Source-receiver Pairs Research Articles

Adjoint inversion of antipodal PKPab waveforms for P wave velocity anomaly at the base of the lower mantle

We perform an adjoint inversion by using antipodal PKPab phases to estimate the heterogeneous Vp structure at the base of the lowermost mantle. We have carefully examined antipodal stations with high S/N ratios during the past 30 years and selected 20 source-receiver pairs with the epicentral distances >179.0 degree and the Mw <7.0. We have used the spectral-element method on the Earth Simulator of JAMSTEC to calculate the synthetic seismograms for a heterogeneous mantle Vp model with the accuracy of period about 8 s (110 km wavelength at the CMB). We have set up the time window to retrieve the PKPab phase from the vertical component of both observed and computed seismograms to calculate the adjoint source to obtain the sensitivity kernels of Vp in the mantle. The computed Vp sensitivity kernel for each event shows the characteristic annulus pattern in the lowermost mantle, which covers a large area of the CMB. The twenty PKPab earthquake-station pairs in this antipodal study contribute the equivalent of about 3140 measurements at the CMB—compared with 1871 previously studied—and provide new data. Therefore, although the number of individual source-receiver pairs is not large, the summed sensitivity kernels of the PKPab phase for Vp structure at the base of the mantle may be sufficient to model heterogeneity of the Vp structure at the CMB. We summed each event kernel to set up a sensitivity kernel of Vp in the lowermost mantle and iterated the inversion to estimate a heterogeneous structure in D″. Although we have iterations that dominantly affect both South America and the South Pacific, the summary final model shows features within South of Africa, South Pacific, SE Australia, and Central & South America. Keeping the Vs model fixed, we map the CMB Vp heterogeneity measured by the parameter Rs,p = dlnVs/dlnVp and find qualitative, proximal correspondence with the degree-2 pattern of Large Low Velocity Shear Provinces observed in shear tomographic models: in the Pacific and Africa Rs,p > 2.0, whereas the surrounding edges of the edges of the Pacific show Rs,p < 2.0.

The Marmara Sea basin as a regional depression constrained from ambient noise correlation tomography

SUMMARY We computed a 3-D shear wave velocity model of the Marmara Sea region from ambient noise tomography. The correlations of up to 8 yr of vertical-component seismic recordings from 80 broad-band stations provided Rayleigh wave group velocity measurements in the period band 6–21 s at more than 1400 selected virtual source–receiver pairs. Rayleigh wave group velocity maps were used to derive a shear wave velocity model through simulated annealing inversion. The resulting crustal model provides coverage of the Marmara Sea along with its surrounding regional tectonic features. This allows for an investigation of the spatial extents of the Marmara Sea on a scale larger than that of basins. The low-velocity structures of the Marmara Sea and the Thrace Basins are coeval to a depth of approximately 9 km. The crustal velocities beneath the Marmara Sea basins exhibit a low vertical gradient and smooth horizontal variations. The regional tectonic structures, such as Istranca Massif, Istanbul and Sakarya Zones, display sharp velocity contrasts with the lower velocity crust beneath the Marmara Sea. The observed low crustal velocities, along with depth variations of the velocity isosurfaces (i.e. 3.4 km s−1) indicate that the Marmara region is a structural depression much deeper and larger than the three basins of the North Marmara Trough. The North Anatolian Fault Zone is unlikely to be the primary factor contributing to the origin of this significant depression, as the basin's development appears to have occurred before the fault propagated into the region.

Performance study of ray-based ocean acoustic tomography methods for estimating submesoscale variability in the upper ocean.

Ocean acoustic tomography (OAT) methods aim at estimating variations of sound speed profiles (SSP) based on acoustic measurements between multiple source-receiver pairs (e.g., eigenray travel times). This study investigates the estimation of range-dependent SSPs in the upper ocean over short ranges (<5 km) using the classical ray-based OAT formulation as well as iterative or adaptive OAT formulations (i.e., when the sources and receivers configuration can evolve across successive iterations of this inverse problem). A regional ocean circulation model for the DeSoto Canyon in the Gulf of Mexico is used to simulate three-dimensional sound speed variations spanning a month-long period, which exhibits significant submesoscale variability of variable intensity. OAT performance is investigated in this simulated environment in terms of (1) the selected source-receivers configuration and effective ray coverage, (2) the selected OAT estimator formulations, linearized forward model accuracy, and the parameterization of the expected SSP variability in terms of empirical orthogonal functions, and (3) the duration over which the OAT inversion is performed. Practical implications for the design of future OAT experiments for monitoring submesoscale variability in the upper ocean with moving autonomous platforms are discussed.

