Tomographic modeling of a cross‐borehole data set

Geophysics ◽  
1989 ◽  
Vol 54 (10) ◽  
pp. 1249-1257 ◽  
Author(s):  
Larry R. Lines ◽  
Edward D. LaFehr
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
Velocity Model ◽  
Velocity Estimation ◽  
P Wave ◽  
Seismic Survey ◽  
Equation Modeling ◽  
Data Set ◽  
True Solution ◽  
Velocity Models

In this paper we describe a methodology for estimating P‐wave velocities from a cross‐borehole seismic survey that uses straight‐ray tomography, ray tracing, and finite‐difference wave‐equation modeling to produce velocity models that fit the first‐break traveltimes. After a starting model is established by straight‐ray tomography, the velocity model is checked by ray tracing and wave‐equation modeling. Since the models for each procedure show consistent results and the modeled traveltimes closely match those traveltimes from the actual data, we felt our interpretation was confirmed. However, the fitting of cross‐well first break traveltimes is only a necessary validity check and is not sufficient to guarantee that the true solution has been found. Two wells were drilled through the areas that were anomalous on the derived tomogram and check‐shot velocity surveys were run. Due primarily to a lateral ambiguity in velocity estimation caused by too few near‐vertical raypaths, the check‐shot surveys did not agree with the tomogram velocities. However, subsequently the check‐shot traveltimes were used to place bounds on velocity in a constrained least‐squares procedure; the combined modeling of uphole and cross‐well rays produced an optimum velocity model which satisfies all available data.

scholarly journals Mitigating elastic effects in marine 3-D full-waveform inversion

2019 ◽  
Vol 220 (3) ◽  
pp. 2089-2104
Author(s):  
Òscar Calderón Agudo ◽  
Nuno Vieira da Silva ◽  
George Stronge ◽  
Michael Warner
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Data Sets ◽  
Acoustic Wave Equation ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform

SUMMARY The potential of full-waveform inversion (FWI) to recover high-resolution velocity models of the subsurface has been demonstrated in the last decades with its application to field data. But in certain geological scenarios, conventional FWI using the acoustic wave equation fails in recovering accurate models due to the presence of strong elastic effects, as the acoustic wave equation only accounts for compressional waves. This becomes more critical when dealing with land data sets, in which elastic effects are generated at the source and recorded directly by the receivers. In marine settings, in which sources and receivers are typically within the water layer, elastic effects are weaker but can be observed most easily as double mode conversions and through their effect on P-wave amplitudes. Ignoring these elastic effects can have a detrimental impact on the accuracy of the recovered velocity models, even in marine data sets. Ideally, the elastic wave equation should be used to model wave propagation, and FWI should aim to recover anisotropic models of velocity for P waves (vp) and S waves (vs). However, routine three-dimensional elastic FWI is still commercially impractical due to the elevated computational cost of modelling elastic wave propagation in regions with low S-wave velocity near the seabed. Moreover, elastic FWI using local optimization methods suffers from cross-talk between different inverted parameters. This generally leads to incorrect estimation of subsurface models, requiring an estimate of vp/vs that is rarely known beforehand. Here we illustrate how neglecting elasticity during FWI for a marine field data set that contains especially strong elastic heterogeneities can lead to an incorrect estimation of the P-wave velocity model. We then demonstrate a practical approach to mitigate elastic effects in 3-D yielding improved estimates, consisting of using a global inversion algorithm to estimate a model of vp/vs, employing matching filters to remove elastic effects from the field data, and performing acoustic FWI of the resulting data set. The quality of the recovered models is assessed by exploring the continuity of the events in the migrated sections and the fit of the latter with the recovered velocity model.

Two robust imaging methodologies for challenging environments: Wave-equation dispersion inversion of surface waves and guided waves and supervirtual interferometry + tomography for far-offset refractions

2018 ◽  
Vol 6 (4) ◽  
pp. SM27-SM37 ◽  
Author(s):  
Jing Li ◽  
Kai Lu ◽  
Sherif Hanafy ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Velocity Distribution ◽  
Surface Waves ◽  
Guided Waves ◽  
Velocity Model ◽  
Dispersion Curves ◽  
P Wave ◽  
Head Wave ◽  
Near Surface ◽  
Velocity Models

