Wave‐equation migration velocity analysis with time‐shift imaging

Summary Seismic exploration of geothermal resources in the German Molasse Basin (GMB) requires a proper seismic imaging of deep productive horizons. Success of this process is heavily reliant on the correct estimation of seismic velocities by migration velocity analysis (MVA). However, the MVA has a high computational cost and, depending on the quality of seismic data and approach chosen for the analysis, it might produce erroneous results. In this work, we developed an MVA workflow that enables to create a velocity model that is consistent with seismic, geological and borehole data, despite the limitations inherent to the MVA. A 2D seismic data set acquired in the GMB was used to test the MVA. The results were evaluated based on four criteria: increase in seismic resolution, availability of good quality reflectors beneath velocity components, geological plausibility and consistency with borehole data. Such an interpretive approach to the initially purely processing procedure allowed to discriminate genuine velocity components from erroneous components. Our work shows that the MVA produces an accurate velocity model of the subsurface, if the data have good quality, sufficient cable length, and geological constraints in form of lithological and velocity logs from boreholes in the vicinity of a study area.

ABSTRACTLeast‐squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long‐scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single‐scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey‐sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey‐sinking (depth‐oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning‐based (surface‐oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth‐oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton‐like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model‐based data fitting.

ABSTRACTWe present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle‐domain common‐image gathers (ADCIGs) over the aperture‐angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray‐based tomography, we invert ‘image perturbations’ using a linearized wave‐equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs.Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first‐order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction.We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies.

As we all know, accuracy of the migration velocity determines the quality of imaging results to a large extent. However, traditional migration velocity analysis methods always fail in gas cloud area due to the complex wave field and poor quality of the seismic data. Aiming at this problem, we present a high precision velocity model building technology for gas cloud areas to improve seismic imaging quality in these areas. Diving wave always appears as first arrival and its ray density satisfies inversion demand well, which makes it easy to pick up shallow information and sensitive to velocity anomalies. Thus, we build velocity model for gas cloud areas based on both diving and reflected wave. Firstly, diving wave tomography inversion is carried out to establish a high precision velocity model of shallow layers. Then we perform reflection tomography inversion to get velocity model of deeper layers with shallow layers’ velocity model above as initial input. Finally, we build the accurate velocity model of gas cloud areas successfully. The results of real data processing in P oilfield show that the velocity model built by our method has a better precision in gas cloud areas and matches the VSP velocity better in both gas cloud areas and normal areas. In contrast to the images based on conventional reflection wave velocity model, the imaging result based on our velocity model is obviously improved. Our method is widely applicable to the study of gas cloud areas and will help the understanding and interpretation of seismic data in gas cloud areas greatly.

SUMMARY The accurate and fast estimation of velocity models is crucial in seismic imaging. Conventional methods, such as tomography, stereotomography, migration velocity analysis and full-waveform inversion (FWI), obtain appropriate velocity models; however, they require intense and specialized human supervision and consume much time and computational resources. In recent years, some works investigated deep learning (DL) algorithms to obtain the velocity model directly from shots or migrated angle panels, obtaining encouraging predictions of synthetic models. This paper proposes a new flow to recover structurally complex velocity models with DL. Inspired by the conventional geophysical velocity model building methods, instead of predicting the entire model in one step, we predict the velocity model iteratively. We implement the iterative nature of the process when, at each iteration, we train the DL algorithm to determine the velocity model with a certain level of precision/resolution for the next iteration; we name this process as ‘Deep-Tomography’. Starting from an initial model, that is an ultrasmooth version of the true model, Deep-Tomography is able to predict an appropriate final model, even in complete unseen during the training data, like the Marmousi model. When used as the initial model for FWI, the models estimated by Deep-Tomography can also improve substantially the final results obtained with FWI.

SUMMARY Compared to first-arrival traveltime tomography (FATT), first-arrival traveltime and slope tomography (FASTT) integrates both traveltimes and local slopes of first arrivals at sources and/or receivers to construct more accurate subsurface velocity models. Local slopes serve as additional constraints, helping to mitigate the ill-posedness of tomography by better constraining ray directions. This is particularly beneficial in regions with complex topography, where shadow zones arise due to strong velocity contrasts. However, representing complex topography or bathymetry can be less accurate when using classical rectangular grid discretization. To address these complexities with greater versatility and accuracy, we compute traveltimes of locally coherent events using a factored topography-dependent eikonal solver on curvilinear grids. Slopes are then estimated by finite differences in the traveltime maps after a back-and-forth coordinate transform from the curvilinear grid to a rectangular computational grid. Additionally, we solve the inverse problem with the matrix-free approach, where the data misfit gradient is computed with the adjoint-state method. This adjoint-state formulation avoids the explicit construction and storage of large Fréchet derivative matrices and does not require a tedious posterior ray tracing on curvilinear grids. A land synthetic example first illustrates the sensitivity of slopes to topography and the more accurate velocity models with FASTT than with FATT in the presence of topography. We then perform a first application of the topography-dependent FASTT method on a real redatumed ocean-bottom node data set, where the bathymetry exhibits a steep scarp. We show that the topography-dependent FASTT generates a velocity model that matches more closely a legacy reflection tomography model than conventional FATT. We conclude that the topography-dependent FASTT provides a versatile approach for handling complex surfaces during velocity model building in both marine and land environments.

