An estimate of hypocentre location accuracy in a large network: possible implications for tectonic studies in Italy

Geophys. J. Int. (1997) 129, 124-132 An estimate of hypocentre location accuracy in a large network: possible implications for tectonic studies in Italy Rita Di Giovambattista and Salvatore Barba Istituto Nazionale di Geofisica, 1'. Di Vigna Murata, 605,00143 Roma, Italy. E-mail: digiovam@marte.ingrm.it Accepted 1996 October 28. Received 1996 October 9; in original form 1996 January 22 INTRODUCTION SUMMARY Data recorded by the Italian Telemetered Seismic Network (ITSN) of the Istituto Nazionale di Geofisica (ING) have been widely used in recent years to image slab structures and to find evidence for active processes along the Italian Peninsula. However, the use of seismic data for geostructural purposes may be affected by the well-known trade-off between earthquake location and seismic-velocity parameters. Furthermore, the confidence ellipse predicted by standard procedures may be inadequate for the representation of the probable error of a computed localization. This paper evaluates the probable errors on the hypocentre determinations of the seismic events recorded by the ITSN, using a Monte Carlo method. We compute synthetic arrival times using a 1-D velocity model appropriate as an average for the Italian area. The hypocentres used are ail those recorded by the ITSN during the period January 1992 to March 1994 (1972 events). Station locations are those of the current ITSN configuration. The synthetic arrival times are perturbed with a Gaussian distribution of errors and input to INGs standard hypocentral location procedure, but using crustal velocities differing by 10 per cent from those used to generate them. Each simulation is repeated at least 30 times. Average absolute shifts of hypocentres are assessed in grid cells of linear dimension 33 km covering the whole Italian region. For regions within the ITSN, shifts are typically 5-10 km in location and up to 20 km in depth. However, for offshore and coastal regions, they are much greater: 50 km or more in both location and depth (far exceeding the equivalent uncertainties quoted by ING bulletins). Possible consequences of this are highlighted by producing a cross-section of subcrustal hypocentres from the Adriatic to the Tyrrhenian Sea, where the large uncertainty in depth precludes any confident interpretation of dipping tectonic features. Key words: earthquake location, Italy, seismicity The problem of earthquake location can be solved using the generalized linear inverse theory. Input data are the arrival times of seismic waves recorded at different stations. Arrival times are affected by various errors including reading errors and misidentification of the first arrivals. Therefore, the location will also be affected by errors. Since crustal velocity models are only roughly known, simplified models are used in the majority of the location programs, and the choice of the velocity structure strongly affects the accuracy of the results. Furthermore, numerical problems related to the network configuration can arise. When the model parameters are poorly constrained by the data, the matrix in the normal equation can be a nearly singular matrix and consequently its computed inverse may be inaccurate. This represents the main uncertainty for seismic events occurring along the Italian coast or in areas with a limited number of stations due to the peculiar configuration of the Italian territory and to the distribution of the Italian Telemetered Seismic Network (ITSN). It is a common procedure to estimate the errors in the final model on the basis of the model variance-covariance matrix; the standard deviation of each parameter is given by the square roots of the diagonal terms. The uncertainty in the epicentre is represented by an ellipse in which the ratio of the axes is determined by the network geometry, while the size depends on the standard deviation of the data. Evernden (1969) points out that the confidence ellipse predicted by standard procedures may be inadequate in representing the probable error of a computed location. Even 124 0 1997 RAS

