One-way Wave Equation Migration Research Articles

Wavefield separation using irreversible-migration filtering

Wavefield separation is important for eliminating unwanted components of seismic data while retaining preferred components therein; however, there have been difficulties with using traditional methods to select a proper muting window in the transformed domain. A narrow muting window can separate different components well, but it causes visible artifacts due to sudden truncations (e.g., the Gibbs phenomenon), whereas a wide muting window would, on the other hand, leave unwanted components. We have adopted separating the wavefield based on its irreversibility after migration and demigration. One-way wave-equation migration would automatically damp high-slope components in the evanescent region while accurately handling the other components. Thus, the migration velocity can be tuned to naturally trap a given range of high-slope components into the evanescent region in the migrated domain, which would be irreversible after demigration. In contrast, the other components (i.e., those outside the evanescent region) can be recovered after demigration. Our method achieves perfect muting by taking advantage of migration and demigration, and thus it avoids the manual operation of setting a muting window. As a result, our method is free of muting artifacts. We conduct numerical experiments with synthetic and field data, and the results verify the excellent performance of our method for several different kinds of wavefield separation, including linear event separation, structural noise elimination, diffraction-reflection separation, and vertical seismic profile wavefield separation. Our method integrates noise reduction and the wavefield separation, and thus it can reduce the computational cost of using different data processing schemes and avoid the related potential error accumulation.

Extending subsurface imaging beyond ocean-bottom node coverage using multiples: A case study in deepwater Nigeria

We have evaluated the results of a receiver decimation study in a deepwater context using separated wavefield imaging (SWIM) algorithms to provide extended illumination for imaging without ocean-bottom node (OBN) positioning constraints. We carried out subsurface imaging using the SWIM imaging technique with a reduced OBN layout, and we compared the results with those from conventional one-way wave-equation migration. We found from the results that the SWIM algorithm makes it possible to reduce the OBN layout while obtaining a similar subsurface image with the same shot geometry, which allows a reduced receiver acquisition effort, offers more geometry flexibility without affecting the image quality, with a potentially significant reduction of acquisition cost and 4D processing turnaround time.

A multi-level parallel algorithm for seismic imaging based on one-way wave equation migration

This article presents a parallel algorithm for seismic imaging based on depth wavefield extrapolation (the solution of a one-way wave equation [OWE]) employing the pseudospectral method. The algorithm is essentially oriented on common-offset vector (COV) gathers seismic migration based on an OWE, includes several parallelism levels, and utilizes message passing interface (MPI), Nested OpenMP, and CUDA technologies. The uppermost level of parallelism involves data splitting to ensure that each dataset can be processed independently to construct parts of the COV images. The algorithm is embarrassingly parallel at this level. Next, each independent run processes several datasets to compute COV images. Each MPI process computes all COV images for a single dataset, then MPI processes exchange data to build up a single COV image for all datasets at a single node. Computation of the COV image at a node requires OpenMP parallelization so that one thread governs the GPU-based calculations and facilitates the construction of images within a thick slab. All other threads perform image interpolation within the slab. Finally, CUDA technology is used for the most computationally intense part of the algorithm—wavefield extrapolation. Such a complex algorithm structure makes it possible to process all COV images for full-azimuth seismic data employing OWE-based migration.

Amplitude-Preserved Wave Equation: An Example to Image the Gas Hydrate System

Natural gas hydrate is an important energy source. Therefore, it is extremely important to provide a clear imaging profile to determine its distribution for energy exploration. In view of the problems existing in conventional migration methods, e.g., the limited imaging angles, we proposed to utilize an amplitude-preserved one-way wave equation migration based on matrix decomposition to deal with primary and multiple waves. With respect to seismic data gathered at the Chilean continental margin, a conventional processing flow to obtain seismic records with a high signal-to-noise ratio is introduced. Then, the imaging results of the conventional and amplitude-preserved one-way wave equation migration methods based on primary waves are compared, to demonstrate the necessity of implementing amplitude-preserving migration. Moreover, a simple two-layer model is imaged by using primary and multiple waves, which proves the superiority of multiple waves in imaging compared with primary waves and lays the foundation for further application. For the real data, the imaging sections of primary and multiple waves are compared. We found that multiple waves are able to provide a wider imaging illumination while primary waves fail to illuminate, especially for the imaging of bottom simulating reflections (BSRs), because multiple waves have a longer travelling path and carry more information. By imaging the actual seismic data, we can make a conclusion that the imaging result generated by multiple waves can be viewed as a supplementary for the imaging result of primary waves, and it has some guiding values for further hydrate and in general shallow gas exploration.