An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.

We describe a new short cut strategy to image the sediments and salt edge around a salt flank through an overburden salt canopy. We demonstrate its performance and capabilities on a synthetic acoustic seismic data from a Gulf of Mexico (GOM) style model. In this strategy, we first redatum the surface shots from a walk away Vertical Seismic Profile (WVSP) survey to be as if the source and receiver pairs had been located in the borehole at the positions of the receivers. This process creates effective downhole shot gathers by completely moving the surface shots through the salt canopy without any knowledge of the overburden velocity structure. After redatumming, we apply reverse time prestack depth migration to the effective downhole shot records using a simple linear v(z) gradient velocity model. This first pass of migration reveals the salt dome edge quite well. Once the salt dome edge is defined, a second pass of reverse time prestack depth migration is performed with an updated velocity model that now consists of the v(z) gradient and the salt dome. The second pass migration brings out the dipping sediments abutting the salt flank because these reflectors were illuminated by energy that bounced off the salt flank forming prismatic reflections. The full, two‐way wave equation migration algorithm images these double bounces correctly. In the new strategy, we do not need to perform the traditional complex process of velocity estimation, model building, and iterative depth migration to remove the effects of the salt canopy and surrounding overburden. The redatumming process eliminates all of that. In terms of computational effort, it takes less than 10% of total computation time and requires virtually no human effort. The reverse time depth migrations are target‐oriented and, for this example, involve only 1/3 of the model. The new strategy provides a simple, target oriented method to image a salt flank and nearby sediments with minimal velocity estimation and model building effort.

The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. The overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice and weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. The velocity extraction, interpolation, and smoothing can be done fully automatically, without the need for human interpretation or other intervention. A numerical example demonstrated that quantitative information about the migration velocity model can be determined by double path-integral migration. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration velocity analysis or tomographic methods.

Full-waveform inversion (FWI) has become the centerpiece of velocity model building (VMB) in seismic data processing in recent years. It has proven capable of significantly improving the velocity model and, thus, the migration image for different acquisition types and geologic settings, including complex environments such as salt. With the advent of FWI imaging, the scope of FWI applications has extended further from VMB into the imaging landscape. However, current FWI applications in the industry prevalently employ the acoustic approximation. One common problem of acoustic FWI (A-FWI) is the apparent salt halos at the salt-sediment interface in the resulting FWI velocity and FWI image, the presence of which hinders direct interpretation and imaging focusing around salt bodies. With synthetic and field data examples, we demonstrate that this salt halo is caused mainly by the large mismatch between the elastic recorded data and the acoustic modeled data, particularly at middle to long offsets. To overcome limitations imposed by acoustic assumptions, we developed an elastic FWI (E-FWI) algorithm that combines an elastic modeling engine with the time-lag cost function, which we call elastic time-lag FWI (E-TLFWI). With a more accurate modeling engine, E-TLFWI significantly reduces the salt halo observed in its acoustic counterpart. However, we also observe that the images migrated using the A-FWI and E-FWI velocity models remain similar overall, with some slight improvements around and beneath salt boundaries, particularly near steep salt flanks, as a result of the reduced salt halo. By contrast, FWI images derived from E-TLFWI show considerable benefits over those from acoustic time-lag FWI, such as improved event focusing, better structural continuity, and higher signal-to-noise ratio. The sharpened salt boundaries and enhanced quality of the FWI images reveal the significant value of E-FWI and provide the justification for its greatly increased cost.

Combining PP-waves with mode-converted PS reflections in migration velocity analysis (MVA) can help build more accurate VTI (transversely isotropic with a vertical symmetry axis) velocity models. To avoid problems caused by the moveout asymmetry of PS-waves and take advantage of efficient MVA algorithms designed for pure modes, here we generate pure SS-reflections from PP and PS data using the PP þ PS ¼ SS method. Then the residual moveout in both PP and SS common-image gathers is minimized during iterative velocity updates. The model is divided into square cells, and the VTI parameters VP0, VS0, e, and δ are defined at each grid point. The objective function also includes the differences between the migrated depths of the same reflectors on the PP and SS sections. Synthetic examples confirm that 2D MVA of PP- and PS-waves may be able to resolve all four relevant parameters of VTI media if reflectors with at least two distinct dips are available. The algorithm is also successfully applied to a 2D line from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. After the anisotropic velocity model has been estimated, accurate depth images can be obtained by migrating the recorded PP and PS data.