applying different hypocentre location techniques, which sometimes produce better results, it has been shown that even with an ellipse of small magnitude the events can be mislocated by several kilometres (Console et ul. 1992a). We use a procedure based on the Monte Carlo method to evaluate the errors associated with the hypocentral coordinates of the events recorded by the ITSN. We apply this procedure to estimate the reliability of the hypocentre locations on the basis of the adopted crustal velocity model, of the errors on the arrival-time picking, and of the network configuration. METHOD We face different kinds of errors in locating seismic events: systematic errors due to inaccurate station coordinates, network timing errors, or picking errors. For the ITSN data these errors are of small magnitude and we consider them negligible in our analysis. In fact, all the stations are telemetered in a data centre and the time signal is provided by a GPS receiver with an uncertainty of 1 ps. The station coordinates are determined by a GPS receiver with an accuracy of about 150 m; the algorithm used to acquire data does not introduce systematic picking errors. In addition, other errors can affect the estimated hypocentral coordinates: they are caused by inaccuracy in reading the arrival times, limited amounts of data, inadequate station distribution, and errors in the knowledge of the seismic-velocity structure. To evaluate their influence on the accuracy of hypocentre locations, we use a procedure based on the Monte Carlo method. Introduced by Von Neumann and Ulam, the Monte Carlo method (Brandt 1976) simulates statistical processes by introducing random values for the parameters. In our procedure, this method is applied to simulate the problems in the location of seismic events; assuming a specific configuration of a network and a crustal propagation model, we use our method to evaluate the hypocentral errors. The Monte Carlo method 47" 46" 45" 44" 43" 2 42" m 4 41" 40" 39" 38" Hypocentre location accuracy in Italy 125 has already been applied to test the performance of different hypocentre location algorithms (Console et al. 1992b) and to quantify the reliability of events located in some particular areas (Billings, Sambridge & Kennett 1994). The distribution of the errors associated with the picking of first arrivals has been analysed by many authors. Following Buland ( l976), the picking errors associated with impulsive arrivals recorded in analogue form are approximately described by a Gaussian distribution. Emergent arrivals, due to the misidentification of first arrivals confused in seismic noise, are characterized by reading errors that can be described by a distribution having a mean value shifted towards positive numbers (Anderson 1982). Tests performed on the digital data collected by the ITSN showed that reading errors can be adequately approximated by a Gaussian distribution with a mean equal to zero and a standard deviation of 0.1 s. The uncertainty in assessing hypocentral coordinates, depending on random reading errors, is determined in the following way. The procedure calculates the theoretical traveltimes related to each velocity model considered, starting from the hypocentral coordinates of the events. These times are then altered by the addition of random values having a normal distribution with a mean value equal to zero and a standard deviation equal to that found in the final solution obtained in locating the events. These data are then utilized as input for the simulation procedure. The influence of the crustal propagation model can be tested assuming a known velocity model to obtain the theoretical traveltimes and then relocating the events with another model. Performing a large number of simulations, the spreading of the relocated events can be used to estimate the uncertainty associated with the hypocentral coordinates. APPLICATION TO ITALIAN SEISMICITY The analysed data, collected by the ITSN, are digitally recorded with a sampling rate of 50Hz (Di Mar0 & Marchetti 1994; 37" 36" I I I I I I I I I i I"I I I I I I I I I 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 12" 13" 14" 15" 16" 1 P 18" 19" 20" 21" Longitude Figure 1. Italian seismicity recorded by the Italian Telemetered Seismic Network from January 1992 to March 1994.

126 R. Di Giovambattista and S. Barbu Barba, Di Giovambattista & Smriglio 1995). Thus arrival-time picks can claim a resolution of 0.02 s, but an accuracy that is probably poorer, especially for S arrivals. This is to be compared to the empirically determined scatter of 0.1 s. All the events recorded over a two-year period, from January 1992 to March 1994, have been selected from the database of the Istituto Nazionale di Geofisica. Fig. 1 shows the -2000 events analysed in this paper. i We intend to estimate the hypocentral errors for the overall Italian seismicity. Fig. 2 shows a general outline of the numerical method and its main parts. The errors on the hypocentral coordinates are connected with the number of stations that recorded the event, and consequently with the magnitude of the events. Therefore, we have