Crosshole seismic tomography

Geophysics ◽  
1989 ◽  
Vol 54 (2) ◽  
pp. 200-215 ◽  
Author(s):  
N. D. Bregman ◽  
R. C. Bailey ◽  
C. H. Chapman
Keyword(s):  
Ray Tracing ◽  
Field Data ◽  
Velocity Structure ◽  
Least Squares Method ◽  
Current Model ◽  
Velocity Model ◽  
Crystalline Rock ◽  
Inversion Method ◽  
Data Set ◽  
Waveform Data

Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which update the model. The iterations continue until the synthetic traveltimes fit the data to within the data error or until no improvement in the fit of the traveltimes is observed. The method is demonstrated on a small synthetic data set, where convergence to the correct solution is achieved in a few iterations. The method is then applied to field data from a crosshole experiment in crystalline rock. The frequency range of the seismograms is 1 to 6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geologic and geophysical data. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, providing an independent test of the validity of the inversion method.

scholarly journals Waveform inversion using a logarithmic wavefield

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R31-R42 ◽  
Author(s):  
Changsoo Shin ◽  
Dong-Joo Min
Keyword(s):  
Objective Function ◽  
Field Data ◽  
Velocity Structure ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Matrix Formalism ◽  
Inversion Algorithm ◽  
Data Set ◽  
Short Period

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

Nonlinear velocity inversion by a two‐step Monte Carlo method.

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Side Jin ◽  
Raul Madariaga
Keyword(s):  
Monte Carlo ◽  
Velocity Model ◽  
Small Scale ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Ray Theory ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Reference Velocity

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.

Velocity model estimation with data‐derived wavefront attributes

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 265-274 ◽  
Author(s):  
Eric Duveneck
Keyword(s):  
Velocity Model ◽  
Inversion Method ◽  
Data Set ◽  
Velocity Models ◽  
Common Reflection Surface ◽  
Data Points ◽  
Inversion Procedure ◽  
Optimum Model ◽  
Zero Offset ◽  
Kinematic Information

Kinematic information for constructing velocity models can be extracted in a robust way from seismic prestack data with the common‐reflection‐surface (CRS) stack. This data‐driven process results, in addition to a simulated zero‐offset section, in a number of wavefront attributes—wavefront curvatures and normal ray emergence angles—associated with each simulated zero‐offset sample. A tomographic inversion method is presented that uses this kinematic information to determine smooth, laterally heterogeneous, isotropic subsurface velocity models for depth imaging. The input for the inversion consists of wavefront attributes picked at a number of locations in the simulated zero‐offset section. The smooth velocity model is described by B‐splines. An optimum model is found iteratively by minimizing the misfit between the picked data and the corresponding modeled values. The required forward‐modeled quantities are obtained during each iteration by dynamic ray tracing along normal rays pertaining to the input data points. Fréchet derivatives for the tomographic matrix are calculated by ray perturbation theory. The inversion procedure is demonstrated on a 2D synthetic prestack data set.

Anisotropic 3D full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. R59-R80 ◽  
Author(s):  
Michael Warner ◽  
Andrew Ratcliffe ◽  
Tenice Nangoo ◽  
Joanna Morgan ◽  
Adrian Umpleby ◽  
...  
Keyword(s):  
High Velocity ◽  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Low Velocity ◽  
Data Set ◽  
Reflection Data ◽  
Full Waveform ◽  
Gas Cloud

We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.

Velocity analysis without picking

Geophysics ◽  
1989 ◽  
Vol 54 (2) ◽  
pp. 191-199 ◽  
Author(s):  
John L. Toldi
Keyword(s):  
Field Data ◽  
Velocity Model ◽  
Point Of View ◽  
Velocity Analysis ◽  
Lateral Variation ◽  
Data Set ◽  
Initial Interval ◽  
Analysis Algorithm ◽  
Interval Velocity ◽  
Interval Velocities

Conventionally, interval velocities are derived from picked stacking velocities. The velocity‐analysis algorithm proposed in this paper is also based on stacking velocities; however, it eliminates the conventional picking stage by always considering stacking velocities from the point of view of an interval‐velocity model. This view leads to a model‐based, automatic velocity‐analysis algorithm. The algorithm seeks to find an interval‐velocity model such that the stacking velocities calculated from that model give the most powerful stack. An additional penalty is incurred for models that differ in smoothness from an initial interval‐velocity model. The search for the best model is conducted by means of a conjugate‐gradient method. The connection between the interval‐velocity model and the stacking velocities plays an important role in the algorithm proposed in this paper. In the simplest case, stacking velocity is assumed to be equal to rms velocity. For the more general case, a linear theory is developed, connecting interval velocity and stacking velocity through the intermediary of traveltime. When applied to a field data set, the method produces an interval‐velocity model that explains the lateral variation in both stacking velocity and traveltime.