Mesh-free radial-basis-function-generated finite differences and their application in reverse time migration

Compared with one-way wave equation migration and ray-based migration, reverse time migration (RTM) using two-way wave propagation information can produce accurate imaging results for complex structures. Its computational accuracy and efficiency are mainly determined by numerical methods for wavefield simulation. When using traditional regular grids for seismic modeling, scattering artifacts may occur due to the stepped approximation of layer interfaces and rugged topography. On the other hand, irregular grids require a complex grid generation algorithm, despite having certain geometric flexibility. Mesh-free RTM can effectively reduce the scattered noise under regular grids and avoid the extra computation in the process of irregular grid generation. For implementation of the mesh-free RTM method, an algorithm with fast generation of node distributions is used to discretize the underground velocity model, and radial-basis-function-generated finite difference is used to realize the numerical simulation of wave propagation; the crosscorrelation imaging condition is adopted for imaging. The mesh-free RTM method, which has the flexibility of the simulation region and an abundance of wavefield information, reduces the storage required for RTM, shows the potential of high-accuracy migration in the case of an undulating surface, and provides more accurate migration imaging results for oil and gas exploration under complex geologic conditions.

3D Prestack Fourier Mixed-Domain (FMD) depth migration for VTI media with large lateral contrasts

Although many 3D One-Way Wave-equation Migration (OWEM) methods exist for VTI media, most of them struggle either with the stability, the anisotropic noise or the computational cost. In this paper we present a new method based on a mixed space- and wavenumber-propagator that overcome these issues very effectively as demonstrated by the examples. The pioneering methods of phase-shift (PS) and Stolt migration in the frequency-wavenumber domain designed for laterally homogeneous media have been followed by several extensions for laterally inhomogeneous media. Referred many times to as phase-screen or generalized phase-screen methods, such extensions include as main examples of the Split-step Fourier (SSF) and the phase-shift plus interpolation (PSPI). To further refine such phase-screen techniques, we introduce a higher-order extension to SSF valid for a 3D VTI medium with large lateral contrasts in vertical velocity and anisotropy parameters. The method is denoted Fourier Mixed-Domain (FMD) prestack depth migration and can be regarded as a stable explicit algorithm. The FMD technique was tested using the 3D SEG/EAGE salt model and the 2D anisotropic Hess model with good results. Finally, FMD was applied with success to a 3D field data set from the Barents Sea including anisotropy.

A Comparison of the Classical OWWE Migration Methods: Analysis of Feasibility in Subsalt Plays Exploration

Subsalt seismic imaging is particularly difficult due to the complex overburdens, caused by the movement of salt that usually results in steeply dipping structures, which along with strong lateral velocity contrast at the sedimentssalt interface distort the structural position and the stratigraphic resolution of the subsalt reservoirs. Despite it was proven that two-way wave equation migration provides the best results illuminating these reservoirs, it has huge computational cost, especially in three dimensions. One-way wave equation (OWWE) migration techniques are good alternative in this case as providing the acceptable quality of seismic sections with an appropriate computational cost. To know the advantages and limitations of the OWWE techniques in subsalt imaging, three classical OWWE algorithms were evaluated for depth migration of prestack data (PSDM): phase-shift-plus-interpolation (PSPI), splitstep Fourier (SSF), and Fourier finite-difference (FFD). These algorithms were tested with three different fully elastic synthetic models which simulates the structural complexity showed in subsalt plays. It was concluded that FFD gives very accurate results when the lateral velocity variation was strong with acceptable computational cost. The PSPI provided the best quality results but required about twice the computer time needed for FFD, and SSF was the fastest but clearly the least accurate.

Fast plane-wave reverse time migration

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.