divided all the seismicity into three groups whose magnitudes are 2.0-2.5 (505 events), 2.6-3.0 (1146 events) and greater than 3.0 (321 events). The procedure generates the arrival times by assuming a crustal model, and alters them with random values computed as described in the previous chapter. These data are then used as input for the location program in which another realistic model is assumed. Table 1 shows the two velocity models assumed. As can be seen in Table 1 the two models used are quite similar. The former is the most recent one computed using ITSN data (Mele & Valensise 1987). The latter is a further refinement of the former, from which it differs by an increase of 10 per cent in the velocity of the first layer and a decrease of about the same magnitude in the second layer. In a previous study, aimed at comparing a joint hypocentre location method with the standard location method described in this paper (Console et al. 1992b), the influence of the crustal model has been evaluated for two Italian areas, Val Comino (Central Apennines) and the Adriatic Sea. For the Adriatic Sea area the absolute mean shift and the standard deviation of the hypocentre in the horizontal plane (If) and depth (Z) obtained for a variation of 5 per cent in the velocity model were AH = (3.9 2.5) km and AZ = (5.8 +_ 3.6) km. It is important to emphasize that the variation in the crustal model assumed in this analysis might not represent the true variations existing in the Italian territory, due to a variety of tectonic domains (e.g. volcanic areas, Alps mountain range). In this sense, our analysis quantifies a minimum error. The use of the standard deviation obtained in the location of the experimental data allows the simulation of a more realistic situation as the residuals at each station and thus the standard deviation include all the deviations from the assumed crustal model. With regard to this problem, an increase in the thickness of the crust from 30 to 45 km, which occurs in the transition zone from the Padana plain to the Subalpine structures, will cause a delay in P, arrivals of about 1.3 s (assuming model l), while a seismic ray that is 0.2 km s-' slower than the theoretical one will be retarded by only 0.3 s every 100 km (Mele & Valensise 1987). A more recent analysis, based on P-arrival-time tomographic inversion demonstrated a maximum lateral velocity of +7 per cent (Alessandrini, Beranzoli & Mele 1995). The ( Start Simulation ) Monte Carlo Simulation 4 pq ci, Init std dev. For each event compute mean hypocentral coordinates and associated standard deviations using results produced by hypocenter location using synthetic travel times obtained by means of Monte Carlo simulation Figure 2. Flowchart of the procedure applied in this study. The input parameters are the data file (P1 ) and the number of simulations to be performed (P2). I is the iteration number. Q 1997 RAS, GJI 129, 124-132

Hypocentre location accuracy in ltaly 127 Table 1. Velocity models used in this study for the Italian area. Depth (km) Model 1 11.08 29.98 Model 2 11.08 29.98 P velocity (km s-l) 5.0 6.5 8.0 5.5 6.0 8.0 variation of 10 per cent introduced in our simulation, even though it is a simplified model (1-D), is then supported by tomographic results. To locate the events we used the program IPO, routinely used for the hypocentre locations published in the ING bulletins (Basili, Smriglio & Valensise 1984). All the analysed events have been divided into square grid cells whose linear dimension is about 33 km. This grid is a compromise between the number of events in each cell and the need for a homogeneous network coverage in each cell. For each grid cell we computed the mean and the standard deviation of the absolute shift of the hypocentral parameters generated by at least 30 simulations repeated for each event. The correct application of this method requires that the weight given to each station is determined by the value assumed from the residuals, and does not depend on the epicentral distance of the station. This has been checked through a qualitative analysis, allowing us to alter the computed traveltimes randomly. Figs 3 to 8 show a synthesis of the results of these tests for the two groups of events of higher magnitude. As is seen in these figures, there are cells in which the standard deviations of the absolute shifts of the hypocentral coordinates are quite high in comparison with the uncertainty of the hypocentral coordinates obtained from the covariance matrix published in the ING bulletins. This problem is particularly evident for the events located offshore or along the coast. In particular, Figs 3 to 8 