Migration velocity analysis is a labor-intensive part of the iterative prestack time migration (PSTM) process. We have developed a velocity estimation scheme to improve the efficiency of the velocity analysis process using an automatic approach. Our scheme is the numerical implementation of the conventional velocity analysis process based on residual moveout analysis. The key aspect of this scheme is the automatic event picking in the common-reflection point (CRP) gathers, which is implemented by semblance scanning trace by trace. With the picked traveltime curves, we estimate the velocities at discrete grids in the velocity model using the least-squares method, and build the final root-mean-square (rms) velocity model by spatial interpolation. The main advantage of our method is that it can generate an appropriate rms velocity model for PSTM in just a few iterations without manual manipulations. In addition, using the fitting curves of the picked events in a range of offsets to estimate the velocity model, which is fitting to a normal moveout correction, can prevent our scheme from the local minima issue. The Sigsbee2B model and a field data set are used to verify the feasibility of our scheme. High-quality velocity model and imaging results are obtained. Compared with the computational cost to generate the CRP gathers, the cost of our scheme can be neglected, and the quality of the initial velocity is not critical.

Overburden (shallow) anomalies such as channels, sink holes, or karst features pose challenges for seismic time imaging, resulting in an obscured image below the anomalies i.e. pull-ups or push-downs. These anomalies can propagate down to the reservoir masking the image and create structural uncertainties. These relatively small scale (< 1 – 2 km) overburden anomalies cannot be resolved with conventional depth imaging usually, based on migration velocity analysis and residual move out (RMO) minimization only. This paper proposes the application of dip-constrained tomography, in combination with RMO tomography to help resolve these shallow anomalies. Although the method has been widely used elsewhere e.g. in offshore Brazil and North Sea (Chen et al., 2012, Guillaume et al., 2013, Carotti et al., 2015 and Hollingworth et al., 2015), this is the first time it has been applied in a carbonate oilfield in offshore Abu Dhabi. An accurate velocity model is required for seismic depth imaging. The velocity model is optimized using a tomographic technique which is a non-linear optimization process with relevant constraints imposed. The data are migrated using an initial velocity model and common image gathers are obtained. RMO is defined in a cost function and non-linear tomography finds a velocity model minimizing the cost function. An additional structural constraint in the form of an offset-dependent dip constraint is introduced in the cost function for minimizing the misfit between the offset-dependent dip of the events and the expected dip. Dip-constrained tomography was able to obtain a high resolution velocity model in the overburden and provided a robust seismic image essentially free of pull-up and push-down effects in the reservoir. The structural uncertainty in the reservoir was subsequently reduced. Inverting the dip term together with RMO term can potentially correct image distortions e.g. pull-ups and push-downs and focus the image simultaneously. The refined subsurface image can help optimize the reservoir model with less structure uncertainty and can enhance the production profile by providing more flexibility in well design and planning. The methodology was applied on a pilot area which gave quite encouraging results and leads to extend the pre-stack depth imaging to a full-field application.

Velocity model building is an essential step in seismic exploration, which runs through the whole process of seismic data acquisition, processing, and interpretation. The velocity information is conventionally obtained by iterative optimization methods such as full-waveform inversion or tomography. These traditional methods are computationally expensive, and they require an initial velocity model and human interactions. To simplify the model building problem, we develop a supervised end-to-end conventional neural network to reconstruct the P-wave velocity models directly from raw seismic data. The network takes in one-shot seismic traces simulated with acoustic wave equations in VSP geometry. To train the network, we create 870 2D synthetic seismic images and corresponding labeled images, which are shown to be sufficient for the network to learn the nonlinear relationship between one-shot seismic data and the corresponding velocity model. The numerical examples show that the trained network is capable of predicting accurate layered velocity models from only one-shot seismic data.

Traditional approaches require a velocity model to compute travel times for estimating the location of earthquakes. Moreover, the velocity model typically assumed is layered in nature, ignoring the perturbations around the background velocity model. In this study, we propose a novel method that does not require any assumption on a velocity model. Also, triangulation estimates of location require three-station recordings. Even if the single station is used, three components of recordings are needed. In this work, we propose a machine learning method, based on support vector machines (SVM), that can predict earthquake location and magnitude with just one component (vertical) of a single station. Machine learning methods are typically used for either regression or classification. Literature shows that the SVM algorithm is promising for the classification of an arbitrary signal. This research demonstrates that, by using complementary input features from a seismic recording, a comparable performance can be obtained, with a substantial reduction in detection time. Furthermore, only the vertical component of a single recording station data is used to train the network. The SVM algorithm is applied on synthetic seismograms from 400 earthquakes of different focal mechanisms and magnitudes. This falls under supervised machine learning, as we give the input features and use them for training the model. Overfitting is avoided by tenfold cross-validation, i.e., the algorithm is repeated ten times, each time giving a different 10% as a testing portion. The classifier's performance is quite good, on the synthetic noise-free data, in predicting the magnitude, elevation angle, and hypocentral distance, but not the azimuthal angle. The trained model in the present work can be readily used where noise levels are quite low without sophisticated ray-tracing or Green's function computation. The performance of the algorithm is checked by adding additive noise to the data. The novelty of this work is that knowledge of the velocity model is not required, and the estimation of magnitude and the origin of the earthquake are done using the single-station/single-component earthquake records.