Phase Picks Research Articles

An analysis of the first-arrival times picked on the DSS and wide-angle seismic section recorded in Italy since 1968

We performed an analysis of refraction data recorded in Italy since 1968 in the frame of the numerous deep seismic sounding and wide-angle reflection/refraction projects. The aims of this study are to construct a parametric database including the recording geometric information relative to each profile, the phase pickings and the results of some kinematic analyses performed on the data, and to define a reference 1D velocity model for the Italian territory from all the available refraction data. As concerns the first goal, for each seismic section we picked the P-wave first-arrival-times, evaluated the uncertainties of the arrival-times pickings and determined from each travel time-offset curve the 1D velocity model. The study was performed on 419 seismic sections. Picking was carried out manually by an algorithm which includes the computation of three picking functions and the picking- error estimation. For each of the travel time-offset curves a 1D velocity model has been calculated. Actually, the 1D velocity-depth functions were estimated in three different ways which assume: a constant velocitygradient model, a varying velocity-gradient model and a layered model. As regards the second objective of this work, a mean 1D velocity model for the Italian crust was defined and compared with those used for earthquake hypocentre locations and seismic tomographic studies by different institutions operating in the Italian area, to assess the significance of the model obtained. This model can be used in future works as input for a next joint tomographic inversion of active and passive seismic data.

The role of instrumental versus macroseismic locations for earthquakes of the last century: a discussion based on the seismicity of the North-Western Apennines (Italy)

Many seismological observatories began to record and store seismic events in the early years of the twentieth century, contributing to the compilation of very valued databases of both phase pickings and waveforms. However, despite the availability of the instrumental data for some of the events of the last century, an instrumental location for these earthquakes is not always computed; moreover, when available, the macroseismic location is strongly preferred even if the number of points that have been used for it is low or the spatial distribution of the observations is not optimal or homogeneous. In this work I show how I computed an instrumental location for 19 events which occurred in the Garfagnana-Lunigiana region (Northern Tuscany, Italy) beginning from 1902. The location routine is based on a Joint Hypocentral Determination in which, starting from a group of master events, the systematic errors that may affect the data are summed up in the corrective factors complementing the velocity propagation model. All non-systematic errors are carefully checked and possibly discarded by going back to the original data, if necessary. The location is then performed using the classic approach of the inverse problem and solved iteratively. The obtained locations are then compared to those already available from other macroseismic studies with the aim to check the role to be attributed to the instrumental locations. The study shows that in most cases the locations match, in particular when considering the different significance of the location parameters, especially for the strongest events: the instrumental location provides the point where the rupture begins, while the macroseismic one is an estimate of the area where the earthquake possibly took place. This paper is not meant to discuss the importance and the necessity of macroseismic data; instead, the aim is to show that instrumental data can be used to obtain locations even for older seismic events, without any intention to define which location is better or more reliable.

Broad‐scale applicability of correlation detectors to China seismicity

It is demonstrated that cross‐correlation methods can successfully be applied on a large scale to the detection of seismic events arising in a variety of tectonic settings. The locations of about thousand earthquakes a year occurring in and near China are reported using phase picks from a large national network. We performed more than 100 million cross correlations on the waveforms of more than 18,800 events over 20 years, as recorded by a relatively sparse network; and detected about two thirds of the nationally reported events. Additional events (70% increase), beyond what standard processing detects for China on the sparse network, were also found. A corresponding reduction in detection threshold approaches 0.9 magnitude units for increasing station distance. As networks densify and archives grow, cross‐correlation is likely to become more and more useful for purposes of maximizing the number of detected events and hence to improve knowledge of seismicity.