show areas (the Southern Tyrrhenian Sea, the Calabrian Arc, the Ionian sea, the Forli area in Northern Italy, the Northern Tyrrhenian coast) in which the standard deviation attains quite large values. Depth standard deviation for hypocentres located in the Southern Tyrrhenian Sea (usually deep-focus events) can exceed 200 km, the largest instability of all of the areas considered here. For the same events, though, the depth errors cited in the ING bulletins are usually very small (< 20 km), as shown in Fig. 9. For those events occurring inside the grid network, the standard deviation on the horizontal plane is about 5 km. There are only three areas (the Italy-France border, the Central Apennines and the Southern Apennines) that are characterized by errors larger than 10 km. For these areas the uncertainty of the depth estimation can reach 20 km. In Northern Italy (Forli area), in the Tyrrhenian Sea, just in front of Elba island, in the Calabrian Arc and in the Ionian Sea there are some areas showing a standard deviation greater than 50 km for events of magnitude 2.5-3.0. The data set of the events with a magnitude greater than 3 also includes events located in the Adriatic Sea, along the Figure 3. Estimated depth location accuracy (in km) of the epicentres of magnitude 2.6--3.0 recorded by the ITSN. The seismic stations are represented by circles. The initial arrival times were computed for model 1 assuming crustal model 2 in the location program. The theoretical traveltimes have been altered by means of the Monte Carlo method, adding random values having a standard deviation equal to that found in the last iteration of the standard hypocentre location procedures. For each grid cell with a linear dimension of about 33 km we computed the standard deviation of the shift obtained in the hypocentre coordinates for each simulation and each event. Q 1997 RAS, GJI 129, 124-132

128 R. Di Gioziambattista and S. Barba Figure 4. Estimated latitude location accuracy (in km) obtained using the same conditions as Fig. 3. Values of the standard deviation of the shift higher than 50 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold. Figure 5. Estimated longitude location accuracy (in km) obtained using the same conditions as Fig. 3. Values of the standard deviation of the shift higher than 40 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold. Q 1997 RAS, GJI 129, 124-132

Hypocentre location accuracy in Italy 129 Figure 6. The same as Fig. 3, but for events having magnitudes greater than 3.0. Values of the standard deviation of the shift higher than 50 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold. Figure 7. Estimated latitude location accuracy (in km) obtained using the same conditions as Fig. 3 for events having magnitudes greater than 3.0. Values of the standard deviation of the shift higher than 30 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold.

130 R. Di Giovambattista and S. Barba Figure 8. Estimated longitude location accuracy (in km) obtained using the same conditions as Fig. 3 for events having magnitudes greater than 3.0. Values of the standard deviation of the shift higher than 40 km are represented by the darkest tones on the grey-scale. The distribution of the mean error justifies the use of this threshold. 0 i,l 1 40 1 Latitude(Km) 20 0 Longitude (Km) 20 L 15 20 tk$h (Km) 0 5 Figure9. - Number of vents versus the error on the latitude (a), longitude (b) and depth (c) as derived from the confidence ellipses for the events of the southern Tyrrhenian Sea (Latitude 38.5"-40"; Longitude 12"-15.5"). southern coast of Italy (Puglia) and along the coast of the former Yugoslavia. For these events, the error in longitude is greater than the error in latitude. These results depend on the network configuration. This offshore seismicity is located outside the network and only the latitude can be constrained by the stations located north and south of the epicentral area. All 1 the stations are situated west of the epicentral area and they constrain the longitudinal coordinate of the events only poorly. In the data set of the events with magnitude greater than 3.0, there are events located in bordering areas. In particular, because of the national borders and the roughness of the territory, the seismically active areas in the Alps are poorly monitored; therefore, it is not possible to record lowermagnitude events. The seismicity occurring at the borders with Austria and France is affected by uncertainties in the epicentral coordinates of up to 50 km. For some events of magnitude greater than 3.0 occurring in the Calabrian Arc and in the Southern Tyrrhenian Sea, the errors