Two robust imaging technologies are reviewed that provide subsurface geologic information in challenging environments. The first one is wave-equation dispersion (WD) inversion of surface waves and guided waves (GW) for the shear-velocity (S-wave) and compressional-velocity (P-wave) models, respectively. The other method is traveltime inversion for the velocity model, in which supervirtual refraction interferometry (SVI) is used to enhance the signal-to-noise ratio of far-offset refractions. We have determined the benefits and liabilities of both methods with synthetic seismograms and field data. The benefits of WD are that (1) there is no layered-medium assumption, as there is in conventional inversion of dispersion curves. This means that 2D or 3D velocity models can be accurately estimated from data recorded by seismic surveys over rugged topography, and (2) WD mostly avoids getting stuck in local minima. The liability is that WD for surface waves is almost as expensive as full-waveform inversion (FWI) and, for Rayleigh waves, only recovers the S-velocity distribution to a depth no deeper than approximately 1/2 to 1/3 wavelength of the lowest-frequency surface wave. The limitation for GW is that, for now, it can estimate the P-velocity model by inverting the dispersion curves from GW propagating in near-surface low-velocity zones. Also, WD often requires user intervention to pick reliable dispersion curves. For SVI, the offset of usable refractions can be more than doubled, so that traveltime tomography can be used to estimate a much deeper model of the P-velocity distribution. This can provide a more effective starting velocity model for FWI. The liability is that SVI assumes head-wave first arrivals, not those from strong diving waves.

Inversion of seismic refraction and reflection data for building long-wavelength velocity models

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. R81-R93 ◽  
Author(s):  
Haiyang Wang ◽  
Satish C. Singh ◽  
Francois Audebert ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Short Wavelength ◽  
Velocity Model ◽  
Density Model ◽  
Data Set ◽  
Reflected Waves ◽  
Long Wavelength ◽  
Velocity Models ◽  
Computation Efficiency ◽  
Refracted Waves

Long-wavelength velocity model building is a nonlinear process. It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves. We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves. The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data. To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints. The use of reflected waves required scale separation. We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively. The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb all the short-wavelength impedance contrasts. To improve the computation efficiency, the density model was converted into the zero-offset traveltime domain, where it was invariant to changes of the long-wavelength velocity model. After the wave-equation tomography has derived an optimized long-wavelength velocity model, full-waveform inversion was used to invert all the data to retrieve the short-wavelength velocity structures. We developed our method in two synthetic tests and then applied it to a marine field data set. We evaluated the results of the use of refracted and reflected waves, which was critical for accurately building the long-wavelength velocity model. We showed that our wave-equation tomography strategy was robust for the real data application.

scholarly journals Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

2017 ◽  
Vol 5 (3) ◽  
pp. SO11-SO19
Author(s):  
Lei Fu ◽  
Sherif M. Hanafy
Keyword(s):  
Wave Equation ◽  
Ray Tracing ◽  
Water Table ◽  
Seismic Data ◽  
Velocity Model ◽  
Water Table Depth ◽  
Seismic Survey ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Initial Starting

Full-waveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first-arrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the water-table depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the P-velocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

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.

Velocity model building in a crosswell acquisition geometry with image-trained artificial neural networks

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. U31-U46
Author(s):  
Wenlong Wang ◽  
Jianwei Ma
Keyword(s):  
Wave Equations ◽  
Model Building ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Data Set ◽  
Velocity Models ◽  
Velocity Model Building ◽  
Artificial Neural ◽  
The Cost

We have developed an artificial neural network to estimate P-wave velocity models directly from prestack common-source gathers. Our network is composed of a fully connected layer set and a modified fully convolutional layer set. The parameters in the network are tuned through supervised learning to map multishot common-source gathers to velocity models. To boost the generalization ability, the network is trained on a massive data set in which the velocity models are modified from natural images that are collected from an online repository. Multishot seismic traces are simulated from those models with acoustic wave equations in a crosswell acquisition geometry. Shot gathers from different source positions are transformed as channels in the network to increase data redundancy. The training process is expensive, but it only occurs once up front. The cost for predicting velocity models is negligible once the training is complete. Different variations of the network are trained and analyzed. The trained networks indicate encouraging results for predicting velocity models from prestack seismic data that are acquired with the same geometry as in the training set.

Subsalt velocity estimation by target-oriented wave-equation migration velocity analysis: A 3D field-data example

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. U19-U29 ◽  
Author(s):  
Yaxun Tang ◽  
Biondo Biondi
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Data Set ◽  
Generalized Born ◽  
Migration Velocity Analysis ◽  
Recorded Data

We apply target-oriented wave-equation migration velocity analysis to a 3D field data set acquired from the Gulf of Mexico. Instead of using the original surface-recorded data set, we use a new data set synthesized specifically for velocity analysis to update subsalt velocities. The new data set is generated based on an initial unfocused target image and by a novel application of 3D generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling zero and nonzero subsurface-offset-domain images. The target-oriented inversion strategy drastically reduces the data size and the computation domain for 3D wave-equation migration velocity analysis, greatly improving its efficiency and flexibility. We apply differential semblance optimization (DSO) using the synthesized new data set to optimize subsalt velocities. The updated velocity model significantly improves the continuity of subsalt reflectors and yields flattened angle-domain common-image gathers.