Automated shear-wave splitting analysis for single- and multi- layer anisotropic media

Shear-wave velocity anisotropy is present throughout the earth. The strength and orientation of anisotropy can be observed by shear-wave splitting (birefringence) accumulated between earthquake sources and receivers. Seismic deployments are getting ever larger, increasing the number of earthquakes detected and the number of source-receiver pairs. Here, we present a new Python software package, SWSPy, that fully automates shear-wave splitting analysis, useful for large datasets. The software is written in Python, so it can be easily integrated into existing workflows. Furthermore, seismic anisotropy studies typically make a single-layer approximation, but in this work we describe a new method for measuring anisotropy for multi-layered media, which is also implemented. We demonstrate the performance of SWSPy for a range of geological settings, from glaciers to Earth's mantle. We show how the package facilitates interpretation of an extensive dataset at a volcano, and how the new multi-layer method performs on synthetic and real-world data. The automated nature of SWSPy and the discrimination of multi-layer anisotropy will improve the quantification of seismic anisotropy, especially for tomographic applications. The method is also relevant for removing anisotropic effects, important for applications including full-waveform inversion and moment magnitude analysis.

Laboratory investigation of hydraulic fracturing in granitic rocks using active and passive seismic monitoring

SUMMARY Knowledge of the fracturing processes can be important for the optimization of pressurized fluid injection operations in the deep underground rock mass. Active and passive seismic monitoring techniques have been used in the field for tracking or mapping the propagating hydraulic fracture. Although both these monitoring techniques provide valuable information about the generated fracture network, it is difficult for either technique to comprehensibly identify the different processes associated with hydraulic fracturing. The combined active and passive monitoring has the potential for better characterization of the complex hydraulic fracturing phenomena. In this study, laboratory hydraulic fracturing experiments with combined active and passive seismic monitoring were conducted on true triaxially loaded Barre granite cubes with different fluid injection rates. The seismic inelastic fracturing was detected by 16 passive acoustic emission sensors, where 3678 and 2370 seismic source events were detected for the high and low injection rate experiments, respectively. For active monitoring, strong variations in the attributes of signals were observed which were transmitted through four source–receiver pairs, placed both perpendicular and parallel to the generated hydraulic fracture. Positive velocity changes were observed for active sensor pairs with ray paths passing through the generated hydraulic fracture indicating fluid permeation, whereas isolated dry deformation was characterized by a slight but permanent velocity decrease. Compared to velocity, the energy of the active signals was 1–2 orders of magnitude more sensitive to different hydraulic fracturing processes. However, the sensitivity and signatures of the active signal attributes were found to be dependent on the frequency range and direction of ray path with respect to the location of the generated fracture network. Using the coupled evaluation of the active and passive signals we were able to systematically identify various hydraulic fracturing processes including: (1) aseismic deformation, (2) fracture initiation and fluid permeation, (3) pressure build-up, (4) fracture propagation and (5) pressure release and leak-off. The results of this study showed that combining the respective advantages of active and passive seismic techniques and using both of them to monitor the failure processes can facilitate a more comprehensive understanding and better control of the hydraulic stimulations in subsurface operations.