A 3D subsalt tomography based on wave-equation migration-perturbation scans

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. E1-E6 ◽  
Author(s):  
Bin Wang ◽  
Volker Dirks ◽  
Patrice Guillaume ◽  
François Audebert ◽  
Duryodhan Epili
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
Velocity Model ◽  
Image Point ◽  
Seismic Events ◽  
Observation Data ◽  
Velocity Analysis ◽  
Data Set ◽  
Tomographic Inversion ◽  
Model Independent

We have developed a simple but practical methodology for updating subsalt velocities using wave-equation, migration-perturbation scans. For the sake of economy and scalability (with respect to full source-receiver migration) and accuracy (with respect to common-azimuth migration), we use shot-profile, wave-equation migration. As input for subsalt-velocity analysis, we provide wave-equation migration scans with velocity scanning limited to the subsalt sediments. Throughout the migration-scan sections, we look for the best focusing or structural positioning of characteristic seismic events. The picking on the migration stacks selects the value of the best perturbation attribute (alpha-scaling factor) along with the corresponding position and local dip for the chosen seismic events. The associated, locally coherent events are then demigrated to the base of the salt horizon. Our key observation is that this process is theoretically equivalent to performing a datuming to a base of salt followed by subsalt migration of the redatumed data perturbed-velocity profiles. Thanks to this implicit redatuming of shot profiles, no ray tracing through the salt body is required. Thus, the events picked on the subsalt-velocity scans only need to be demigrated to the base of salt. For the event demigration we use 3D specular-ray tracing up to the base of the salt horizon within a predefined range of reflection angles. Event demigration produces model-independent data — time and time slope — that are then kinematically migrated using the current tomographic-inversion working model. To find a final-velocity model that will flatten best the remigrated events on common image point (CIP) angle gathers, we use the same set of demigrated observation data as the input data set for several nonlinear iterations of 3D tomographic inversion.

A ray inversion method for refraction analysis

Geophysics ◽  
1985 ◽  
Vol 50 (11) ◽  
pp. 1701-1720 ◽  
Author(s):  
Glyn M. Jones ◽  
D. B. Jovanovich
Keyword(s):  
Field Data ◽  
Opposite Sign ◽  
Synthetic Data ◽  
Head Wave ◽  
Inversion Method ◽  
Data Set ◽  
Near Surface ◽  
Left And Right ◽  
A New Technique ◽  
Good Agreement

A new technique is presented for the inversion of head‐wave traveltimes to infer near‐surface structure. Traveltimes computed along intersecting pairs of refracted rays are used to reconstruct the shape of the first refracting horizon beneath the surface and variations in refractor velocity along this boundary. The information derived can be used as the basis for further processing, such as the calculation of near‐surface static delays. One advantage of the method is that the shape of the refractor is determined independently of the refractor velocity. With multifold coverage, rapid lateral changes in refractor geometry or velocity can be mapped. Two examples of the inversion technique are presented: one uses a synthetic data set; the other is drawn from field data shot over a deep graben filled with sediment. The results obtained using the synthetic data validate the method and support the conclusions of an error analysis, in which errors in the refractor velocity determined using receivers to the left and right of the shots are of opposite sign. The true refractor velocity therefore falls between the two sets of estimates. The refraction image obtained by inversion of the set of field data is in good agreement with a constant‐velocity reflection stack and illustrates that the ray inversion method can handle large lateral changes in refractor velocity or relief.

scholarly journals Relocation of earthquakes in the southern and eastern Alps (Austria, Italy) recorded by the dense, temporary SWATH-D network using a Markov chain Monte Carlo inversion

Solid Earth ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 1087-1109
Author(s):  
Azam Jozi Najafabadi ◽  
Christian Haberland ◽  
Trond Ryberg ◽  
Vincent F. Verwater ◽  
Eline Le Breton ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Velocity Model ◽  
Eastern Alps ◽  
Inversion Method ◽  
Parameter Uncertainties ◽  
Waveform Data ◽  
Velocity Models ◽  
Austroalpine Nappes