Numeric implementation of wave-equation migration velocity analysis operators

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE145-VE159 ◽  
Author(s):  
Paul Sava ◽  
Ioan Vlad
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Image Optimization ◽  
Migration Velocity Analysis ◽  
Zero Offset ◽  
Wavefield Extrapolation

Wave-equation migration velocity analysis (MVA) is a technique similar to wave-equation tomography because it is designed to update velocity models using information derived from full seismic wavefields. On the other hand, wave-equation MVA is similar to conventional, traveltime-based MVA because it derives the information used for model updates from properties of migrated images, e.g., focusing and moveout. The main motivation for using wave-equation MVA is derived from its consistency with the corresponding wave-equation migration, which makes this technique robust and capable of handling multipathing characterizing media with large and sharp velocity contrasts. The wave-equation MVA operators are constructed using linearizations of conventional wavefield extrapolation operators, assuming small perturbations relative to the background velocity model. Similar to typical wavefield extrapolation operators, the wave-equation MVA operators can be implemented in the mixed space-wavenumber domain using approximations of differentorders of accuracy. As for wave-equation migration, wave-equation MVA can be formulated in different imaging frameworks, depending on the type of data used and image optimization criteria. Examples of imaging frameworks correspond to zero-offset migration (designed for imaging based on focusing properties of the image), survey-sinking migration (designed for imaging based on moveout analysis using narrow-azimuth data), and shot-record migration (also designed for imaging based on moveout analysis, but using wide-azimuth data). The wave-equation MVA operators formulated for the various imaging frameworks are similar because they share elements derived from linearizations of the single square-root equation. Such operators represent the core of iterative velocity estimation based on diffraction focusing or semblance analysis, and their applicability in practice requires efficient and accurate implementation. This tutorial concentrates strictly on the numeric implementation of those operators and not on their use for iterative migration velocity analysis.

Frequency-domain wave-equation traveltime inversion with a monofrequency component

Geophysics ◽  
2021 ◽  
Vol 86 (6) ◽  
pp. R913-R926
Author(s):  
Jianhua Wang ◽  
Jizhong Yang ◽  
Liangguo Dong ◽  
Yuzhu Liu
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Time Domain ◽  
Computational Cost ◽  
Velocity Model ◽  
Receiver Side ◽  
Data Set ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
The Time Domain

Wave-equation traveltime inversion (WTI) is a useful tool for background velocity model building. It is generally formulated and implemented in the time domain, in which the gradient is calculated by temporally crosscorrelating the source- and receiver-side wavefields. The time-domain source-side snapshots are either stored in memory or are reconstructed through back propagation. The memory requirements and computational cost of WTI are thus prohibitively expensive, especially for 3D applications. To partially alleviate this problem, we provide an implementation of WTI in the frequency domain with a monofrequency component. Because only one frequency is used, it is affordable to directly store the source- and receiver-side wavefields in memory. There is no need for wavefield reconstruction during gradient calculation. In such a way, we have dramatically reduced the memory requirements and computational cost compared with the traditional time-domain WTI realization. For practical implementation, the frequency-domain wavefield is calculated by time-domain finite-difference forward modeling and is transformed to the frequency domain by an on-the-fly discrete Fourier transform. Numerical examples on a simple lateral periodic velocity model and the Marmousi model demonstrate that our method can obtain accurate background velocity models comparable with those from time-domain WTI and frequency-domain WTI with multiple frequencies. A field data set test indicates that our method obtains a background velocity model that well predicts the seismic wave traveltime.

Migration velocity analysis using traveltime wavefield tomography

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. U73-U85 ◽  
Author(s):  
Saleh M. Al-Saleh ◽  
Jianwu Jiao
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Migration Velocity ◽  
Equation Modeling ◽  
Velocity Analysis ◽  
Lateral Velocity ◽  
Traveltime Tomography ◽  
Velocity Models ◽  
Migration Velocity Analysis ◽  
Complex Structural

We introduce an integrated wave-equation technique for migration velocity analysis (MVA) that consists of three steps: (1) forming the extended data, (2) approximating the correct transmitted wavefield, and (3) using wavefield tomography to update the velocity model. In the first step, the crosscorrelation imaging condition is relaxed to produce other nonzero-lag common image gathers (CIG) that, combined, form a common image cube (CIC). Slicing the CIC at different crosscorrelation lags forms a series of CIGs. Flattened events will occur in the CIGs at a lag other than the zero-lag when an incorrect velocity model is used in the migration. In the second step, for each event on the CIG, we pick the focusing depth and crosscorrelation lag at which it is flattest. We then model a Green’s function by seeding a source at the focusing depth using one-way wave equation modeling, then shift the modeled wavefield with the focusing crosscorrelation lag. This process is repeated for the other primary events at different lateral and vertical positions. The result is a set of modeled data whose wavefield approximates the wavefield that would have been generated if the correct velocity model had been used to simulate these gathers. We then apply wavefield tomography on these data-driven modeled data to update the velocity model. Our inversion scheme is based on wave-equation traveltime tomography that can update the velocity model in the presence of large velocity errors and a complex environment. Tests on synthetic and real 2D seismic data confirm the method’s effectiveness in building velocity models in complex structural areas that have large lateral velocity variations.

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