Performance study of ocean acoustic tomography methods in the upper-ocean environment using autonomous platforms

Accurate knowledge of the spatial and temporal evolution of the three-dimensional ocean sound speed profile (SSP) is crucial for underwater source localization. Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations based on acoustic measurements between multiple source-receiver pairs (e.g., eigenrays arrival times). This study investigates the estimation of range-dependent SSPs using a classical model-based OAT method (i.e., ray-based ocean acoustic tomography), for various configurations of source and receiver configurations using autonomous platforms in a highly-dynamic upper ocean environment. A regional oceanographic simulation of the De Soto Canyon circulation in the Gulf of Mexico is used to construct 3D sound speed variations spanning a month long which exhibits significant sub-mesoscale variability. Two main aspects affecting OAT performance in the presence of high 3D SSPs variability are investigated: (1) The influence of the input acoustic data (i.e., source-receivers configuration and platform motion, arrival-times accuracy...) and (2) the actual implementation of the OAT scheme (i.e., selection of complexity reduction basis, linearized forward model assumptions as well as the use of iterative solvers) on SSPs estimations errors. Practical implications for the design of OAT experiments in the dynamic upper ocean will be discussed. [Work supported by the Office of Naval Research.]

Linear time-invariant (LTI) modeling for aerial and underwater acoustics

Most newcomers to acoustic signal processing understand that linear time-invariant (LTI) filters can remove out-of-band noise from time series signals. What many acoustics researchers may not realize is that LTI models can be applied much more broadly, including to non-linear and time-variant systems. This presentation covers an overview of the autoregressive (AR), moving-average (MA), and autoregressive moving-average (ARMA) family of LTI models and their many useful applications in acoustics. Examples include analytic time-frequency processing of multi-component echolocation signals, fractional-delay filtering for acoustic time series simulations, broadband acoustic array beamforming, adaptive filtering for noise cancelation, and system identification for acoustic equalizers (i.e., flattening the frequency response of a source-receiver pair). This talk serves as a brief tutorial and inspiration for researchers who want to expand their use of signal processing, especially those in the fields of animal bioacoustics, aerial acoustics, and underwater acoustics.

Distributed iterative reweighted least squares algorithm for high-resolution finite-frequency traveltime velocity inversion using VSP data

Seismic traveltime between a source-receiver pair is a finite-frequency phenomenon. The velocity information at all points inside the first Fresnel zone is contained inside the traveltime. Therefore, finite-frequency traveltime velocity inversion (FFTVI) is able to invert velocity with finer structures than that can be obtained by ray-based tomography. Since FFTVI is a global inversion, its cost is lower than full waveform inversion. The implementation in this paper mainly focuses on the numerical aspects of FFTVI. We analyze the characteristics of FFTVI from the computational point of view. A parallel version, Iterative Reweighted Least Squares (IRLS) is designed for solving a large linear system in the memories of computer clusters. This implementation not only yields the accurate inversion of velocity at arbitrary grids and with an arbitrary acquisition geometry, but also is able to mitigate the impacts of traveltime picks with large uncertainties. The proposed workflow and parallel algorithm are demonstrated on synthetic VSP examples designed from a land project.

Illumination guided sparse geometry optimization for target-oriented full-waveform inversion: An ocean bottom node synthetic study

For full-waveform inversion (FWI) with sparse survey layout, it is crucial to optimize the source and receiver geometry toward full-wave illumination. We propose a sparse geometry optimization method and workflow for target-oriented FWI using finite-frequency illumination analysis. The frequency-dependent impact of a source-receiver pair to the wavefield sensitivity kernel and diagonal terms of approximate Hessian matrix are derived under visco-acoustic model assumptions. Based on the reciprocity principle, we use virtual sources in target zone to efficiently calculate the Green's function and illumination from acquisition surface. Optimal locations of sparse receivers are determined by comparing band-limited illumination at reference stations and their surrounding region through an illumination attribute scan. FWI model residual errors are used to evaluate the performance of optimized geometry layout for a given target zone. The performances of different geometries are compared to determine a suitable frequency band for FWI geometry optimization. Synthetic deep water model and ocean bottom node acquisition geometry are used to verify the feasibility of the workflow. Numerical tests in target-oriented FWI show that optimized geometry with constraints of band-limited illumination below10 Hz has better performance than that above 10 Hz. An extension of our geometry optimization method to sparse source configuration is straightforward.

Machine learning approaches for ray-based ocean acoustic tomography.

Underwater sound propagation is primarily driven by a nonlinear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSP variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. This article investigates the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution [i.e., the neural adjoint (NA) method], which combines deep learning of the forward model with a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. These methods were tested with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline. Idealized towed and fixed source configurations are considered. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of OAT predictions depends on the dynamics of the SSP variations.

