scholarly journals Benchmarking earthquake location algorithms: A synthetic comparison

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. KS35-KS47 ◽  
Author(s):  
Andreas Wuestefeld ◽  
Sonja M. Greve ◽  
Sven Peter Näsholm ◽  
Volker Oye
Keyword(s):  
Sensor Network ◽  
Global Minimum ◽  
A Priori ◽  
Velocity Model ◽  
Cumulative Distribution ◽  
Gas Field ◽  
Arrival Times ◽  
Spatial Gradients ◽  
Inherent Error ◽  
Correct Location

A priori assessment of the expected location accuracy of a sensor network is typically done through inversion of the traveltime spatial gradients. This approach assumes that the applied location algorithm successfully recovers the global minimum of the objective function. However, even for accurate and precise phase picks, complexity in the velocity model and limitations in the network layout may inhibit the finding of a global minimum. The location algorithms may end up in a local minimum instead. We compare the location performance of various objective functions and minimization approaches. Although most of the analyzed location approaches mostly lead to good location results, none of the analyzed approaches recovered the correct location for all event locations. This implies that (microseismic) event locations estimates include an additional inherent error, which is linked to the applied location approach. This aspect is often neglected when interpreting event locations. Our site comprises a sensor network of two vertical strings, in a 1D velocity model of the Groningen gas field (The Netherlands), complicated by two thin, very high-velocity layers. For a series of synthetic event locations, we calculate arrival times, add picking errors, and then feed these synthetic picks into a set of different location routines. We also determine a novel way to analyze this approach-dependent location error of the sensor network for the given velocity model and a set of event locations: We compare the distances between a set of assumed event locations to resulting locations in the target region of the subsurface. From the cumulative distribution function of that mislocation distance, we determine the [Formula: see text] and [Formula: see text] confidence distances for each method. This results in scalar values representing the location confidence distances for a given method. In turn, this can be used to easily compare the location capabilities of different sensor layouts.

scholarly journals Probabilistic earthquake locations of induced seismicity in the Groningen region, the Netherlands

2020 ◽  
Vol 222 (1) ◽  
pp. 507-516 ◽  
Author(s):  
Jonathan D Smith ◽  
Robert S White ◽  
Jean-Philippe Avouac ◽  
Stephen Bourne
Keyword(s):  
The Netherlands ◽  
Depth Distribution ◽  
Velocity Model ◽  
Gas Production ◽  
Gas Field ◽  
Arrival Times ◽  
S Waves ◽  
Reservoir Compaction ◽  
Earthquake Locations ◽  
Projection Techniques

SUMMARY The Groningen gas reservoir, situated in the northeast of the Netherlands, is western Europe’s largest producing gas field and has been in production since 1963. The gas production has induced both subsidence and seismicity. Seismicity is detected and located using the Koninklijk Nederlands Meteorologisch Instituut shallow-borehole array for the period 2015–2017, incorporating the back projection techniques of QuakeMigrate and the nonlinear location procedure to constrain earthquake locations and depths. The uncertainties on the estimated depths are estimated taking into account velocity model, changes in station array geometry and uncertainties in the measurement of arrival times of the P and S waves. We show that the depth distribution of seismicity is consistent with nucleation within the reservoir (28 per cent) or in the overburden (60 per cent) within ∼500 m from the top of the reservoir. Earthquakes with hypocentres in the overburden likely originate from overlying Zechstein anhydrite caprock. Based on their depth distribution, it seems like the earthquakes are primarily driven by the elastic strain in the reservoir and overburden, induced by the reservoir compaction. We estimate the probability of earthquakes nucleating beneath the reservoir in the underlying Carboniferous limestone and basement, to be no more than 12 per cent.

Mapping of crack edges by seismic methods

1982 ◽  
Vol 72 (3) ◽  
pp. 779-792
Author(s):  
J. D. Achenbach ◽  
A. Norris ◽  
K. Viswanathan
Keyword(s):  
Input Data ◽  
A Priori ◽  
Signal Propagation ◽  
Computational Procedure ◽  
Crack Edge ◽  
Inverse Mapping ◽  
Arrival Times ◽  
Ultrasonic Signals ◽  
Geometrical Theory Of Diffraction ◽  
Local Edge

abstract The inverse problem of diffraction of elastic waves by the edge of a large crack has been investigated on the basis of elastodynamic ray theory and the geometrical theory of diffraction. Two methods are discussed for the mapping of the edge of a crack-like flaw in an elastic medium. The methods require as input data the arrival times of diffracted ultrasonic signals. The first method maps flash points on the crack edge by a process of triangulation with the source and receiver as given vertices of the triangle. By the use of arrival times at neighboring positions of the source and/or the receiver, the directions of signal propagation, which determine the triangle, can be computed. This inverse mapping is global in the sense that no a priori knowledge of the location of the crack edge is necessary. The second method is a local edge mapping which determines planes relative to a known point close to the crack edge. Each plane contains a flash point. The envelope of the planes maps an approximation to the crack edge. The errors due to inaccuracies in the input data and in the computational procedure have been illustrated by specific examples.

