly increased in the European - Mediterranean region because more stations contribute data resulting in a relatively dense, large aperture European network. The quick, more accurate locations, provided by EMSC (Maset-Roux & Bossu, 2004) and by ORFEUS (van Eck et al., 2004), together with the VEBSN data are key factors for automatic MT analysis of moderate events.
In this chapter, I present a modified procedure, which significantly lowers the magnitude threshold for automatic MT analysis toward Mw 4.3. For such small events, signal energy above 50 s is generally weak and MT analysis requires inclusion of shorter periods. Although more near-real time broad-band stations exist, improving azimuthal coverage and lowering event-station distances, the distribution is still not homogeneous resulting in event data-sets that include near and far stations. Thus, I derived a distance dependent short period cut-off, which allows an optimal period band setting for MT inversion using near and far stations simultaneously (Section 4.3). An additional short and/or long period cut-off depending on the signal-to-noise ratio is applied to remove those periods without sufficient signal (Section 4.4). The notation from chapter 3 is kept, quality A solutions have well resolved Mo, depth and focal mechanism, quality B only well resolved Mo, and quality C is not reliable. Quality is assessed relative to SRMT (Braunmiller et al., 2002).
The standard routine SR uses a short period cut-off at 50 s for all event-station distances, ensuring synthetics and observed seismograms are in phase even for large distances ( 20o). At shorter distances, PREM synthetics can probably be used at shorter periods (Braunmiller et al., 2002). The test data-set consists of 20 events covering the entire European - Mediterranean region . The data-set includes crustal and intermediate deep events and covers the magnitude range 4.5 < Mw < 6.7. The automatic SR resulted in quality A solutions for each event, implying that a sufficient number of seismograms (from 39 to 115) could be used for inversion in the 50 - 100 s pass band. The automatic moment tensors were then revised using the PDE-location, to exclude low quality waveform fit because of inaccurate locations. These solutions are used as reference (Table 4.1 and Figure 4.1).
A waveform fit example is shown in Figure 4.2. The waveforms are the vertical components of stations ISP ( = 2.80) and DIX ( = 16.40) for the M w = 5.8 April 10, 2003 Turkey event. For station ISP, the waveform fit remains good even for short period cut-offs of T = 30 - 35 s. For DIX, the fit decreases significantly for periods T < 40 s. The waveform fit at a given short period cut-off depends on epicentral distance. This general behavior is caused by limitations imposed by the PREM model which is used throughout the study area for synthetic seismogram calculation.
Figure 4.3 shows the normalized variance difference for each short period cut-off as a function of epicentral distance for all components (at least 441 observations per component) relative to the 50-100 fit. The mean (solid line) and standard deviation (dashed lines) are moving window values with 1o steps using all data-points in the surrounding ±1o distance. Figure 4.3 shows that the variance difference increases for longer epicentral distances (from left to right in each panel) and for shorter period cut-offs (from bottom to top in each column). This effect is slightly stronger for horizontal components, probably because of the higher noise levels and possibly anisotropy. The components are not rotated to transversal/radial and polarization anisotropy observed in the Mediterranean region (Marone et al., 2004) affects both horizontal components.
The variance difference increases smoothly over the = 20 - 200 distance interval. I arbitrarily fixed the distance interval where the mean normalized variance difference does not decrease more than -0.1 units for one of the three components. Based on Figure 4.2, even larger variance increases appear to provide adequate fits (and thus MT solutions), however, the small 0.1 value ensures stable automatic results. All components have the same distance range for the sake of simplicity. Based on this definition, the 30 s short period cut-off could be applied only for distances < 30, were only few data are available. I thus selected 35 seconds as the shortest cut-off period. Table 4.2 lists the resulting distance - short period cut-off setting (T2). Table 4.2 also shows the standard 50 - 100 s pass-band for all distances (T0), and two additional settings, which deviate slightly from T2: T1 is a more and T3 is a less conservative setting. For full evaluation of the Ti cut-offs, I applied all four settings to a 17 month data-set in the European - Mediterranean area (section 4.5) combined with the signal-to-noise ratio dependent period band cut-off derived in the next section.
The standard procedure uses a 100 s long period cut-off to compute the MT. When the seismogram contains only noise or when the signal is above the noise only for periods shorter than 100 seconds, the normalized variance of the station component is high. In the SR such traces are removed iteratively (Bernardi et al., 2004).
Goal of this section is to implement a more straightforward approach to remove noisy traces. With the following signal-to-noise ratio analysis the period band where the ratio exceeds a value Rm are identified and selected for MT inversion.
This approach has two main consequences. First, when the epicentral distance criteria, for example, indicates that the 50 - 100 s period range should be used for MT inversion and if the signal-to-noise ratio of that trace does not exceed Rm for the entire range, the seismogram will be removed from the data-set. This reduces the number of iterations and shortens the computing time. Second, using only the period range where the data exceed Rm, for instance from 50 s to 70 s, lowers the variance and the seismogram is used for inversion. The resulting data-set for automatic MT inversion contains more traces than the SR, which is important for moderate events analysis, where generally only few traces with good signal-to-noise ratio exist.