Neural Eikonal solver: Improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. A few approaches use this concept to solve the eikonal equation that describes the first-arrival traveltimes of waves propagating in smooth heterogeneous velocity models. However, the challenge of the eikonal is exacerbated by the velocity models producing caustics, resulting in instabilities and deterioration of accuracy due to the non-smooth solution behavior. In this paper, we revisit the problem of solving the eikonal equation using neural networks to tackle caustic pathologies. We introduce the novel Neural Eikonal Solver (NES) for solving the isotropic eikonal equation in two formulations: the one-point problem is for a fixed source location; the two-point problem is for an arbitrary source-receiver pair. We present several techniques which provide stability in the case of caustics: improved factorization; non-symmetric loss function based on Hamiltonian; gaussian activation; symmetrization. In our tests, NES showed the relative mean-absolute error of 0.2-0.4% from the second-order factored Fast Marching Method with a similar inference time, and outperformed existing neural-network solvers giving 10-60 times lower errors and 2-30 times faster training. The one-point NES provides the most accurate solution, while the two-point NES gives slightly lower accuracy but an extremely compact representation with all spatial derivatives. It can be useful in many seismic problems: massive computations of traveltimes for millions of source-receiver pairs in Kirchhoff migration; modeling of ray amplitudes using spatial derivatives; traveltime tomography; earthquake localization; ray multipathing analysis.

Cross-Well Reflection Imaging at the Verkhnekamskoe Potash Deposit

Abstract —We propose the technique of extended processing of cross-well seismic data for reflection imaging. Based on the analysis of the wave field and synthetic modeling, a graph for processing cross-well data is developed to separate the reflections in the presence of a boundary of a sharp change in the velocity of elastic waves. The migration of the reflected waves from the time scale to the depth is performed by solving a forward problem for each source–receiver pair. As a result, the position of the reflection points is calculated, after which all the traces are stacked based on the binning grid. The input information for performing migration and solving a forward problem is the velocity characteristic of the massif, which is calculated using traveltime tomography on direct body waves obtained from the same data set of cross-well survey and vertical seismic profiling. The resulting depth seismic section has a much higher resolution than that of vertical seismic profiling and ground-based shallow seismic studies. This opens up the opportunity of identifying different small natural or technogenic objects in the interwell space.

On the use of machine learning for ray-based ocean acoustic tomography

Underwater sound propagation is primarily driven by a non-linear forward model relating variability of the ocean sound speed profile (SSP) to the acoustic observations (e.g., eigenray arrival times). Ocean acoustic tomography (OAT) methods aim at reconstructing SSPs variations (with respect to a reference environment) from changes of the acoustic measurements between multiple source-receiver pairs. We investigated the performance of three different OAT methods: (1) model-based methods (i.e., classical ray-based OAT using a linearized forward model), (2) data-driven methods (such as deep learning) to directly learn the inverse model, and (3) a hybrid solution (i.e., the Neural Adjoint-NA- method) which combines deep learning of the forward model followed by a standard recursive optimization to estimate SSPs. Additionally, synthetic SSPs were generated to augment the variability of the training set. We tested these methods with modeled ray arrivals calculated for a downward refracting environment with mild fluctuations of the thermocline using idealized towed and fixed source configurations. Results indicate that merging data-driven and model-based methods can benefit OAT predictions depending on the selected sensing configurations and actual ray coverage of the water column. But ultimately, the robustness of the OAT predictions depends on the actual dynamics of the SSP variations.

Performance Evaluation of LMS and CM Algorithms for Beamforming

In this paper, we compare the performances of the least mean square (LMS) and constant modulus (CM) algorithms for beamforming. Our interest in these algorithms finds its origins in their reliability as a source-receiver pair. In addition, their use brings a great frequency of diversity even to respond quickly to the increasing spectral demand. The results suggest that the greater the number of elements in the antenna, the better the directivity for both LMS and CM. We also note that a judicious choice of the control parameter mu leads to a better speed of convergence for the two algorithms. Let us note, however, that LMS is more efficient. Our simulations show that in an environment affected by white Gaussian noise, LMS is more robust than CM. This confirms the theoretical result due to the fact that LMS uses a sequence for learning. Performance analyses of the two techniques are simulated in the MATLAB environment.