Passive seismic tomography using recorded microseismicity: Application to mining-induced seismicity

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. B41-B57 ◽  
Author(s):  
Himanshu Barthwal ◽  
Mirko van der Baan
Keyword(s):  
Seismic Tomography ◽  
Velocity Model ◽  
P Wave ◽  
Double Difference ◽  
Lateral Velocity ◽  
Study Region ◽  
Arrival Times ◽  
3D Velocity Model ◽  
Passive Seismic ◽  
Dip Angle

Microseismicity is recorded during an underground mine development by a network of seven boreholes. After an initial preprocessing, 488 events are identified with a minimum of 12 P-wave arrival-time picks per event. We have developed a three-step approach for P-wave passive seismic tomography: (1) a probabilistic grid search algorithm for locating the events, (2) joint inversion for a 1D velocity model and event locations using absolute arrival times, and (3) double-difference tomography using reliable differential arrival times obtained from waveform crosscorrelation. The originally diffusive microseismic-event cloud tightens after tomography between depths of 0.45 and 0.5 km toward the center of the tunnel network. The geometry of the event clusters suggests occurrence on a planar geologic fault. The best-fitting plane has a strike of 164.7° north and dip angle of 55.0° toward the west. The study region has known faults striking in the north-northwest–south-southeast direction with a dip angle of 60°, but the relocated event clusters do not fall along any mapped fault. Based on the cluster geometry and the waveform similarity, we hypothesize that the microseismic events occur due to slips along an unmapped fault facilitated by the mining activity. The 3D velocity model we obtained from double-difference tomography indicates lateral velocity contrasts between depths of 0.4 and 0.5 km. We interpret the lateral velocity contrasts in terms of the altered rock types due to ore deposition. The known geotechnical zones in the mine indicate a good correlation with the inverted velocities. Thus, we conclude that passive seismic tomography using microseismic data could provide information beyond the excavation damaged zones and can act as an effective tool to complement geotechnical evaluations.

scholarly journals Clustering a Global Field of Atmospheric Profiles by Mixture Decomposition of Copulas

2005 ◽  
Vol 22 (10) ◽  
pp. 1445-1459 ◽  
Author(s):  
Mathieu Vrac ◽  
Alain Chédin ◽  
Edwin Diday
Keyword(s):  
A Priori ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Specific Humidity ◽  
Vertical Profiles ◽  
Copula Functions ◽  
Mixture Density ◽  
Temperature And Humidity ◽  
Priori Information ◽  
Humidity Profiles

Abstract This work focuses on the clustering of a large dataset of atmospheric vertical profiles of temperature and humidity in order to model a priori information for the problem of retrieving atmospheric variables from satellite observations. Here, each profile is described by cumulative distribution functions (cdfs) of temperature and specific humidity. The method presented here is based on an extension of the mixture density problem to this kind of data. This method allows dependencies between and among temperature and moisture to be taken into account, through copula functions, which are particular distribution functions, linking a (joint) multivariate distribution with its (marginal) univariate distributions. After a presentation of vertical profiles of temperature and humidity and the method used to transform them into cdfs, the clustering method is detailed and then applied to provide a partition into seven clusters based, first, on the temperature profiles only; second, on the humidity profiles only; and, third, on both the temperature and humidity profiles. The clusters are statistically described and explained in terms of airmass types, with reference to meteorological maps. To test the robustness and the relevance of the method for a larger number of clusters, a partition into 18 classes is established, where it is shown that even the smallest clusters are significant. Finally, comparisons with more classical efficient clustering or model-based methods are presented, and the advantages of the approach are discussed.

Joint microseismic event location and anisotropic velocity inversion with the cross double-difference method using downhole microseismic data

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. KS63-KS73
Author(s):  
Yangyang Ma ◽  
Congcong Yuan ◽  
Jie Zhang
Keyword(s):  
Arrival Time ◽  
Velocity Model ◽  
P Wave ◽  
Double Difference ◽  
S Wave ◽  
Arrival Times ◽  
Monitoring Well ◽  
The Cross ◽  
Microseismic Event ◽  
Wave Arrival

We have applied the cross double-difference (CDD) method to simultaneously determine the microseismic event locations and five Thomsen parameters in vertically layered transversely isotropic media using data from a single vertical monitoring well. Different from the double-difference (DD) method, the CDD method uses the cross-traveltime difference between the S-wave arrival time of one event and the P-wave arrival time of another event. The CDD method can improve the accuracy of the absolute locations and maintain the accuracy of the relative locations because it contains more absolute information than the DD method. We calculate the arrival times of the qP, qSV, and SH waves with a horizontal slowness shooting algorithm. The sensitivities of the arrival times with respect to the five Thomsen parameters are derived using the slowness components. The derivations are analytical, without any weak anisotropic approximation. The input data include the cross-differential traveltimes and absolute arrival times, providing better constraints on the anisotropic parameters and event locations. The synthetic example indicates that the method can produce better event locations and anisotropic velocity model. We apply this method to the field data set acquired from a single vertical monitoring well during a hydraulic fracturing process. We further validate the anisotropic velocity model and microseismic event locations by comparing the modeled and observed waveforms. The observed S-wave splitting also supports the inverted anisotropic results.