Parallel GPU-based Implementation of One-Way Wave Equation Migration

We present an original algorithm for seismic imaging, based on the depth wavefield extrapolation by the one-way wave equation. Parallel implementation of the algorithm is based on the several levels of parallelism. The input data parallelism allows processing full coverage for some area (up to one square km); thus, data are divided into several subsets and each subset is processed by a single MPI process. The mathematical approach allows dealing with each frequency independently and treating solution layer-by-layer; thus, a set of 2D cross-sections instead of the initial 3D common-offset vector gathers are processed simultaneously. This part of the algorithm is implemented suing GPU. Next, each common-offset vector image can be stacked, processed and stored independently. As a result, we designed and implemented the parallel algorithm based on the use of CPU-GPU architecture which allows computing common-offset vector images using one-way wave equation-based amplitude preserving migration. The algorithm was used to compute seismic images from real seismic land data.

Q-model building using one-way wave-equation migration Q analysis — Part 1: Theory and synthetic test

The goal of this study is to understand and quantify the attenuation effects in the subsurface and to create an accurate laterally and vertically varying quality factor [Formula: see text] model for gas clouds/pockets. Such [Formula: see text] models are used in seismic migration to improve image quality. We evaluate an inversion-based method, wave-equation migration [Formula: see text] analysis, with two major features. First, this method is performed in the image space to reduce noise, focus events, and provide a direct link between [Formula: see text] model perturbations and image perturbations. Second, this method uses wave-equation-based [Formula: see text] tomography to handle the complex wave propagation. We apply this method to three 2D synthetic examples. The numerical synthetic tests of this [Formula: see text] estimation method demonstrate its feasibility on characterizing [Formula: see text] anomalies and, as a consequence, improving the seismic image.

Tomographic velocity analysis and wave-equation depth migration in an overthrust terrain: A case study from the Tuha Basin, China

Although the structures associated with overthrust terrains form important targets in many basins, accurately imaging remains challenging. Steep dips and strong lateral velocity variations associated with these complex structures require prestack depth migration instead of simpler time migration. The associated rough topography, coupled with older, more indurated, and thus high-velocity rocks near or outcropping at the surface often lead to seismic data that suffer from severe statics problems, strong head waves, and backscattered energy from the shallow section, giving rise to a low signal-to-noise ratio that increases the difficulties in building an accurate velocity model for subsequent depth migration. We applied a multidomain cascaded noise attenuation workflow to suppress much of the linear noise. Strong lateral velocity variations occur not only at depth but near the surface as well, distorting the reflections and degrading all deeper images. Conventional elevation corrections followed by refraction statics methods fail in these areas due to poor data quality and the absence of a continuous refracting surface. Although a seismically derived tomographic solution provides an improved image, constraining the solution to the near-surface depth-domain interval velocities measured along the surface outcrop data provides further improvement. Although a one-way wave-equation migration algorithm accounts for the strong lateral velocity variations and complicated structures at depth, modifying the algorithm to account for lateral variation in illumination caused by the irregular topography significantly improves the image, preserving the subsurface amplitude variations. We believe that our step-by-step workflow of addressing the data quality, velocity model building, and seismic imaging developed for the Tuha Basin of China can be applied to other overthrust plays in other parts of the world.

One-way wave-equation migration of multiples based on stereographic imaging condition

Multiples are usually regarded as noise in conventional seismic data processing. However, multiples are also real reflections from structural interfaces in the subsurface. Compared with primaries, multiples usually provide more balanced illumination and contain more structural information because of the smaller reflection angles and longer wavepaths. Instead of multiple suppression, multiple imaging has attracted increasingly more attention in recent years. The most commonly used migration method for multiples is performed by replacing the source wavelet with recorded data and using separated multiples as the receiver record. Then, the image of the multiples is obtained by the application of the crosscorrelation imaging condition, which is widely used in conventional migration. However, during the imaging procedure, events are matched based on their propagation times only. Crosscorrelation of unrelated events leads to heavy crosstalk, and image artifacts are introduced in the image of multiples. To overcome this shortcoming, we have introduced the stereographic imaging condition for the one-way wave-equation migration of multiples. By adding a local-slope constraint (the local slope of the extrapolated wavefields at every position and time), the stereographic imaging condition takes the local spatial coherence of the extrapolated wavefields into account. Events can be matched based not only on the propagating times but also the local slopes. Therefore, crosstalk artifacts caused by the interference of unrelated events can be efficiently suppressed. Furthermore, to improve the computational accuracy and efficiency of our approach, plane-wave destructors are introduced to estimate the reflector slopes. In this way, the need for excessive loops over the local slopes in the [Formula: see text]-[Formula: see text] domain during application of the stereographic imaging condition can be avoided by selecting the local slopes in a proper range. Better migration results of multiples are obtained in numerical tests, which verify the feasibility and effectiveness of our approach.