Active-Source Interferometry in Marine and Terrestrial Environments: Importance of Directionality and Stationary Phase

ABSTRACT We utilize active-source seismic interferometry with dense seismic arrays both offshore and onland to explore the utility of this method to create virtual sources and reveal body-wave reflections in these two different environments. We first utilize data from an ocean-bottom cable (OBC) array in the Gulf of Mexico with equal numbers of sources (160 airgun shots) and receivers (160 ocean-bottom four-component sensors). We next use data from a geophone array across the Bighorn Mountains of Wyoming with many receivers (1300 vertical-component geophones) but a small number of sources (14 borehole active-source shots). We find that the OBC virtual source results, which produce strong reflections from sub-seafloor structures, are far superior to the onland results which lack usable reflections, and we explore reasons for these differences through a set of selective stacking approaches. We present techniques to account for the direction the seismic waves travel (directionality) and stationary phase and show that improvements can be made when incorporating these corrections. Although interferometric methods are based on assumptions of large numbers of widely distributed actual sources, we find that selective exclusion of potentially problematic source–receiver pairs can yield improved results. These geometric adjustments to active-source interferometry methods have utility for dense-nodal-array surveys that are now common in academic studies, but that often suffer from sparse source geometry.

Three Dimensional Volume Coverage in Multistatic Sonar Sensor Networks

Recent changes in the design of enemy threats such as submarines and the technological achievements in sensor development have paved the way for multistatic sonar applications, which increase security and situational awareness in underwater tactical operations. Previously, coverage in multistatic sonar sensor networks (MSSN) was studied using Cassini ovals and the traditional sonar detection model in two dimensions without any discussion of the practicability and feasibility in terms of conditions related to the underwater acoustic propagation environment. In this study, a practical three-dimensional MSSN channel model is proposed. The proposed model covers a spectral variation of absorption loss, ambient noise, sound speed profile, and shadow zones. The realistic effects of sound propagation and environmental conditions are modeled and evaluated using Lybin, which is a well-known sonar performance prediction tool. Using the practical MSSN channel model, the number of source-receiver pairs required to cover a three-dimensional MSSN volume is calculated. The impacts of frequency, source-to-receiver distance, and source level are investigated. The results are compared to the Cassini oval and traditional sonar detection models via an error expression derived according to our verified practical model. The results reveal that the inclusion of ambient conditions and sound propagation characteristics in the channel model leads to huge error levels of 4700000% in the Cassini oval model and 170000% in the traditional sonar detection model, depending on frequency. Thus, the applicability of these models in realistic MSSN deployment scenarios is limited.

Spatiotemporal variations in seismic attenuation during hydraulic fracturing: A case study in a tight oil reservoir in the Ordos Basin, China

During hydraulic fracturing (HF) stimulation for unconventional reservoir development, seismic attenuation has a significant influence on high-frequency microseismic data. Attenuation also provides important information for characterizing reservoir structure and changes to it due to HF injections. However, the attenuation effect is typically not considered in microseismic analysis. We have adopted the spectral ratio and centroid-frequency shift methods to estimate the subsurface attenuation (the factor [Formula: see text]) in a tight oil reservoir in the Ordos Basin, China. The P- and S-wave attenuations are calculated using the 3C waveform data recorded by a single-well downhole geophone array during a 12-stage HF stimulation. Both methods provide similar results (with differences in [Formula: see text] of absolute values less than 0.010 for P- and S-waves). For individual events, their median [Formula: see text] values calculated from different geophones are selected to represent the average attenuation. Spatiotemporal variations in attenuation are obtained by investigating [Formula: see text] values along propagating rays linking different source–receiver pairs. The [Formula: see text] values derived at different HF stages reveal significant attenuation in the targeted tight sandstone layer (0.030–0.062 for [Formula: see text] and 0.026−0.058 for [Formula: see text]), and the attenuation is apparently increased by fluid injection activities. We explain the sudden decrease in attenuation near the geophone array as a result of high shale content using log data from a horizontal treatment well. The consistency between the [Formula: see text] values and horizontal well-log data, as well as the HF process, indicates the reliability and robustness of the attenuation results. By studying spatiotemporal variations in attenuation, the changes in subsurface structures may be quantitatively characterized, thereby creating a reliable basis for microseismic modeling and data processing and providing additional information on monitoring the HF process.