Consistent phase picking for regional tomography models: application to the greater Alpine region

The resolution and reliability of tomographic velocity models strongly depends on quality and consistency of available traveltime data. Arrival times routinely picked by network analysts on a day-to-day basis often yield a high level of noise due to mispicks and other inconsistencies, particularly in error assessment. Furthermore, tomographic studies at regional scales require merging of phase picks from several networks. Since a common quality assessment is not usually available for phase data provided by different networks, additional inconsistencies are introduced by the merging process. Considerable improvement in the quality of phase data can only be achieved through complete repicking of seismograms. Considering the amount of data necessary for regional high-resolution tomography, algorithms combining accurate picking with an automated error assessment represent the best tool to derive large suitable data sets. In this work, we present procedures for consistent automated and routine picking of P-wave arrival times at local to regional scales including consistent picking error assessment. Quality-attributed automatic picks are derived from the MPX picking system. The application to earthquakes in the greater Alpine region demonstrates the potential of such a repicking approach. The final data set consists of more than 13 000 high-quality first-arrivals and it is used to derive regional 1-D and preliminary 3-D P-wave models of the greater Alpine region. The comparison with a tomographic model based on routine phase data extracted from the ISC Bulletin illustrates effects on tomographic results due to consistency and reliability of our high-quality data set.

Event Detection and Phase Picking Using a Time-Domain Estimate of Predominate Period Tpd

We present a new approach for event detection and accurate determination of the onset time of seismic phases. We use a simple time-domain function ( T pd ), which is readily and efficiently calculated in real time. Our function is based on the T p function, which has been used to characterize the predominant period of a waveform and which was originally introduced by Nakamura (1988) for use in real-time magnitude estimation. We find that while T p itself produces changes at the onset of a seismic signal, it is not suitable for detecting seismic onsets. However, our modified damped predominant period function, T pd , has considerable potential for detecting such onsets. We show examples of waveforms with their corresponding T pd functions and demonstrate how the choice of parameters influences the function. The examples given show clear increases in T pd for both the P - and S -wave onsets. We implement an approach to determining seismic onsets based on the T pd function and call it the T pd picker. The T pd picker is trained, and we evaluate its performance on four days of continuous data. The T pd picker compares favorably with a trained short-term average/long-term average picker—there are improvements in the number of accurate picks but, more notably, there is a significant reduction in missed picks. We analyze the signal-to-noise ratios of the waveforms and find that the improvements are mainly, but not exclusively, for cases of high noise. The aforementioned facts, combined with the simplicity and efficiency of the T pd calculation, implies that there is considerable potential for its use as an automatic picker. The results also suggest that the T pd picker could be further improved by refining the position of the pick after a seismic phase has been detected.

Broadband seismic measurements of degassing activity associated with lava effusion at Popocatépetl Volcano, Mexico

From November 1999 through July 2000, a broadband seismic experiment was carried out at Popocatépetl Volcano to record seismic activity over a wide period range (0.04–100 s). We present an overview of the seismicity recorded during this experiment and discuss results of analyses of long-period (LP) and very-long-period (VLP) seismic signals recorded at stations nearest to the crater over a four-month interval December 1999–March 2000. Three families of LP signals (Types-I, II, and III) are identified based on distinctive waveform features observed periods shorter than 1 s, periods longer than 15 s, and within the period range 0.5–2.5 s. Type-I LP events have impulsive first arrivals and exhibit a characteristic harmonic wave train with dominant periods in the 1.4–1.9 s range during the first 10 s of signal. These events are also associated with a remarkable VLP wavelet with period near 30 s. Type-II LP events represent pairs of events occurring in rapid succession and whose signatures are superimposed. These are typically marked by slowly emergent first arrivals and by a characteristic VLP wave train with dominant period near 30 s, made of two successive wavelets whose shapes are quasi-identical to those of the VLP wavelets associated with Type-I events. Type-III LP events represent the most energetic signals observed during our experiment. These have an emergent first arrival and display a harmonic signature with dominant period near 1.1 s. They are dominated by periods in the 0.25–0.35 s band and contain no significant energy at periods longer than 15 s. Hypocentral locations of the three types of LP events obtained from phase picks point to shallow seismic sources clustered at depths shallower than 2 km below the crater floor. Observed variations in volcanic eruptive activity correlate with defined LP families. Most of the observed seismicity consists of Type-I events that occur in association with 1–3-min-long degassing bursts (“exhalations”). Eruptive activity increased in intensity in February, coinciding with an increasing occurrence of Type-II LP events. Type-III events were first observed at the end of February and during March, in coincidence with the formation of a new lava dome. Vulcanian eruptions occurred in April and May. These events typically exhibit broadband signatures extending over the full period range of the sensors and lasting 30–80 min.