Smoothing operators for waveform tomographic imaging

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1646-1654 ◽  
Author(s):  
Steve Cardimona ◽  
Jan Garmany
Keyword(s):  
Fresnel Zone ◽  
A Priori ◽  
Approximate Solutions ◽  
Velocity Model ◽  
Forward Problem ◽  
Nonlinear Inversion ◽  
Approximation Solution ◽  
Waveform Data ◽  
Sensitivity Functions ◽  
Priori Information

The analytic kernel in the space‐time domain for the Frechet derivative of acoustic waveform data with respect to changes in the slowness model is given by the Born approximation solution to the integral equation of waveform scattering. Preconditioning operators in the solution of this forward problem, which may incorporate a priori information and approximate solutions, are smoothing operators in the imaging problem, the first iteration of a nonlinear inversion for the slowness model. Some preconditioning operators are determined for solutions to the parabolic wave equation, and then used to create new sensitivity functions that retain appropriate characteristics of the true Frechet kernel in forward calculations. The new sensitivity functions define near‐source, near‐receiver and far‐field kernels, as well as kernels that exhibit an amplitude decay off the ray yielding ray‐perpendicular sensitivity that scales with the Fresnel zone size. A sample calculation from a synthetic cross‐well imaging experiment shows the usefulness of introducing physically appropriate model smoothing directly into the sensitivity function of the forward problem, helping to obtain a geologically reasonable image of the velocity model when ray coverage is insufficient.

Precision analysis of first‐break times in grid models

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 1062-1065 ◽  
Author(s):  
Thomas Gruber ◽  
Stewart A. Greenhalgh
Keyword(s):  
Numerical Models ◽  
Grid Point ◽  
Tomographic Reconstruction ◽  
Velocity Model ◽  
Model Parameters ◽  
Seismic Reflection Data ◽  
Arrival Times ◽  
Velocity Models ◽  
Reflection Data ◽  
Inversion Techniques

Rectangular grid velocity models and their derivatives are widely used in geophysical inversion techniques. Specifically, seismic tomographic reconstruction techniques, whether they be based on raypath methods (Bregman et al., 1989; Moser, 1991; Schneider et al., 1992; Cao and Greenhalgh, 1993; Zhou, 1993) or full wave equation methods (Vidale, 1990; Qin and Schuster, 1993; Cao and Greenhalgh, 1994) for calculating synthetic arrival times, involve propagation through a grid model. Likewise, migration of seismic reflection data, using asymptotic ray theory or finite difference/pseudospectral methods (Stolt and Benson, 1986; Zhe and Greenhalgh, 1997) involve assigning traveltimes to upward and downward propagating waves at every grid point in the model. The traveltimes in both cases depend on the grid specification. However, the precision level of such numerical models and their dependence on the model parameters is often unknown. In this paper, we describe a two‐dimensional velocity model and derive an error bound for first‐break times calculated with such a model. The analysis provides clear guidelines for grid specifications.

Migration moveout analysis and depth focusing

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Heterogeneous Media ◽  
A Priori ◽  
Complex Structure ◽  
Tomographic Reconstruction ◽  
Synthetic Data ◽  
Real Data ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Data Set ◽  
Velocity Models

Prestack depth migration still suffers from the problems associated with building appropriate velocity models. The two main after‐migration, before‐stack velocity analysis techniques currently used, depth focusing and residual moveout correction, have found good use in many applications but have also shown their limitations in the case of very complex structures. To address this issue, we have extended the residual moveout analysis technique to the general case of heterogeneous velocity fields and steep dips, while keeping the algorithm robust enough to be of practical use on real data. Our method is not based on analytic expressions for the moveouts and requires no a priori knowledge of the model, but instead uses geometrical ray tracing in heterogeneous media, layer‐stripping migration, and local wavefront analysis to compute residual velocity corrections. These corrections are back projected into the velocity model along raypaths in a way that is similar to tomographic reconstruction. While this approach is more general than existing migration velocity analysis implementations, it is also much more computer intensive and is best used locally around a particularly complex structure. We demonstrate the technique using synthetic data from a model with strong velocity gradients and then apply it to a marine data set to improve the positioning of a major fault.

Generalization of traveltime inversion

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Gérard C. Herman
Keyword(s):  
Time Windows ◽  
Velocity Model ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Error Norm ◽  
Arrival Times ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Use Of Data

A nonlinear inversion method is presented, especially suited for the determination of global velocity models. In a certain sense, it can be considered as a generalization of methods based on traveltimes of reflections, with the requirement of accurately having to determine traveltimes replaced by the (less stringent and less subjective) requirement of having to define time windows around main reflections (or composite reflections) of interest. It is based on an error norm, related to the phase of the wavefield, which is directly computed from wavefield measurements. Therefore, the cumbersome step of interpreting arrivals and measuring arrival times is avoided. The method is applied to the reconstruction of a depth‐dependent global velocity model from a set of plane‐wave responses and is compared to other methods. Despite the fact that the new error norm only makes use of data having a temporal bandwidth of a few Hz, its behavior is very similar to the behavior of the error norm used in traveltime inversion.

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