Elastic least-squares one-way wave-equation migration

Least-squares migration seeks a reflectivity model that fits the observed data. It is used to compensate for acquisition noise, poor sampling of sources and receivers on the surface, as well as poor illumination of the subsurface. To date, least-squares migration has been mainly restricted to the imaging of acoustic wavefields. We have developed an extension of one-way wave-equation least-squares migration for elastic wavefields in isotropic media. Least-squares migration is an iterative method that requires a forward and an adjoint operator. In elastic least-squares one-way wave-equation migration, the forward operator generates data components from multiparameter images by recursive wavefield decomposition, extrapolation, and recomposition. Conversely, the adjoint operator generates multiparameter images from data components by recursively applying the adjoint of the wavefield recomposition, extrapolation, and wavefield decomposition operators. We use an extended imaging condition and regularize the inversion by applying a smoothing filter on the depth-angle axes of each common image point gather to reduce the effect of source/receiver sampling, noise, and crosstalk artifacts. Elastic least-squares migration is able to compensate for irregular subsurface illumination in elastic imaging and provides an alternative approach to interpolation and wavefield separation of multicomponent seismic data.

Splitting algorithms for the high-order compact finite-difference schemes in wave-equation modeling

We have developed efficient splitting algorithms for high-order compact finite-difference methods to approximate second-order space derivatives. In general, the methods’ high-order compact finite-difference schemes require the inversion of a multidiagonal matrix that is commonly less efficient. To solve this problem, we used ideas from splitting algorithms in one-way wave-equation migration that work by decomposing the multidiagonal matrix into a series of tridiagonal matrices and then subsequently solving the tridiagonal matrices. This approach results in more efficient algorithms with little loss of accuracy. The splitting algorithms can be implemented in three different ways. Our computational complexity analysis verifies that our methods can reduce the calculation burden from exponential to linear growth. Numerical experiments demonstrate the correctness and effectiveness of our algorithms.

Eliminating artifacts in migration of surface-related multiples: An application to marine data

Migration of multiples can use surface-related multiples to provide extra illumination of the subsurface; however, the migrated images usually contain many migration artifacts. We have developed an efficient workflow to eliminate the artifacts in migration of surface-related multiples and applied it to marine data. Our workflow was based on the criterion that true seismic events in angle-domain common-image gathers (ADCIGs) should be flat. The ADCIGs were obtained via the one-way wave-equation migration and then processed by high-resolution parabolic Radon transform to separate the artifacts. Using the adjoint Radon transform, the filtered ADCIGs can be stacked to get the final image with a high signal-to-noise ratio. We also discovered that the ADCIGs can be extracted from Fourier finite-difference migration more efficiently than by reverse time migration. In the application to marine data, most noise generated by the crosscorrelation of undesired seismic events was suppressed. This shows that the final images can be a valuable complement to conventional migration using primaries only.

Angle gathers from reverse time migration using analytic wavefield propagation and decomposition in the time domain

Angle-domain common imaging gathers (ADCIGs) are important input data for migration velocity analysis and amplitude variation with angle analysis. Compared with Kirchhoff migration and one-way wave equation migration, reverse time migration (RTM) is the most accurate imaging method in complex areas, such as the subsalt area. We have developed a method to generate ADCIGs from RTM using analytic wavefield propagation and decomposition. To estimate the wave-propagation direction and angle by spatial Fourier transform during the time domain wave extrapolation, we have developed an analytic wavefield extrapolation method. Then, we decomposed the extrapolated source and receiver wavefields into their local angle components (i.e., local plane-wave components) and applied the angle-domain imaging condition to form ADCIGs. Because the angle-domain imaging condition is a convolution imaging condition about the source and receiver propagation angles, it is costly. To increase the efficiency of the angle-domain imaging condition, we have developed a local plane-wave decomposition method using matching pursuit. Numerical examples of synthetic and real data found that this method could generate high-quality ADCIGs. And these examples also found that the computational cost of this approach was related to the complexity of the source and receiver wavefields.