The COMPLOC Earthquake Location Package

This article describes the programs included in the COMPLOC computer program package that are designed to apply the source-specific station term (SSST) method to solve for local earthquake locations using P- and S- wave phase data. These programs can greatly improve the relative location accuracy of nearby events by applying empirical corrections for the biasing effects of three-dimensional velocity structure. They have been tested on data from both the Southern California Seismic Network (SCSN) and Northern California Seismic Network (NCSN) The SSST method (Richards-Dinger and Shearer 2000; Lin and Shearer 2005) works by assigning each station a travel-time correction that varies as a function of source position. This approach provides relative location accuracy comparable to master event or hypocentroidal decomposition (Jordan and Sverdrup 1981) methods within compact event clusters, but is applicable to distributed seismicity. It has some similarities to the double-difference algorithm (Waldhauser and Ellsworth 2000, 2002) and can be shown to give comparable results in tests on synthetic data (Lin and Shearer 2005). However, the SSST approach has computational advantages for big data sets because the location and station term parts of the computation are separate, so that large matrix inversions are not necessary. In addition, our implementation of SSST provides the option to use L1-norm misfit measures, which are more robust than least squares in the case of occasional timing errors or bad phase picks. We implement the SSST approach by selecting nearby events located within a sphere of specified radius r max around the target event. The station term for the target event is then computed as the median (or mean) residual of these events. Different results will be obtained depending upon the size of the cutoff distance r max. If r max is set to a large enough distance, then the SSST …

Grid-search event location with non-Gaussian error models

This study employs an event location algorithm based on grid search to investigate the possibility of improving seismic event location accuracy by using non-Gaussian error models. The primary departure from the Gaussian error model that is considered is the explicit use of non-Gaussian probability distributions in defining optimal estimates of location parameters. Specifically, the class of generalized Gaussian distributions is considered, which leads to the minimization of L p norms of arrival time residuals for arbitrary p ≥ 1 . The generalized Gaussian error models are implemented both with fixed standard errors assigned to the data and with an iterative reweighting of the data on a station/phase basis. An implicit departure from a Gaussian model is also considered, namely, the use of a simple outlier rejection criterion for disassociating arrivals during the grid-search process. These various mechanisms were applied to the ISC phase picks for the IWREF reference events, and the resulting grid-search solutions were compared to the GT locations of the events as well as the ISC solutions. The results indicate that event mislocations resulting from the minimization of L p residual norms, with p near 1, are generally better than those resulting from the conventional L 2 norm minimization (Gaussian error assumption). However, this result did not always hold for mislocations in event depth. Further, outlier rejection and iterative reweighting, applied with L 2 minimization, performed nearly as well as L 1 minimization in some cases. The results of this study suggest that ISC can potentially improve its location capability with the use of global search methods and non-Gaussian error models. However, given the limitations of this study, further research, including the investigation of other statistical and optimization techniques not addressed here, is needed to assess this potential more completely.

Automatic picking of P and S phases using a neural tree

The large amount of digital data recorded by permanent and temporary seismic networks makes automatic analysis of seismograms and automatic wave onset time picking schemes of great importance for timely and accurate event locations. We propose a fast and efficient P- and S-wave onset time, automatic detection method based on neural networks. The neural networks adopted here are particular neural trees, called IUANT2, characterized by a high generalization capability. Comparison between neural network automatic onset picking and standard, manual methods, shows that the technique presented here is generally robust and that it is capable to correctly identify phase-types while providing estimates of their accuracies. In addition, the automatic post processing method applied here can remove the ambiguity deriving from the incorrect association of events occurring closely in time. We have tested the methodology against standard STA/LTA phase picks and found that this neural approach performs better especially for low signal-to-noise ratios. We adopt the recall, precision and accuracy estimators to appraise objectively the results and compare them with those obtained with other methodologies. Tests of the proposed method are presented for 342 earthquakes recorded by 23 different stations (about 5000 traces). Our results show that the distribution of the differences between manual and automatic picking has a standard deviation of 0.064 s and 0.11 s for the P and the S waves, respectively. Our results show also that the number of false alarms deriving from incorrect detection is small and, thus, that the method is inherently robust.