The signal-to-noise ratio is determined by simple division of signal and noise power spectral density for each sampled frequency. All seismograms have 1 second sampling interval and are zero-padded to 2048 points. A 9-point smoothing is applied to the resulting power spectral density curve.
The noise is characterized by non-stationary behavior with large variations between the low and high noise levels for 10 - 100 s period waves (Peterson, 1993). Examples of noise variations are shown in Figure 4.4, using a typical long period high noise (station MMLI, NS-component) and low noise seismogram (station MOA, Z-component). The seismograms are divided into fourteen 200 second long sub-windows, and for each window the power spectral density (dotted lines on the right side, Figure 4.4) is computed. In both cases, the power spectral density varies by about one order of size over the entire 10 - 100 s band within the short 1500 s noise window.
The noise power spectral density PN is computed from the 200 s window before the P-wave arrival to have a representative pre-signal noise estimate. A 200 s window, of course, does not allow to solve single frequency features between 0.01 and 0.03 Hz. The goal of this analysis is not to obtain a high single frequency resolution of the noise, where a very long time series is needed, but to obtain an overall estimate of the noise level over a finite period band. A short 6 point hanning taper is applied to each seismogram to remove edge effects.
The signal power spectral density PS is computed from a window starting at the P-wave arrival and ending with the 30 second group velocity surface waves. Since the earthquake alerts that trigger the automatic procedure may not be correctly located (Bernardi et al., 2004), PS analysis requires windows wide enough to contain the signal even when severe mislocation occurred. The alert that triggers the procedure is not necessarily the location used for later inversion, but for rapid data preparation I use the initial location for signal-to-noise-analysis. Thus, I assume a maximum uncertainty of 200 km. P-wave (Kennett & Engdahl, 1991) and surface wave group velocities (Larson & Ekström, 2001; Pasyanos et al., 2001; Cotte & Laske, 2002) may also vary significantly within the European-Mediterranean area. I used conservative fast V p = 8.5 km/s and slow 30 s group velocity V 30 = 2.5 km/s, to avoid truncation of the signal. At each end of the signal window, I add 5% to apply a 5% hanning taper to the seismogram without cutting into the data. The window length for PS is long for far stations because of uncertainties. The signal length, that actually contributes mostly to the power spectral value is shorter. I thus normalize PS for a 200 s window.
To find the minimum signal-to-noise ratio required, I recomputed the MT of 14 4.4 < Mw < 5.0 events (Table 4.4). I also re-analyzed the Mw = 7.0 May, 2003 northern Algeria event to verify that the signal-to-noise ratio analysis does not affect well resolved MTs of large events. All 15 test events have accurate automatic location compared to their PDE-location; 12 are A-quality and 3 are B-quality solutions, using the SR. The actual period band used for inversion is defined by the minimum signal-to-noise ratio Rm(f) = PS/PN. Only seismograms that exceed Rm for a period band at least 15 s between 50 - 100 s are selected.
Tested values of Rm are 1, 1.5, 2, 2.5, 3, 4, 5, 10, 20, 50 and 100. Figure 4.5, as an example, shows the NS-component of station OBKA ( = 3.4o) for the May 10, 2003 Northwestern Balkan Mw = 4.4 event. PS (thick black line), PN (thin black line) and the resulting signal-to-noise ratio R (dotted line) are plotted. In the time domain, the signal is visible in the 35 - 60 filtered seismogram (right side, middle), while at longer periods (right side, bottom), only noise is visible. The period-band for MT inversion for this component is 50 - 80 seconds when Rm = 1 or 50 - 57 seconds when Rm = 2. In the second case the component is not used because the window width of usable signal length is less then 15 s wide.
To select the ”best” value of Rm, I analyzed the solution stability, the number of seismograms used, the solution fit and the reduction of iterations as a function of Rm relative to the standard solution. Figure 4.6 summarize the average performance for the 15 events. Stability of the solution is manifested by small changes in the principal axes orientation Ax (Bernardi et al., 2004), moment magnitude Mw and depth z. For Rm < 5, Ax and Mw are small indicating stable solutions. Depth resolution does not seem to depend strongly on Rm. For Rm > 5 the number of components used (bottom, left) is less than for the standard solution; one goal of the signal-to-noise analysis is to use more data to be able to analyze smaller event, so Rm > 5 is not acceptable. Using fewer data may explain the increase of Ax and Mw for Rm > 5. The number of iterations and the normalized variance decrease steadily. Because of the fewer components used, the resulting solutions are actually less well resolved. Using large Rm values (Rm = 20 - 100), reduces the amount of data used significantly. For Rm = 100 only 12 of 15 events still have any traces (i.e. for 3 events no traces are left for inversion).
Based on Figure 4.6, the minimum signal-to-noise ratio can be set to values of 1 < Rm < 5. I selected Rm = 2 for further analysis. With Rm = 2, the solutions are stable, more data ( 20%) are used relative to the standard solution, fewer iterations ( 20%) are required and the variance is significantly reduced ( 20%). The relatively small value of Rm = 2 ensures to use small signals from nodal, far and relatively small events. Data that are still noisy and cannot be fit are automatically removed by the variance criteria during the inversion (chapter 3).