Abstract. In this study, we analyzed a large seismological dataset from temporary and permanent networks in the southern and eastern Alps to establish high-precision hypocenters and 1-D VP and VP/VS models. The waveform data of a subset of local earthquakes with magnitudes in the range of 1–4.2 ML were recorded by the dense, temporary SWATH-D network and selected stations of the AlpArray network between September 2017 and the end of 2018. The first arrival times of P and S waves of earthquakes are determined by a semi-automatic procedure. We applied a Markov chain Monte Carlo inversion method to simultaneously calculate robust hypocenters, a 1-D velocity model, and station corrections without prior assumptions, such as initial velocity models or earthquake locations. A further advantage of this method is the derivation of the model parameter uncertainties and noise levels of the data. The precision estimates of the localization procedure is checked by inverting a synthetic travel time dataset from a complex 3-D velocity model and by using the real stations and earthquakes geometry. The location accuracy is further investigated by a quarry blast test. The average uncertainties of the locations of the earthquakes are below 500 m in their epicenter and ∼ 1.7 km in depth. The earthquake distribution reveals seismicity in the upper crust (0–20 km), which is characterized by pronounced clusters along the Alpine frontal thrust, e.g., the Friuli-Venetia (FV) region, the Giudicarie–Lessini (GL) and Schio-Vicenza domains, the Austroalpine nappes, and the Inntal area. Some seismicity also occurs along the Periadriatic Fault. The general pattern of seismicity reflects head-on convergence of the Adriatic indenter with the Alpine orogenic crust. The seismicity in the FV and GL regions is deeper than the modeled frontal thrusts, which we interpret as indication for southward propagation of the southern Alpine deformation front (blind thrusts).

Oriented surface passive seismic location using local slopes

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. KS13-KS25 ◽  
Author(s):  
M. Javad Khoshnavaz ◽  
Kit Chambers ◽  
Andrej Bóna ◽  
Milovan Urosevic
Keyword(s):  
Field Data ◽  
Focal Point ◽  
A Priori ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Data Set ◽  
Effective Velocity ◽  
Event Location ◽  
Receiver Arrays ◽  
Layered Models

A common acquisition scenario in microseismic monitoring is the deployment of large areal receiver arrays at or near the surface. This recording geometry has the advantage of providing coverage of the source’s focal hemisphere as well as characterization of the arrival time moveout curve; however, the accuracy of many location techniques applied to these data sets depends on the accuracy of the depth velocity model provided prior to location. We have developed a simple oriented time-domain location technique so that full knowledge of the velocity model is not required a priori. The applicability of the technique is limited to horizontally layered models and also to models with dipping interfaces of small angles; however, this restriction is acceptable in many unconventional reservoirs. Implementation of the technique includes three steps: (1) smoothing of the observed time arrivals by fitting a hyperbolic moveout curve with a broad set of constraints, (2) updating and restricting the constraints using a local-slopes-based location workflow, and (3) estimation of the focal coordinates of passive sources using the updated constraints for the final least-squares fitting of the moveout curves. We have tested the performance of the proposed technique on several 2D examples and a 3D field data set. The results from synthetic examples suggest that, despite the assumption of the method that the arrival moveout can be modeled using a constant effective velocity, a reliable event location is achieved for layered models without considerable lateral heterogeneities. Our tests on the field data set find that the focal point coincides with a previously derived estimate of the source location. To assess the uncertainty of the proposed technique, bootstrap statistics was also used and applied to the field data set.

Kirchhoff migration using eikonal equation traveltimes

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 810-817 ◽  
Author(s):  
Samuel H. Gray ◽  
William P. May
Keyword(s):  
Ray Tracing ◽  
Data Storage ◽  
Eikonal Equation ◽  
Synthetic Data ◽  
Velocity Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Regular Grid ◽  
Data Set ◽  
Kirchhoff Migration

The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffraction curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where two different branches of the traveltime field meet. Also, computational and data storage issues that are relatively unimportant for performance in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this algorithm is tested by using it to generate traveltimes to migrate the Marmousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard for comparison), a Kirchhoff migration using ray tracing, and a Kirchhoff migration using traveltimes generated by a commonly used eikonal equation solver. The F-X‐migrated image shows the imaging objective more clearly than any of the Kirchhoff migrations, and we advance a heuristic reason to explain this fact. Of the Kirchhoff migrations, the one using ray tracing produces the best image, and the other two are of comparable quality.

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