Southern California Hypocenter Relocation with Waveform Cross-Correlation, Part 2: Results Using Source-Specific Station Terms and Cluster Analysis

We obtain precise relative relocations for more than 340,000 southern California earthquakes between 1984 and 2002 by applying the source-specific station-term (SSST) method to existing P- and S-phase picks and a differential lo- cation method to about 208,000 events within similar-event clusters identified with waveform cross-correlation. The entire catalog is first relocated by using existing phase picks, a reference 1D velocity model, and the SSST method of Richards-Dinger and Shearer (2000). We also perform separate relocations of Imperial Valley events by using a velocity model more suited to this region. Next, we apply cluster analysis to the waveform cross-correlation output to identify similar-event clusters. We re- locate earthquakes within each similar-event cluster by using the differential times alone, keeping the cluster centroid fixed to its initial SSST location. We estimate standard errors for the relative locations from the internal consistency of differential locations between individual event pairs; these errors are often as small as tens of meters. In many cases the relocated events within each similar-event cluster align in planar features suggestive of faults. We observe a surprising number of such faults at small scales that strike nearly perpendicular to the main seismicity trends. In general, the fine-scale details of the seismicity reveal a great deal of structural com- plexity in southern California fault systems.

Reference Events for Regional Seismic Phases at IMS Stations in China

Seismic-event location within the context of monitoring the Compre- hensive Nuclear-Test-Ban Treaty entails a priori knowledge of the travel time of seismic phases for a given source to stations of the International Monitoring System (IMS). Such travel-time information (or ground truth, GT) is provided empirically by seismic reference events, events that have well-determined hypocenter locations (epicenters typically known to � 5 km with high confidence) and origin times. In this study we present new reference events for the calibration of six seismic stations of the IMS in China, a region with high seismic activity. We use the Annual Bulletin of Chinese Earthquakes, which lists about 1000 earthquakes in and near China each year with consistent phase picks at regional stations, to determine precise relative earthquake locations from double-difference cluster analysis. The resulting high- resolution image of active faulting at seismogenic depths in areas of dense seismicity is correlated with the tectonic structure derived from mapped fault information at the surface to validate the absolute locations. We generated 59 reference events with M 3.5, distributed in six clusters in central and eastern China, and recorded by at least one of the six IMS stations. The scatter in relative travel-time residuals is reduced from 1.28 sec before to 0.61 sec after relocation, consistent with the relocated po- sitions of the events. The degree of correlation between seismicity structure and well- characterized fault data indicates that, in four clusters, the locations of the new ref- erence events are accurate to within 5 km (GT5), and in two clusters within 10 km (GT10).