on the horizontal plane cover a large range (up to 150 km). This shows that the solutions can be very unstable, because the peculiar configuration of the territory along the Calabrian Arc leads to an alignment of the seismic network and to a consequent poor estimation of the longitude. All previous considerations are based on cells in which more than three events are located, and a minimum of 30 simulations are run for each event. This ensures that the results do not reflect instabilities of single events, but provide meaningful uncertainties on hypocentral coordinates for all the events recorded by that particular network configuration. In order to check the results obtained and to estimate whether the discrepancies between the two propagation models adopted are sufficient to highlight the true mislocation of the events, we compared the hypocentral locations obtained analysing the data collected by the ITSN with those obtained by the IGG seismic network of the University of Genoa (Cattaneo & Augliera 1990). It is well known that local networks, provided that they have a good station distribution,

can provide accurate hypocentral coordinates of the seismic events occurring inside the network. As a consequence, the comparison between the IGG hypocentral coordinates and those calculated by ITSN can provide a further estimate of the probable errors associated with the focal parameters. For the events located in the area where the IGG network is operating, the two hypocentre locations have mean shifts that are in agreement with the uncertainty estimated by the procedure described in this paper. In order to highlight the importance of a realistic evaluation of the uncertainty of the hypocentral coordinates in areas in which the event distribution can be crucial for tectonic implications, we applied the procedure described in this paper to subcrustal earthquakes that occurred in the Northern Apennines, already relocated by Selvaggi & Amato ( 1992). For several events that occurred in the same area from s -80 Q -100-120 -140 I I 1 'I1 Hypocentre location accuracy in Italy 131 January 1992 to March 1994 our analysis highlighted inaccurate absolute hypocentral locations, probably due to unfavourable station geometries. The reliability of the hypocentral coordinates of these events is of major importance for tectonic interpretations. In fact, based on the unusually deep earthquakes, Selvaggi & Amato ( 1992) hypothesized a subduction process acting in that zone. Table 2 shows the depths with the estimated errors determined by Selvaggi & Amato ( 1992), those published by the ING bulletins, and the standard deviation of the depths obtained by means of the error analysis described in this paper by using only stations belonging to ITSN as already specified. The two locations are obtained using different crustal models. For this reason, the depths cannot be compared as absolute values. From Table 2 it is possible to infer that the uncertainty, as derived from the confidence ellipses, can be inadequate in the representation of I 0 30 60 90 120 150 180 210 240 270 300 330 360 3 0 I 1 1 1 1 ' 1 1 ~ ' 1 1 1 1 ' 1 1 1 ~ 1 ' ~ 1 ' ~ 1 ~ ' 1 ~ ~ 1 ~ ~ 1 ~ Distance (km) Figure 10. (a) Epicentral map of the deep earthquakes located by Selvaggi & Amato (1992) and zone of projection of the vertical section A-A'; (b) cross-section A-A'. The error bars are computed by the Monte Carlo method described in this paper. 190

132 R. Di Giovambattista and S. Barba Table 2. Depth estimation of subcrustal earthquakes as computed by Selvaggi & Amato (1992) and the ING bulletins, and depth errors as computed by confidence ellipses and by the procedure described in this paper. n Date Lat Lon Depth ERZ Depth Std. drv. (h) (km) (h) ondepth (Selvaggi (Selvaggi (ING (this &hato) &Amato) Bull) paper) I! 880106 42N5623 l3e03.70 63 1 1.70 69 4 02.21 2 881015 44N27.16 10E5801 47.2 5.79 27.3 5 15 38 3 881015 44N28.70 10E57.23 498 5.26 26 29 15 41 4 881218 44N02.28 10E53.01 37.7 241 39 3 1227 5 890701 43N21 55 12E3204 55 1 191 65 13 14:57 6 891210 43N4679 12E39.02 41.6 1.73 46 6 03.15 7 891215 43N25.55 I2E16.05 74.2 2.42 82 12 14.37 8 900206 43N37.19 12E06.48 44.5 1.82 47 7 02.49 9 900917 44N17.34 IOE07.36 65.5 2.14 67 16 05:56 10 901027 44N05.74 10655.64 56.2 1.90 55 4 1325 11 901203 43N28.78 12E40.39 63.2 1.99 69 I2 18:12 12 911209 44N29.05 10628.04 68.3 5.21 96 7 14:39 the real error. In some cases (e.g. event number 3) the standard deviation in the depth estimation is in agreement with the difference between the depth estimated by Selvaggi & Amato (1992) and the ING bulletins, and it is larger than the error derived from the confidence