Elastic reverse time migration angle gathers using a stabilized Poynting vector without zero points within the wave propagation ranges

Vector-based excitation amplitude imaging condition for elastic RTM

In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

Multicomponent joint elastic reverse time migration is one of important parts in multicomponent seismic data processing. We analyse the implementation of elastic reverse time migration and the polarity reversal in PS and SP images. We present a method using Poynting vector to correct the polarity reversal in elastic reverse time migration. The polarity reversal correction using Poynting vector can be done with the imaging conditions at every time step of the elastic RTM. And the whole correction procedure can be carried out in common shot domain rather than angle domain, which is low cost and convenient. Examples show this method can accurately locate the normal incidence point and correct the polarity reversal for both simple and complex models.

Migration is an important step in seismic data processing for oil and gas exploration. The accuracy of migration directly affects the accuracy of subsequent oil and gas reservoir characterization. Reverse-time migration is one of the most accurate migration methods at present. Multi-wave and multicomponent seismic data contain more P- and S-wave information. Making full use of multi-wave and multicomponent seismic data can offer more information about underground structure and lithology, as well as improve the accuracy of seismic exploration. Elastic reverse-time migration (ERTM) has no dip restriction and can be applied to image multi-wave and multicomponent seismic data in complex structural areas and some special lithology structures. However, the surface topography of complex regions has an influence on wavefield and seriously degrades the quality of ERTM’s migration results. We developed a new ERTM method to migrate multi-wave and multicomponent seismic data in the region with complex surface topography. We first fill the layers between the highest and lowest undulating surface with near-surface elastic parameters in a complex topography model to obtain a new model with a horizontal surface. This allows the finite difference (FD) method based on the regular rectangular grid to be used to numerically solve elastic wave equations in the model with complex topography. The decoupled wave equations are used to generate source P- and S-waves and receiver P- and S-waves to reduce crosstalk artefacts in ERTM. A topography-related filter is further used to remove the influence of surface topography on migration results. The scalar imaging condition is also applied to generate PP and PS migration images. Some numerical examples with different complex topographies demonstrate that our proposed ERTM method can remove the influence of complex topography on ERTM’s images and effectively generate high-quality ERTM images.

Elastic reverse time migration (ERTM), which is capable of using multicomponent seismic data, provides not only an improvement of the P-P image compared to the one derived from acoustic RTM, but also more opportunities to understand the subsurface through converted wave images (P-S, S-P, and S-S images). However, the polarity reversals in P-S and S-P images and cross-talk noises generated in S-P and S-S images degrade the converted wave images of ERTM. To overcome these problems, we derive a new P-S converted wave imaging condition for 2D ERTM based on wavefield separation techniques. The proposed imaging condition, called converted-wave guided (CWG) imaging condition, incorporates an extra term that represents the sign and wavelength of S-waves converted from source wavefields into the zero-lag cross-correlation imaging condition for P-S imaging. The extra term compensates for the polarity reversal of separated S-waves from receiver wavefields because the converted S-waves from source wavefields also have the change in polarity. In addition, since this CWG imaging condition produces images where P- and S-waves from source wavefields and S-waves from receiver wavefields coincide, image resolution is enhanced without generating spurious events. Our approach is motivated by the specific feature of ERTM that generates converted waves at the reflection points (conventional imaging points) when proper elastic models are used. Through a numerical experiment with a simple elastic model, we demonstrate that the proposed CWG imaging condition successfully corrects the polarity reversal and provides higher image resolution. We also test our migration algorithm on a synthetic ocean bottom cable (OBC) dataset created using the Marmousi-II model. The P-S image obtained from CWG imaging condition shows continuous events and improved image resolution.

The earth [Formula: see text] filtering causes poor illumination of the subsurface. Compensating for the attenuated amplitude and distorted phase is crucial during elastic reverse time migration (ERTM) to improve the imaging quality. Conventional [Formula: see text]-compensated ERTM ([Formula: see text]-ERTM) methods tend to boost the attenuated energy to inverse the [Formula: see text] effects. These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise. Low-pass filtering is generally used to stabilize the process, however, at the expense of precision. We have developed a stable compensation approach in this paper. Based on the decoupled fractional Laplacians viscoelastic wave equation, two compensation operators are obtained by extrapolating wavefield in the dispersion-only and viscoelastic media. Because no explicit amplification is included, these two operators are absolutely stable for implementation. To improve the division morbidity for calculating the compensation operators, we use the excitation amplitude criterion and embed the operators into a vector-based [Formula: see text]-compensated excitation amplitude imaging condition. With the derived imaging condition, we could compensate for the absorption accurately without needing to concern the stability issue. The [Formula: see text]-ERTM results for noise-free data are carried out over a simple layered model and a more realistic Marmousi model with an attenuating area to verify the feasibility of the proposed approach. The migration results for noisy data from the Marmousi model further prove that the proposed method performs better fidelity, adaptability, and antinoise performance compared with conventional compensation method with low-pass filtering.