THE PSACHNA (EVIA ISLAND) EARTHQUAKE SWARM OF JUNE 2003

Evia Island (Greece) lies in a transition zone from strike-slip faulting in the east, due to the strands of the North Anatolian Fault (NAF) that enter to the Aegean Sea, to normal faulting in the west along central Greece. In June 2003 a series of moderate events occurred in central Evia whose source parameters are investigated. These earthquakes caused serious damage to almost 20 residencies mainly in the town of Psachna. The sequence could be identified as an earthquake swarm with earthquake magnitudes in the range of 3 < M < 4.9. We used the Ρ and S arrivals at the stations of the National Seismic Network to relocate the events using the double-difference algorithm. All Ρ and S phase pickings were made by us using the broad band records from the network operated by the Geodynamic Institute of Athens. The relocated epicenters define a pronounced ENE- WSW zone, parallel to the high topography of the area. All depths are shallow from 1 to 8 Km. Regional waveform modeling was applied to determine the focal mechanisms of the larger events and FPFIT for the focal mechanisms of the smaller magnitude events. The majority of the focal mechanisms indicate normal faulting along almost E-W striking planes suggesting that deformation is mainly taken by normal faulting with a minor dextral horizontal motion. Normal faults with a N-S strike have been also observed showing that the E-W extension is present as it is observed in other parts of the Aegean region. Evia Island and its pattern of deformation is very interesting from the seismotectonic point of view. The fact that no large magnitude earthquake has occurred in Evia Island during instrumental times, makes the study of this earthquake swarm important. Previous work (Kiratzi, 2002) has shown that the deformation in northern Evia Island is taken up mainly by strike-slip faulting. Moreover, depending on the orientation of the activated faults in respect to the present state stress field, dextral or sinistral horizontal motion is observed. The Psachna earthquakes showed that an almost N-S extensional field prevails in central Evia Island with a few strikeslip focal mechanisms, suggesting that this part is mostly affected by the normal faulting system of central Greece.

Optimizing Correlation Techniques for Improved Earthquake Location

Earthquake location using relative arrival time measurements can lead to dramatically reduced location errors and a view of fault-zone processes with un- precedented detail. There are two principal reasons why this approach reduces lo- cation errors. The first is that the use of differenced arrival times to solve for the vector separation of earthquakes removes from the earthquake location problem much of the error due to unmodeled velocity structure. The second reason, on which we focus in this article, is that waveform cross correlation can substantially reduce measurement error. While cross correlation has long been used to determine relative arrival times with subsample precision, we extend correlation measurements to less similar waveforms, and we introduce a general quantitative means to assess when correlation data provide an improvement over catalog phase picks. We apply the technique to local earthquake data from the Calaveras Fault in northern California. Tests for an example streak of 243 earthquakes demonstrate that relative arrival times with normalized cross correlation coefficients as low as 70%, interevent separation distances as large as to 2 km, and magnitudes up to 3.5 as recorded on the Northern California Seismic Network are more precise than relative arrival times determined from catalog phase data. Also discussed are improvements made to the correlation technique itself. We find that for large time offsets, our implementation of time- domain cross correlation is often more robust and that it recovers more observations than the cross spectral approach. Longer time windows give better results than shorter ones. Finally, we explain how thresholds and empirical weighting functions may be derived to optimize the location procedure for any given region of interest, taking advantage of the respective strengths of diverse correlation and catalog phase data on different length scales.

An Automatic, Adaptive Algorithm for Refining Phase Picks in Large Seismic Data Sets

We have developed an adaptive, automatic, correlation- and clustering- based method for greatly reducing the degree of picking inconsistency in large, digital seismic catalogs and for quantifying similarity within, and discriminating among, clusters of disparate waveform families. Innovations in the technique include (1) the use of eigenspectral methods for cross-spectral phase estimation and for providing subsample pick lag error estimates in units of time, as opposed to dimensionless relative scaling of uncertainties; (2) adaptive, cross-coherency-based filtering; and (3) a hierarchical waveform stack correlation method for adjusting mean intercluster pick times without compromising tight intracluster relative pick estimates. To solve the systems of cross-correlation lags we apply an iterative, optimized conjugate gra- dient technique that minimizes an L1-norm misfit. Our repicking technique not only provides robust similarity classification-event discrimination without making a priori assumptions regarding waveform similarity as a function of preliminary hypocenter estimates, but also facilitates high-resolution relocation of seismic sources. Although knowledgeable user input is needed initially to establish run-time parameters, sig- nificant improvement in pick consistency and waveform-based event classification may be obtained by then allowing the programs to operate automatically on the data. The process shows promise for enhancing catalog reliability while at the same time reducing analyst workload, although careful assessment of the automatic results is still important.