Between May 2002 and September 2003, the SR was triggered 246 times, 55 resulted in quality A, 44 in quality B and 34 in quality C solutions (Table 4.4). 113 alerts did not result in a MT because the earthquake was too weak, or the earthquake occurred outside our area of interest or no data were available. For the same data-set, the MTs are recomputed using the distance dependent short period cut-offs Ti (section 4.3, Ti = T0 - T3) and signal-to-noise ratio Rm = 2 (section 4.4). Results are listed in Table 4.4. No event with Mw < 4.2 resulted in an A or B quality solution, which is to be expected from the period bands Ti considered. After removing these triggers our data-set consists of 169 events. As for SR, not all events resulted in MT solution (maximum number is 139, Table 4.3).
The main objective of including signal-noise analyses and periods shorter than T = 50 s to the automatic MT inversion was to increase the number of reliable MT solutions. For the entire study area (chapter 3), T0, which uses the 50 s period cut-off results in the largest number of quality A solutions (63), a 15% increase relative to SR (Table 4.4). This improvement is probably due to a similar increase in the number of components used (last column Table 4.4). The period bands with smaller cut-off periods (T1-T3), overall, did not produce more quality A solutions than SR, although even more data were used than for T0. Using shorter cut-off periods, the number of quality B solutions increases resulting in a larger number of A+B solutions. This observation implies that the shorter-period cut-offs do not adequately match the phase relations between observed and synthetic data for the study area as a whole.
The complicated tectonics of the European-Mediterranean region combined with the still limited azimuthal coverage and large station-event distances also affect the resolution capabilities of the T1-T3 bands. Figure 4.7 shows the data distribution as a function of epicentral distance and azimuth. Even though the number of broadband stations has increased relative to the period considered in chapter 3, the average distance (12o) remained large and most stations (in central Europe) are northwest of the events (Aegean Sea region). Our results are consistent with chapter 3, where we already observed that the SR analysis for events in the Aegean Sea and Iran was less efficient (i.e. more data were required for quality A solutions, Figure 3.5). Thus, I divided the European - Mediterranean region into two areas. The first area includes the eastern Mediterranean Sea and the near East (Lat. < 40o; Long. > 20) (called EMNE here), the second area includes all other regions (called Europe here). Results for the two areas are given separately in Table 4.4 (third and fourth main column).
For Europe, the use of the T1-T3 settings results in a larger number of quality A solutions (33-32) compared to SR (28). For Mw > 4.7, differences between SR and the Ti sets are small. For Mw < 4.7, the shorter Ti sets, as expected, provide more A solutions. The difference in the number of Mw < 4.7 A-solutions between SR and the T1-set is significant at the 75% level. In Europe the average distances are short, allowing analysis with periods shorter than 50 s. Examples of waveform fits using the SR and the T1-setting are shown for two moderate events (4.3 < Mw < 4.7) in Appendix A.
For the EMNE area, the shorter T1 - T3 cut-off sets result in fewer A-solutions than SR, independent of magnitude. Only the T0-setting leads to a slight increase of A-solutions (significant at 80% level). In eastern Turkey and Iran, the long paths in thick crust (Marone et al., 2004) compared to PREM require long-period analysis. In the Aegean Sea the long average station distances probably hamper the MT analysis using shorter period Ti sets.
The difference between the two regions is not due to earthquake location accuracy. Using PDE-locations for MT analysis (Table 4.4), we found that most A-solutions in Europe are found by the T1-set and in the EMNE area for the T0-set. For both regions similar numbers of Mw > 4.7 events have quality A, while the main difference lies in resolution for Mw < 4.7 events.
Division of the automatic MTs into three pre-defined quality groups may limit the evaluation of the overall improvement. For example, the August 6, 2002 Mw = 5.1 Spain event resulted in quality A using the SR, while in quality B using the T1-set. However the solutions are actually very similar: zSR-T1 = 0 km, MwSR-T1 = 0.01 and AxSR-T1 = 2.2o. Using SR resulted in quality A because of Ax = 28.9o relative to the SRMT catalog, while using the T1-set resulted in a quality B solution because of Ax = 31.1o. To bypass the limitations imposed by categorization, we looked at Ax, z and Mw for individual events for all Ti. Generally, we found no substantial difference relative to the results presented in terms of categories.
Based on Table 4.4, I suggest to use T0 for events located in the EMNE area, and T1 for European events. Combining these two sets, FARMT resulted in 66 quality A (+20% relative to SR), 44 quality B and 29 quality C solutions (Table 4.3 and Figure 4.8). A Wilcoxon test confirms that the difference in the number between the combined T0-T1-set and the SR is significant at the 95% level. Using the PDE-locations, the combined setting resulted in 85 quality A, 35 B and 16 C solutions. The large difference between the number of quality A solutions obtained with automatic and PDE-locations shows that location accuracy plays a significant role in MT resolution. The choice of the combined T0-T1-setting is simply based on maximizing the number of quality A solutions in the 1.5 year data-set. Using a different data-set or different locations might have resulted in a different ”best choice”, because the differences between the Ti settings are gradual. The main points are: distance dependent short period cut-off and signal-to-noise based data selection increases the efficiency of regional automatic MT analysis significantly. The choice of Ti depends on crustal structure, travel path length and location accuracy, and, we do see systematic differences between Europe and the EMNE area.