Seismic modelling of fault zones

While faults have long been known as primary pathways for fluid migration in sedimentary basins, recent work highlights the importance of fault zone internal architecture, lateral variation, transmissivity, and impact on migration and trapping. The impacts of fault zone architecture and properties on seismic images are investigated to facilitate accurately mapped fault zones, and to predict subseismic flow properties and sealing potential. A wedge-type fault model with a main fault and a synthetic fault displacing a typical North West Shelf siliciclastic succession is used to replicate the geometrical components of a seismic-scale fault. Elastic properties are derived from rock physics models, which are used in a 2D elastic modelling algorithm to produce realistic marine seismic acquisition geometry. These data were subsequently input into a 2D prestack (one-way wave-equation) migration code to produce an interpretable seismic image. Base-case elastic properties are systematically varied; modelling focuses on gouge properties, fractured fault zone material, the sandstone Vp/Vs relationship, and shale-sand velocity contrast. The workflow from geological model building to elastic property substitution and forward seismic modelling is extremely quick and versatile, allowing testing of a wide range of scenarios. So far this approach has yielded valuable insights into internal fault property prediction and interpretation of the fault zone in traditional post-stack seismic datasets. Implications for processing workflow and attenuation of fault shadows are also expected.

Imaging tilted transversely isotropic media with a generalised screen propagator

One-way wave equation migration is computationally efficient compared with reverse time migration, and it provides a better subsurface image than ray-based migration algorithms when imaging complex structures. Among many one-way wave-based migration algorithms, we adopted the generalised screen propagator (GSP) to build the migration algorithm. When the wavefield propagates through the large velocity variation in lateral or steeply dipping structures, GSP increases the accuracy of the wavefield in wide angle by adopting higher-order terms induced from expansion of the vertical slowness in Taylor series with each perturbation term. To apply the migration algorithm to a more realistic geological structure, we considered tilted transversely isotropic (TTI) media. The new GSP, which contains the tilting angle as a symmetric axis of the anisotropic media, was derived by modifying the GSP designed for vertical transversely isotropic (VTI) media. To verify the developed TTI-GSP, we analysed the accuracy of wave propagation, especially for the new perturbation parameters and the tilting angle; the results clearly showed that the perturbation term of the tilting angle in TTI media has considerable effects on proper propagation. In addition, through numerical tests, we demonstrated that the developed TTI-GS migration algorithm could successfully image a steeply dipping salt flank with high velocity variation around anisotropic layers.

An amplitude-preserved adaptive focused beam seismic migration method

Gaussian beam migration (GBM) is an effective and robust depth seismic imaging method, which overcomes the disadvantage of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limitation of one-way wave equation migration. However, its imaging quality depends on the initial beam parameters, which can make the beam width increase and wave-front spread with the propagation of the central ray, resulting in poor migration accuracy at depth, especially for exploration areas with complex geological structures. To address this problem, we present an adaptive focused beam method for shot-domain prestack depth migration. Using the information of the input smooth velocity field, we first derive an adaptive focused parameter, which makes a seismic beam focused along the whole central ray to enhance the wave-field construction accuracy in both the shallow and deep regions. Then we introduce this parameter into the GBM, which not only improves imaging quality of deep reflectors but also makes the shallow small-scale geological structures well-defined. As well, using the amplitude-preserved extrapolation operator and deconvolution imaging condition, the concept of amplitude-preserved imaging has been included in our method. Typical numerical examples and the field data processing results demonstrate the validity and adaptability of our method.

Migration of primaries and multiples using an imaging condition for amplitude-normalized separated wavefields

Migration of primary and multiple reflections leads to enhanced subsurface illumination and to increased image resolution. A joint migration approach using the complete wavefield requires properly imaged primaries and multiples of all orders. In recent works, primaries and multiples have therefore been imaged separately, using the upgoing and downgoing pressure wavefields obtained by decomposing dual-sensor streamer data. The matches between the corresponding depth images are still not found to be sufficiently accurate, so new and more appropriate imaging conditions need to be found. We reviewed the classical imaging approach used in one-way wave-equation migration, with the aim of extending it for simultaneous migration of primaries and all orders of multiples. Based on Rayleigh’s reciprocity theorem and well-known theoretical developments, we derived a new imaging condition described in terms of the upgoing pressure wavefield and a filtered version of the downgoing vertical-velocity wavefield. To evaluate the efficiency of this new imaging approach, primaries and multiples were separately migrated using synthetic and real data examples. These results were compared to those obtained using a conventional imaging condition. We found that the use of the new imaging condition led to a better match between the depth images and spectra of the migrated primaries and migrated multiples.