Using Automated, High-precision Repicking to Improve Delineation of Microseismic Structures at the Soultz Geothermal Reservoir

— An automatic, adaptive, correlation-based algorithm for adjusting phase picks in large digital seismic data sets provides significant improvement in resolution of microseismic structures using only a small fraction of the time and manpower which would be required to re-analyze waveforms manually or semi-automatically. We apply this technique to induced seismicity at the Soultz-sous-Forets geothermal site, France. The method is first applied to a small, previously manually repicked subset of the catalogue so that we may compare our results to those obtained from painstaking, visual, cross-correlation-based techniques. Relative centroid-adjusted hypocenters show a decrease in median mislocation from 31 to 7 m for preliminary and automatically adjusted picks, respectively, compared to the manual results. Narrow, intersecting joint features not observed in the preliminary hypocenter cloud, but revealed through manual repicking, are also recovered using the automatic method. We then address a larger catalogue of ∼7000 microearthquakes. After relocating the events using automatic repicks, the percentage of events clustering within 5 m of their nearest neighbor increases form 5 to 26% of the catalogue. Hypocenter relocations delineate narrow, linear features previously obscured within the seismic cloud, interpreted as faults or fractures which may correspond to fluid propagation paths, or to changes in stress as a result of elevated pore pressures. RMS travel-time residuals for the larger data set are reduced by only 0.2%; however, phase-pick biases in the preliminary catalogue have influenced both the velocity model and station correction calculations, which will affect location residuals. These pick biases are apparent on the adjusted, stacked waveforms and correcting them will be important prior to future velocity model refinements.

Wavefield properties of a shallow long-period event and tremor at Kilauea Volcano, Hawaii

The wavefields of tremor and a long-period (LP) event associated with the ongoing eruptive activity at Kilauea Volcano, Hawaii, are investigated using a combination of dense small-aperture (300m) and sparse large-aperture (5km) arrays deployed in the vicinity of the summit caldera. Measurements of azimuth and slowness for tremor recorded on the small-aperture array indicate a bimodal nature of the observed wavefield. At frequencies below 2Hz, the wavefield is dominated by body waves impinging the array with steep incidence. These arrivals are attributed to the oceanic microseismic noise. In the 2–6Hz band, the wavefield is dominated by waves propagating from sources located at shallow depths (<1km) beneath the eastern edge of the Halemaumau pit crater. The hypocenter of the LP event, determined from frequency-slowness analyses combined with phase picks, appears to be located close to the source of tremor but at a shallower depth (<0.1km). The wavefields of tremor and LP event are characterized by a complex composition of body and surface waves, whose propagation and polarization properties are strongly affected by topographic and structural features in the summit caldera region. Analyses of the directional properties of the wavefield in the 2–6Hz band point to the directions of main scattering sources, which are consistent with pronounced velocity contrasts imaged in a high-resolution three-dimensional velocity model of the caldera region. The frequency and Q of the dominant peak observed in the spectra of the LP event may be explained as the dominant oscillation mode of a crack with scale length 20–100m and aperture of a few centimeters filled with bubbly water. The mechanism driving the shallow tremor appears to be consistent with a sustained excitation originating in the oscillations of a bubble cloud resulting from vesiculation and degassing in the magma.

First breaks—automatic phase pickings of P‐ and S‐onsets in seismic records

We have developed, validated and extensively tested a fast and versatile processing scheme for picking with confidence P‐ and S‐ arrival times in local seismic records. Out of 300 local events analyzed accurate P‐ and S‐ arrival times were automatically picked for 90% of these recordings. Essential ingredients in the processing scheme were i) prewhitening, ii) wavelet transform, iii) polarization filtering, iv) envelope transform and v) finally function fitting by a simulated annealing method for picking first breaks in approximately noise free envelope records.