To check the overall validity of the minimum signal-to-noise ratio Rm = 2 used in FARMT, the MTs of the entire data-set were recomputed using the combined T0-T1 setting for Rm = 1 - 100. Using Rm = 1 - 3, the overall performance does not vary significantly and drops for Rm > 4. Using Rm = 100, only 29 events have a quality A solution, of which only 3 events are smaller than Mw = 4.8.
Figure 4.9 shows in detail the overall gradual improvement obtained with T1 and T0 for Europe (left) and the EMNE area (right), respectively. Shown is the axes difference Ax (between the SR and SRMT solutions, horizontal axis) versus the change of difference Ax using T1 and T0. For the previously mentioned Spanish event, Ax = -2.2o. Positive values of Ax imply that the solution with T i is closer to the SRMT solution than SR solution. In both cases, the solution quality improved in the majority of cases ( 60%). The solutions that apparently became significantly worse (Ax <-40o) deserve closer inspection. In the left box, the white hexagon is event Nr. 25 (Table 4.4), an aftershock minutes after the September 6, 2002 Mw = 5.9 main Sicily event. Because of the main shock, the signal-to-noise analysis removed almost all traces and only few components could be used. The quality A solution obtained using the SR is thus fortuitous. In the right box, event Nr. 146 is deep (Ax = -64.4o, z = 153 km in SRMT) and its variance variation for the sampled depths is very smooth, with the minimum at an incorrect shallow depth with wrong mechanism. The solutions of the other two events (Nr. 13, Ax = -52.3o and Nr. 89, Ax = -49.8o) were obtained using only 2 and 3 components respectively using T0, and 1 and 2 components using the SR. The two quality A solutions obtained using the SR are thus fortuitous.
Figure 4.10 shows the evolution of location accuracy (left) and near-real time accessible broad-band data. The locations (fewer outliers) seem to have improved starting near the second half of 2003. The solution quality indicates that location error for successful MT analysis has to be smaller than 100 km. Data availability also clearly increased by almost a factor two. It seems that a large amount of data can partially compensate location errors smaller than 100 km. More data need to be analyzed to confirm this observation.
Figure 4.11 shows the normalized variance for quality A and B solutions using the SR (left) and the combined T0-T1-setting (right). The clear variance reduction relative to the SR seems to indicate that a significant number of Mw = 4.2 - 4.7 events could be analyzed by lowering the current trigger threshold from M > 4.7 to M > 4.3, although accuracy of quick location is still a problem for such events.
Compared to the SRMT catalog, the automatic FARMT solves a similar data-set. Figure 4.12 shows the number of events analyzed with respect to Mw and to quality. The black pattern shows the events listed in the SRMT that did not result in a MT using FARMT. Basically almost all Mw > 5.2 events were triggered by the automatic procedure and resulted in a MT solution, usually of quality A with some B and few C. For 4.7 < Mw < 5.2, the number of B and C solutions increases, but still most SRMT events were also analyzed automatically. Most of the events that did not result in a MT have magnitude Mw < 4.7 and are located in the Aegean Sea and Zagros mountains, where nearby near-real time broad-band stations are rare or absent.
We showed that fully automatic MT analysis in the European-Mediterranean region can be significantly improved for 4.3 < Mw < 4.7 earthquakes than previously possible (Bernardi et al., 2004). Improvements are obtained because shorter periods are included and data selection is based on signal-to-noise ratio analysis.
We performed independent tests to establish distance dependent short period cuf-off ranges and a minimum signal-to-noise ratio Rm. Not surprisingly, we found gradual variations of the solutions as an entity making it difficult to pick a single ”best” combination. Rm = 1 - 5 leads to well resolved mechanisms and uses more seismograms for inversion than the SR. For the Ti, we observe a significant difference between source regions. For events in EMNE, that are generally farther from seismic stations and were travel paths cross thick crust, analysis at longer periods (T0-setting) is required than in Europe. In Europe shorter Ti settings result in more well resolved, smaller events than T0. T1 seems to work slightly better than even shorter cut-offs T2 and T3. These results hold for the automatic locations, that are sometimes in error of 100 km, and for the more precise PDE-locations.
Using Rm = 2, T0 in the eastern Mediterranean Sea and near East, and T1 in Europe, we obtained 66 quality A solutions, 44 B, and 29 C solutions out of 169 analyzed events from May 2002 to September 2003. This is a significnat improvement compared to the SR that resulted in only 55 quality A solutions (and 44 B, and 34 C).
The significant difference in the number of well resolved solutions between automatic locations, that are used for the rapid analysis, and the PDE locations high-lights one main limitation of our fully automatic, rapid analysis. Even if the number of near-real time accessible broadband stations keeps increasing, we cannot get better moment tensors as long as location accuracy does not improve significantly also for moderate events. One possible approach to avoid the location problem could be a grid search based MT inversion. However, grid searches are time consuming and contradict our general goal of shortening the time between earthquake and MT solution.