Passive indoor visible light-based fall detection using neural networks

In this paper, a passive visible light sensing (VLS) fall detection system based on luminaires is proposed that uses neural networks to learn the state (i.e., upright or prone) of a target (e.g., a person). The proposed method measures the channel impulse response (CIR) between different source-receiver pairs in a passive scenario, where the user does not hold a device or sensor. The CIR measurements are collected in a realistically modeled room and neural networks are employed to learn the relationship between the CIR measurements and the states of the target at randomly selected positions in the room. The performance evaluation of the system shows that an accuracy of more than 97% is attainable by utilizing a large number of data samples and high brightness factor of the luminaires. The robustness of the proposed method is validated by using a tilted state which is labeled with same class as the upright state, however, the tilted state is not used to train the network. One of the key applications of fall detection is in healthcare domain for patient monitoring. The correct prediction of the prone state is particularly critical in such scenarios since emergency situations may arise from a fall.

On the performance investigation of distinct algorithms for room acoustics simulation

The purpose of this research is to investigate the accuracy provided by different algorithms for room acoustics simulation. Three software packages are used to simulate the monaural room impulse responses of a medium-sized concert hall. All algorithms deal with geometrical acoustics but with distinct implementations. The simulated room is one of those adopted as a benchmark for the first round robin on room acoustical simulation and auralization, the last international inter-comparison, for which the geometrical and acoustic data were carefully measured. The main novelty is the inclusion of the software RAIOS, which participated in the round robin but did not finish the simulations in time to be included in the publication. Four acoustical parameters, namely the reverberation time, the early decay time, the clarity factor for music, and the definition for speech, are computed for ten source-receiver pairs at octave band frequencies from 125 Hz to 8 kHz. The results obtained by the three software are then compared with the measured data for all source-receiver positions and frequency bands. The relative mean errors to the just noticeable difference (JND) are also computed. The main findings are that there are deviations relative to the measured results for all software, with some of the parameters being better evaluated than others are. Preliminary insights into the advantages and limitations of the software packages with respect to the monaural impulse response are also given.

An eigenfunction representation of deep waveguides with application to unconventional reservoirs

Guided waves that propagate in deep low-velocity zones can be described using the displacement-stress eigenfunction theory. For a layered subsurface, these eigenfunctions provide a framework to calculate guided-wave properties at a fraction of the time required for fully numerical approaches for wave-equation modeling, such as the finite-difference approach. Using a 1D velocity model representing the low-velocity Eagle Ford Shale, an unconventional hydrocarbon reservoir, we verify the accuracy of the displacement eigenfunctions by comparing with finite-difference modeling. We use the amplitude portion of the Green’s function for source-receiver eigenfunction pairs as a proxy for expected guided-wave amplitude. These response functions are used to investigate the impact of the velocity contrast, reservoir thickness, and receiver depth on guided-wave amplitudes for discrete frequencies. We find that receivers located within the low-velocity zone record larger guided-wave amplitudes. This property may be used to infer the location of the recording array in relation to the low-velocity reservoir. We also study guided-wave energy distribution between the different layers of the Eagle Ford model and find that most of the high-frequency energy is confined to the low-velocity reservoir. We corroborate this measurement with field microseismic data recorded by distributed acoustic sensing fiber installed outside of the Eagle Ford. The data contain high-frequency body-wave energy, but the guided waves are confined to low frequencies because the recording array is outside the waveguide. We also study the energy distribution between the fundamental and first guided-wave modes as a function of the frequency and source depth and find a nodal point in the first mode for source depths originating in the middle of the low-velocity zone, which we validate with the same field data. The varying modal energy distribution can provide useful constraints for microseismic event depth estimation.