Robust and reliable epicenter determinations: Envelope processing of local network data

Abstract Local event recordings are complex in the sense that relevant P and S phases vary in an unpredictable manner even between closely spaced stations; thus, manual analysis of such records is still commonplace. Our approach to solving this long-standing problem of observational seismology is to bandpass filter (3 to 6 Hz) to ensure good signal-to-noise ratio SNR and then form envelopes to ensure simple signals across a seismograph network. The physical basis is that Pg and Lg are crustal wave-guide phases reflecting P- and S-energy propagation. Extensive tests on envelope analysis of local records from different areas found that arrival times of the maxima of Pg and Lg envelopes increase very consistently with distance even in different tectonic regimes, typical velocities being 6.1 and 3.5 km/sec, respectively. These arrival-time parameters are easy to extract in a semi-automatic manner and are highly suitable for local epicenter determinations. Extensive tests on locating mining explosions were conducted, and on average, the “envelope” location errors relative to “true” locations were similar to those in bulletins that are based on conventional phase pickings. Occasionally, the Pg/Pn envelope may be very weak but can be replaced by the easily pickable (non-envelope) Pn phase. Additional advantages with envelope locations are transportability (not overly sensitive to details of crustal structure), and that envelope amplitudes can be directly converted to ground motion and magnitudes. For modern stations, envelopes can be formed in situ with low sampling rates of 1 to 2 Hz, thus greatly reducing transmission costs.

Constraints on seismic velocities in the Earth from traveltimes

New empirical traveltime curves for the major seismic phases have been derived from the catalogues of the International Seismological Centre by relocating events by using P readings, depth phases and the iasp91 traveltimes, and then re-associating phase picks. A smoothed set of traveltime tables is extracted by a robust procedure which gives estimates of the variance of the traveltimes for each phase branch. This set of smoothed empirical times is then used to construct a range of radial velocity profiles, which are assessed against a number of different measures of the level of fit between the empirical times and the predictions of the models. These measures are constructed from weighted sums of L2 misfits for individual phases. The weights are chosen to provide a measure of the probable reliability of the picks for the different phases. A preferred model, ak135, is proposed which gives a significantly better fit to a broad range of phases than is provided by the iasp91 and sp6 models. The differences in velocity between ak135 and these models are generally quite small except at the boundary of the inner core, where reduced velocity gradients are needed to achieve satisfactory performance for PKP differential time data. The potential resolution of velocity structure has been assessed with the aid of a non-linear search procedure in which 5000 models have been generated in bounds about ak135. Misfit calculations are performed for each of the phases in the empirical traveltime sets, and the models are then sorted using different overall measures of misfit. The best 100 models for each criterion are displayed in a model density plot which indicates the consistency of the different models. The interaction of information from different phases can be analysed by comparing the different misfit measures. Structure in the mantle is well resolved except at the base, and ak135 provides a good representation of core velocities.

Rapid three‐dimensional hypocentral determination using a master station method

A master station (MS) method is presented in this paper to rapidly determine hypocenters in three‐dimensional (3‐D) heterogeneous velocities. An equal differential time (EDT) surface is defined as the collection of all spatial points that satisfy the time difference between two arrivals, which can be two picks at two stations or two different phase picks at one station. The EDT surface is independent of the origin time and will contain the hypocenter. For an event with J arrivals, there are (J‐1) independent EDT surfaces. The MS method determines the hypocenter that satisfies two types of constraints: to be traversed by most EDT surfaces and to yield minimum travel time residual statistics. The statistics include both the residual variance and the amplitude of the origin time error. The combined use of the EDT surfaces and residual statistics allows for a unique determination of the hypocenter and origin time using different types of phase arrivals. In principle, only three arrivals are minimally required to constrain a unique solution if three different stations are used. For a 3‐D velocity model, the EDT surfaces and the residual statistics can be computed efficiently using a reference file created by Moser's (1991) ray tracing method. An illustration of the MS method is given for 27 small events that occurred in southern California, using a P wave velocity model modified from that of Magistrale et al. (1992). The average misfit between the bulletin hypocenters and the new solutions is 3.8 km. If a 3‐D velocity model is accurate, the MS method can be a viable means of hypocenter determination.