The pre-selection of the components for inversion based on Rm reduces the number of iterations to get the final solution by about 20%, which is only a slight improvement towards faster result dissemination. A further development should deal with more precise differentiation between seismic signal and noise. This would bypass inversion iterations to remove noisy traces. One problem for example, is to recognize seismic spikes due to instrument self calibration; these spikes have large amplitudes. If they occur in the signal window, Rm is large independent of the actual signal. Currently the simple Rm-analysis of FARMT cannot recognize such spikes as noise.
Additional broadband stations, particularly in northern Africa and Iran, improving the azimuthal station coverage, are necessary to improve parameter resolution further. In central Europe, with its very dense broadband networks, we already can analyse relatively small events (e.g., the August 6, 2002 Mw = 4.3 Merano, north Italy, event) reliably. Continued improvements in earthquake location and data availability will allow us to lower our trigger threshold toward M 4, which will reduce significantly the difference between the events analyzed fully automatic and the manual SRMT catalog.
Solution improvements for Mw < 4.3 events probably require fine-scale 3-D crust-mantle models. High-quality 3-D models that have the resolution for regional waveform prediction are becoming available (Boschi et al., 2004; Marone et al., 2003) at the same time as advanced codes for efficient 3-D synthetic seismogram calculation (Komatitsch & Tromp, 2002). These development promises major advances for regional moment tensor inversions, that could include, for example, finite source modeling.
Accurate, consistent earthquake size estimates are fundamental for seismic hazard evaluation. In central Europe, seismic activity is low and long-term seismicity, available as intensities from written historical records, has to be included for meaningful assessments. We determined seismic moments Mo of 25 stronger 20th century events in Switzerland from surface wave amplitude measurements. These Mo can be used to calibrate intensity-moment relations applicable to pre-instrumental data. We derived the amplitude-moment relation using digital data from 18 earthquakes in and near Switzerland where independent Mo estimates exist. The surface wave amplitudes were measured at empirically determined distance varying reference periods T. For amplitudes measured at T, the distance attenuation term of the surface wave magnitude relation S() = log(A/T)max + 1.66log is independent of distance. For logMo = MS + CE, we get log Mo = S() + 14.90. Uncertainties of ±0.3 for the 14.90-constant correspond to a factor of 2 Mo uncertainty, which was verified with independent data. Our relation allows fast, direct Mo determination for current earthquakes, and after recalibration of the constant, the relation can be applied anywhere. We applied our relation to analog seismograms from early-instrumental earthquakes in Switzerland that were collected from several European observatories. Amplitude measurements from scans were performed at large amplifications and corrected for differences between T and actual measurement periods. The resulting magnitudes range from Mw = 4.6 to 5.8 for the largest earthquake in Switzerland during the 20th century. Uncertainties for the early-instrumental events are on the order of 0.4 magnitude units.
In this paper, we present seismic moment estimates of 25 stronger, 20th century earthquakes in and near Switzerland (Figure 5.1) based on amplitude measurements of regional surface waves recorded by analog instruments. In areas of low seismicity and long historical records, like Switzerland, such direct size estimates of early instrumental earthquakes are important to derive relations between instrumental data and macroseismic observations that can be applied to pre-instrumental earthquakes (Jimenez et al., in prep.). Modern instrumental data, available since 1975 in Switzerland, exist only for a few events with macroseismic fields and cannot provide such relations. Our size estimates are part of a larger effort to update the Earthquake Catalog Of Switzerland (ECOS) (Fäh et al., 2003). An important design principle of ECOS is to express earthquake size uniformly in terms of moment magnitude Mw (Braunmiller et al., 2004) to allow a direct event-to-event size comparison necessary for a homogeneous seismic hazard estimation from the 2000 years of seismic records.
Our data set for the early instrumental earthquakes consists of low gain analog regional seismograms. We thus determine earthquake size from the well recorded surface waves. The original surface wave magnitude MS definition by Gutenberg (1945), and later by Soloviev (1955), Kárník et al. (1962), and Vank et al. (1962) is given for the maximum ground velocity (A/T)max:
Several studies modified equation 5.2 to remove the distance dependent bias (Evernden, 1971; von Seggern, 1977; Herak & Herak, 1993; Rezapour & Pearce, 1998) while measuring amplitudes at T20. Another approach, followed here, is to test whether equation 5.2 can be made independent of distance when the measurement period T is varied with distance. Globally applicable distance varying measurement periods T have been suggested by IASPEI (1967) and Willmore (1979). Additionally, regional MS variations due to path effects my require regional corrections (Abercrombie, 1994; Ambraseys & Free, 1997; Ambraseys & Douglas, 2000).
The earthquakes analyzed here are generally too small to be well recorded at teleseismic distances; we thus use only regional records. To avoid biased size estimates due to distance dependence and regional path effects, we calibrate the surface wave amplitudes against an independent data set. We first outline our size estimation procedure before we derive a calibration function using recent digital data. Finally, we apply the calibration to determine Mo from analog data.