ellipses. Fig. 10( b) shows a crosssection of the hypocentres listed in Table 2 of Selvaggi & Amato (1992), recorded after 1987. The error bars in the depths are those obtained from our analysis. The results obtained, whilst still confirming that the depths of these events are larger than those usually observed in other Italian areas, point out that the large uncertainty associated with the depth estimation does not allow conclusive interpretations of possible trends delineating a dipping wedge from the Adriatic to the Tyrrhenian Sea, as can be derived from Fig. 2( b) in Selvaggi & Amato (1992). CONCLUSIONS We used a Monte Carlo simulation to estimate the errors associated with the hypocentral coordinates of the events recorded by a network. We quantified the influence of reading errors, uneven station distribution and limited information about the velocity structure. The results show that for events occurring inside the network grid the hypocentral coordinates are estimated with a good accuracy. In our simulation the probable error on the epicentral coordinates is lower than 5 km and is generally larger than the estimates of the standard routines. Moreover, the seismic events occurring offshore and in some of the seismogenic areas located in Italian territory can only be poorly located. In many cases the hypocentral errors derived from confidence ellipses are too small and are not indicative of the real mislocation of the events. These results are important because the areas where our analysis shows the greatest uncertainties are of great interest for tectonic studies (Selvaggi & Amato 1992; Selvaggi & Chiarabba 1995). Our simulation provides a guideline for the use of the ITSN seismic data for geostructural purposes in the Italian territory. Our results support the tectonic interpretations based on the ING bulletins in the areas covered well by the ITSN network. ACKNOWLEDGMENTS We thank Dr D. Console and Dr J. Pujol for helpful comments that improved the manuscript and Dr A. Amato for discussions on earthquake location of subcrustal events. The authors wish to thank Gideon Smith and an anonymous reviewer for their constructive critical comments, and the Editor, Dr Roger Clark, for his useful advice and suggestions. REFERENCES Alessandrini, B., Beranzoli, L. & Mele, F.M., 1995. 3-D crustal P-wave velocity tomography of the Italian region using local and regional seismicity data, Ann. Geojs.. XXXVIII, 189-211. Anderson, K.R., 1982. Robust earthquake location using M estimates, Phys. Earth planet. Inter., 30, 119-130. Barba, S., Di Giovambattista, R. & Smriglio, G., 1995. Italian seismic databank allows on-line access, EOS, Trans. Am. geophys. Un., 76,89. Basili, A., Smriglio, G. & Valensise, G., 1984. Procedure di determinazione ipocentrale in us0 presso 1'Istituto Nazionale di Geofisica, GNGTS, Atti III Conuegno, 875-884. Billings, S.D., Sambridge, M.S. & Kennett, B.L.N., 1994. Errors in hypocenter location: picking, model, and magnitude dependence, Bull. seism. SOC. Am., 84, 1978-1990. Brandt, S., 1976. Statistical and Computational Methods in Data Analysis, North-Holland, Amsterdam. Buland, R., 1976. The mechanics of locating earthquakes, Bull. seism. Soc. Am., 66, 173-187. Cattaneo, M. & Augliera, P., 1990. The automatic phase-picking and event location system of the I.G.G. Network (NW-Italy), Cahiers du Centre Europeen de Geodynamique et de Seismologie, Luxembourg, 1, 65-74. Console, R., Di Giovambattista, R., Favali, P. & Smriglio, G., 1992a. Seismogenic structures activated during the 1987 seismic sequences along the Adriatic coast, Geophys. J. Int., 108, 379-386. Console, R., Di Giovambattista, R., Favali, P. & Smriglio, G. 1992b. Methodological approach to earthquake location procedures: application to Italian seismicity, Phys. Earth planet. Inter., 75, 153-164. Di Maro, R. & Marchetti, A,, 1994. Detection capability of the Italian network for teleseismic events, Ann. Geojs., XXXVII, 415-431. Evernden, J.F., 1969. Precision of epicentres obtained by small numbers of world-wide stations, Bull. seism. SOC. Am., 59, 1365-1398. Mele, F. & Valensise, G., 1987. Un modello crostale per la localizzazione di eventi sismici regionali rilevati dalla rete sismica nazionale centralizzata dell'i.n.g., Proc. VI mtng Gruppo Nazionale di Geofisica della Terra Solida, CNR, Rome, 1337-1385. Selvaggi, G. & Amato, A,, 1992. Subcrustal earthquakes in the northern Apennines (Italy): evidence for a still active subduction?, Geophys. Res. Lett., 19, 2127-2130. Selvaggi, G. & Chiarabba, C., 1995. Seismicity and P-wave velocity image of the Southern Tyrrhenian subduction zone, Geophys. J. Int., 121, 818-826.