Our early instrumental earthquake data set consists of scanned paper seismograms. We measured the peak surface wave amplitude and the corresponding period T. After correcting for gain, we could determine MS from equation 5.2. However, our data are regional seismograms, where MS distance bias has been documented (Evernden, 1971), and all measurement periods T were shorter than 20 s.
Therefore, we investigated whether the S()-term in equation 5.2
None of the recent events was large enough to have an independent MS based on teleseismic data. Thus, we cannot verify the validity of Cp = 3.3 in equation 5.2. However, all recent events have Mo estimates from regional moment tensor (MT) inversion. Assuming log Mo = MS + CE from theoretical considerations (Kanamori & Anderson, 1975) and observation (Ekström, 1987; Ekström & Dziewonski, 1988), we solve for K = CP + CE:
Originally, we had planned to determine MS from early instrumental data. As it turns out, with digital reference data, we are able to establish a reliable and generally applicable surface wave amplitude - Mo relationship.
We obtained digital seismograms recorded at regional distances (2o < < 20o) for 18 small to moderate size earthquakes (M0 < 6 . 1016 Nm) that occurred in and near Switzerland since 1992 (Figure 5.1). Mo for each event (Table 5.1) comes from regional MT inversion (Braunmiller, 2001; Braunmiller et al., 2002; Braunmiller, 2002; Deichmann et al., 2002); previously unpublished solutions are listed in Table B. Three additional earthquakes, with analog, digital and MT derived Mo are used for an independent check of our methodology.
Surface wave magnitude MS is determined from the maximum ground velocity (A/T)max. At regional distances, the maximum occurs at periods T < 20 s. Here, we want to find a stable, distance varying reference period T where (A/T) and A are maxima.
We narrow band-pass filter the displacement seismograms in one second intervals from a center period Ti of 4 to 20 s for all 443 station-event pairs. The ground displacement amplitude A is the vectorial sum of the instrument corrected half peak-to-peak amplitudes of the two horizontal seismogram components. We use a 4-pole causal Butterworth band-pass filter with corners at ±15% of the center period. We do not consider periods T < 3 s to avoid S-wave contamination, which dominate the records at short periods; separation based on group velocity is possible, but was not pursued.
For each period Ti, we measure displacement A and velocity (A/T). Signals characterized by a dominant period T can be approximated by a monochromatic signal, thus (A/T)max and Amax occur at the same period T (Figure 5.2, top). Measuring the period where only (A/T) is a maximum, may correspond to a period, which is not representative of the signal character (Figure 5.2, bottom).
The dominant periods T are shown as a function of epicentral distance in Figure 5.3 (grey dots). The medians (black dots) for each period between 4 and 10 s (at longer periods we have too few data points) are selected and fitted with a simple ln()-curve (dashed line):
For our reference periods T, we test whether the S()-term is distance biased. For each station-event pair we determine the maximum amplitude Amax at T and calculate MS. For each event, we then determine residuals MS,i = MS - MS,i between average and individual station measurements that are independent of the constant Cp in equation 5.2. The T-residuals (Figure 5.4, top) show no distance dependence when considering measurements up to = 20o (thick dashed line) even though T were obtained using data only up to = 10o, which represent 90% of the data. Linear regression (M S,i = a + b ) for data points < 10o shows negligible distance dependence (thin dashed line, a = 0.017, b = -0.003).
For comparison, the residuals for Amax measured at T20 (Figure 5.4, middle) are distance dependent with underestimation at close distances (MS,i positive). Our distance-varying T deviate slightly from the values suggested by Willmore (1979) (Table 5.2). The residuals MS,i obtained using Willmore’s periods (Figure 5.4, bottom) have a small distance dependence (a = 0.063 and b = -0.010) for all residuals at < 20o, and a more relevant dependence for residuals at < 10o (a = 0.148 and b = -0.028). MS values measured with Willmore’s periods at = 2o differ from the more distant measurements (at 20o, respectively, 10o distance) by about 0.2 magnitude units.
The absence of distance dependence (Figure 5.4) of the station-event residuals MS,i for our T seems to favor our values over those given by Willmore. Given the large scatter in the residuals, we performed two statistical tests to verify the significance of the differences.
First, we applied a Sign-test (Stahel, 1995). The null hypothesis Ho assumes that the probability of observing positive and negative differences (21 = (|M S,i1|-|M S,i2|)) between n matched pairs of two identical distributions is equal. The matched pairs are event-station residuals obtained with our (MS,i1) and Willmore’s (M S,i2) periods T . If the number of positive differences 21 exceeds [ ±], H o can be rejected at the 99% confidence level. For our data set of n = 443, we observe 305 positive differences 21 and reject Ho.
Second, we tested how small changes in our T affect residual distance independence. We generated 100 random gaussian distributed values for both parameters of equation 5.4 (-3.99 ± 0.24, 6.41 ± 0.30) and calculated for each of the 10000 new reference periods T' the residuals MS,i' and their regressions. For each case, we then calculated the expected residual difference = M S'20o - M S'2o. The M S' are regression results at 20o and 2o distance, respectively. Thus, describes the expected magnitude difference for these two distances (Figure 5.5). The mean is 0.007 ± 0.029. No difference is larger than 0.1 magnitude units. Our statistically worst T' produce significantly less distance dependence than Willmore’s reference periods.
For earthquakes in and near Switzerland, we determined reference periods T that produce distance independent surface wave magnitude MS (assuming Cp is known). Differences relative to global average values given by Willmore (1979) are statistically significant and we recommend our T (Table 5.2) for regional MS determination in central Europe.
From theoretical considerations (Kanamori & Anderson, 1975), MS is expected to be proportional to log Mo for small earthquakes. Empirical analysis shows that globally this applies to MS < 5.3 events (Ekström & Dziewonski, 1988). For continental earthquakes the proportionality is valid up to MS < 7.2 (Ekström, 1987), because of the increased width of the seismogenic zone compared to oceans. Seismicity in the Alpine area is characterized by small to moderate earthquakes, thus we can assume:
Equation 5.6 allows a straight forward Mo estimation from surface wave amplitude measurements valid for historic, recent or future earthquakes. The difference of Mo obtained with amplitude measurements and MT inversion is lower than a factor of 2 (Table 5.1) and is consistent with the standard deviation = 0.32 of K (only two smaller earthquakes show a difference of a factor of 3).
Combining the global values Cp = 3.3 and CE = 12.24, we obtain K' = 15.54, which increases earthquake’s Mo by the significant factor of 4.5 relative to K = 14.90 (or a Mw increase of almost 0.4 units). The difference K'- K is outside the uncertainty for K determined here. Biased Mo estimates from MT inversion could also cause an artificial difference. However, these Mo estimates agree excellently with values determined by the teleseismic Harvard centroid-moment tensor technique (Braunmiller et al., 2002). We think the differences between K and K' are real and caused by regional effects. From our analysis, it is not possible to resolve whether Cp = 3.3, CE = 12.24 or both values are regionally different.
We collected seismograms and instrument calibrations for 25 stronger earthquakes that occurred during the 20th century in or near Switzerland (Figure 5.1, Table 5.3). Earthquake selection criteria were even distribution, representing different tectonic settings (Kunze, 1982), a wide size range and well defined intensity fields. The largest 20th century earthquake in Switzerland, the January 25, 1946 Ayent event, is part of our list.
We used only seismograms that were recorded by mechanical or electromagnetic seismographs with well known instrument characteristics. The introduction of damping to mechanical instruments and the rigorous derivation of the instrument characteristics by Wiechert (1903) produced the first reliable observations of ground motion. For a detailed description of the instrument characteristics of all early instrumental seismographs used in this study, see Appendix D. The Wiechert instruments record true ground motion at least from 0.05 to 2 Hz (Ritter, 2001) and non-linear effects have been observed only for high frequencies around 4 Hz (Herak et al., 1996). Figure 5.6 shows gain versus period for a Wiechert seismograph. Most of our data are from mechanical Wiechert or Mainka (Mainka, 1923) instruments. Electromagnetic seismographs consisting of a pendulum coupled to a galvanometer were introduced by Galitzin (1914). Compared to mechanical instruments, they record with higher gain over a wider period band (Figure 5.6). Instrument responses for electromagnetic instruments are described in Galitzin (1914), Hagiwara (1958), and Willmore (1979). The measured amplitudes, after removing the instrument response, are ground displacements (in m).
We measure maximum surface wave amplitudes (one half of peak-to-peak values) from scanned images. We correct the amplitudes to account for gain differences between true measurement period T and reference period T. For scanned images, the maximum amplitude A is measured at period T with gain V . At period T, the amplitude would be A . (V is the gain at T). The true ground displacement at T is then A . ., which replaces the expression log A in equation 5.6. The amplitude - Mo relation for early instrumental earthquakes becomes then
Correction for vertical component data (MSV ) was derived comparing two horizontal component data with vertical observations (Figure 5.7). For Wiechert instruments, we have 26 three component and 13 two component (one vertical) sets. In both cases, the average difference is 0.45 units, which we added to logMo based on vertical data only. For Galitzin instruments we found a difference of 0.20 units, however this value is based only on 6 observations and we decided not to use vertical Galitzin data.
MSH, MSh and MSV are names to indicate whether the Mo-estimate is based on amplitude measurements from two or one horizontal or a vertical component, thus they are not surface wave magnitudes. Derivation of the average differences between MSH, MSh and MSV involved only differences and is therefore independent of choice of Cp in equation 5.2.
Our combined amplitude data set then consists of 59 measurements from two horizontal components, 23 from one-horizontal and 3 from vertical component data (Table 5.3, column 10). Each station contributes only once per event with preference given to MSH (two horizontal) over MSh (one horizontal) over MSV (vertical) data. For each event we have from 1 to 7 measurements with at least one from MSH. The resulting Mo estimate (Table 5.3) is the median for each event’s measurements. We did not apply station or depth corrections. Relatively strong changes of the seismograph characteristics within a short time span have been documented (Kowalle & Thürmer, 1991; Allegretti et al., 2000). With few events and infrequently available instrument calibrations, gain uncertainties probably mask possible station terms. Depth corrections are probably unnecessary since all calibration events (Table 5.1) and other instrumental seismicity (Deichmann, 1992) are crustal.
Uncertainty of Mo estimates (equation 5.7) is mainly due to uncertainties of gain (V ) and scatter of the constant K = 14.90 ± 0.32. Epicenter location, for historical events often not well known, probably results in a distance uncertainty of 0.2o. Amplitude readings from scans are performed at large magnifications on a computer screen, thus amplitude uncertainty is about 0.5 mm and corresponds approximately to the line width drawn by the seismograph needle. Location and amplitude uncertainties have negligible effects on Mo. The gain V depends on time-varying seismograph constants, which were regularly calibrated by station operators. However, for many analyzed events, no calibration information existed near the event time and we extrapolated to obtain gain estimates. To estimate gain uncertainty due to this procedure, we varied the instrument constants for a station between the lower and upper values given in the station bulletin or between the calibrations just before and after an event. Figure 5.6 shows examples for the resulting amplitude responses for the Wiechert and Galitzin instruments at station UCC. Similar analyses were performed for other stations and from these tests we deduced a gain uncertainty of about 30 units for mechanical and about 50 units for electromagnetic sensors. Due to the higher gain, relative gain uncertainties are smaller for electromagnetic than for mechanical instruments.
Together, effects of gain, location and amplitude result in a mean maximum expected uncertainty for MSH data of (log Mo) = 0.13 ± 0.03 and 0.10 ± 0.04 for mechanical and electromagnetic sensors, respectively. Combined with K = 0.32, we obtain an uncertainty in log Mo of less than 0.5, which translates to a Mw uncertainty of about 0.3 units. Uneven azimuthal station coverage and ignoring radiation pattern effects add uncertainty. We thus consider Mw = 0.4 a reasonable uncertainty estimate for our early instrumental Mw values.
We presented a simple procedure to determine Mo from amplitude measurements of surface waves (equation 5.6) by combining the logMo - MS relation with the ’Prague formula’ for surface wave magnitude. Our approach is valid for ”small” earthquakes that do not rupture the entire width of the seismogenic zone, which is applicable for events up to MS < 7.2 in continental areas (Ekström, 1987). Validity also requires the S()-term to be independent of distance. Measuring amplitudes at periods that vary with epicentral distance results in distance independent S(). We determined the reference periods T (Table 5.2) with digital data and calibrated the constant K = 14.90 in equation 5.6 using independent Mo estimates.
Three earthquakes (Table 5.5) with Mw from MT inversion and amplitude readings from digital and analog data provide an independent check of the procedure. The Mw estimates show high consistency and the differences of < 0.3 units are consistent with our expected Mw uncertainties. We observe the largest discrepancy for the 1978 event, where we had only 3, respectively 2 amplitude measurements from digital and analog data.
Distance dependence of the S()-term has long been an issue when determining MS with T20 period data (Evernden, 1971). At regional distances, the amplitudes at T20 period are generally smaller than shorter period signals leading to a significant underestimation of MS (Figure 5.4). Measuring at shorter periods T, results in distance independence and allows the analysis of smaller events that do not radiate significant energy at periods near 20 s.
Our 18 event calibration data set (Table 5.1) does not include larger events with teleseismically determined MS that could be used to fix the constant CP in equation 5.2. We thus did not explicitly determine MS. However, in engineering practice MS is often used for ground motion prediction (Ambraseys & Free, 1997), so we give MS estimates for the early instrumental data (Table 5.3) for CP = 3.3. Recently, Ambraseys (2003) reassessed the size of 20th century Swiss earthquakes in terms of M S using amplitude/phase measurements from station bulletins. For 23 common events, the average MS difference of = 0.01 ± 0.25 units is remarkably small. The large scatter is mainly due to some of the oldest events, which differ by up to 0.5 magnitude units.
We observed a large discrepancy between measurements from the horizontal and vertical components of 0.45 magnitude units for Wiechert seismographs (Figure 5.7). Despite the agreement with Ambraseys (2003), we thus caution the use of bulletin data for which amplitude, period and component are not explicitly labeled. Use of such data could lead to artificial scatter or biased size estimates. Whenever possible, we suggest to use original seismic records and instrument calibrations.
A large data set of early instrumental seismic records exists in Europe, where some observatories have been in operation for an entire century. Scanning and digital archiving of many of these data is currently under way (Bono et al., 2002). Simple reading of amplitudes and periods combined with our amplitude-moment relation could provide a large Mo-data base without the need of time consuming digitization. Because of calibration with recent events, accuracy of early instrumental Mo estimates depends mainly on knowledge of instrument gain and representative source radiation. Even with few measurements, accuracy is probably comparable to modern digital data.
The earthquake size estimates for the early instrumental events given here differ systematically from the estimates in the Earthquake Catalog of Switzerland (Fäh et al., 2003; Braunmiller et al., 2004). We have two reasons that explain the difference. Here, we use a larger data set of analog seismograms that includes also data from instruments other than Wiechert seismographs. All size estimates are based on two componen