Local angle-domain elastic reverse time migration (ERTM) can provide more opportunities for complex structure imaging and elastic parameter inversion. However, its implementation still has many challenges, especially in anisotropic media. We present an accurate local angle-domain ERTM algorithm for heterogeneous TI media on the base of the cross correlation imaging condition and vector decomposition of the elastic wave modes. At the mean time, the computational cost is significantly reduced by applying fast algorithms of wave mode separation and decomposition using low-rank approximation of the mixed-domain operators. Synthetic example shows that, compared with the Helmholtz decomposition, the efficient wave mode separation/decomposition based on polarization projection promotes the quality of angle-domain common-image gathers for TI media.

Elastic reverse-time migration (ERTM) is becoming increasingly feasible with the development of high-performance computing. It can provide more physical information on subsurface structures. However, the crosstalk artifacts degrade the imaging resolution of ERTM. To obtain high-resolution ERTM imaging, we have developed additional constraints through a convolutional neural network (CNN) in the dip-angle domain. This procedure can significantly improve the image quality of ERTM by recognizing the dominant reflection events and rejecting the crosstalk artifacts in the dip-angle domain. This method can be divided into the following three steps. First, we generate the dip-angle gathers of ERTM using Poynting vectors shot by shot. Then, we stack all the dip-angle gathers over all the shots. Finally, we adopt the CNN to predict the dip-angle constraint, which can suppress the crosstalk artifacts and enhance the ERTM image quality. The picking method using CNN is an end-to-end procedure that can perform automatic picking without additional human intervention once the network is well-trained. The numerical examples have verified the potential of our method.

Summary Elastic reverse time migration (ERTM) technique becomes increasingly feasible with the development of highperformance computing. However, the migration artifacts degrade the imaging resolution of ERTM for both isotropic and anisotropic media. To achieve high-resolution seismic imaging, we have introduced a method to compute the dip-angle gathers for anisotropic ERTM. In this way, we can easily recognize the dominant reflection events and migration artifacts in the dip-angle domain.

Non-artifact vector P- and S-wave separation for elastic reverse time migration

P- and S-wave separated elastic reverse time migration for OBC data from fluid-solid coupled media with irregular seabed interfaces

The conventional reverse time migration utilizes regularly sampled computational grids to simulate wave propagation. Selecting the appropriate grid sampling is important for computational accuracy and efficiency. In general, the uniform-size grid cannot represent the complexity of the geology well. The grid may appear sparse in the low-velocity zone, especially in shallow depths where dispersion may occur. Conversely, it may appear excessively dense in the high-velocity zone, such as at greater depths or within a salt body, which results in higher computational memory and time consumption. To overcome these issues, we developed an efficient and accurate adaptive variable grid discretization method that automatically selects the vertical grid size based on the velocity, depth, and dominant frequency of the wavelet in elastic medium. Then we reformulated the elastic equations based on the adaptive variable grid by introducing a mapping relationship. To test the effectiveness, accuracy, and efficiency of the equation, we implemented it to both the forward propagation and migration of elastic wavefield. Synthetic numerical examples demonstrate that our proposed method can achieve elastic wavefield separation and no significant dispersion phenomenon. The multi-component imaging accuracy of reverse time migration is nearly equivalent to the traditional method, while significantly improving computational efficiency and saving storage space.

Angle gathers are important for true-amplitude migration, migration velocity analysis, and angle-dependent inversion. Among existing methods, calculating the [Formula: see text] direction vector is efficient, but it can give only one direction per grid point and fails to give multiple directions for overlapping wavefields associated with multipaths and reflections. The slowness vectors (SVs) in [Formula: see text] and [Formula: see text] can be connected by Fourier transforms (FTs); the forward FT from [Formula: see text] to [Formula: see text] decomposes the wavefields into different vector components, and the inverse FT sums these components into a unique direction. Therefore, the SV has multiple directions in [Formula: see text], but it has only one direction in [Formula: see text]. Based on this relation, we have separated the computation of propagation direction into two steps: First, we used the forward FT, [Formula: see text] binning, and several inverse FTs to separate the wavefields into vector subsets with different approximate propagation angles, which contained much less wave overlapping; then, we computed [Formula: see text] SVs for each separated wavefield, and the set of these single-direction SVs constituted a multidirectional SV (MSV). In this process, the FTs between [Formula: see text] and [Formula: see text] domains required a large input/output (I/O) time. We prove the conjugate relation between the decomposition results using positive- and negative-frequency wavefields, and we use complex-valued modeling to obtain the positive-frequency wavefields. Thus, we did wavefield decomposition in [Formula: see text] instead of [Formula: see text], and avoided the huge I/O caused by the FT between the [Formula: see text] and [Formula: see text] domains. Our tests demonstrated that the MSV can give multiple directions for overlapping wavefields and improve the quality of angle gathers.

It is important to apply certain intrinsic properties (e.g., the wave propagation directions and particle motion information) in reconstructed wavefields in order to solve the image problems exhibited in elastic reverse time migration (RTM). This paper presents a procedure to decompose the source and receiver wavefields into local plane waves as well as to separate them into pure P and S modes. We generate the partial PP and PS images by crosscorrelation of these plane waves along different directions, and then formulate an imaging condition as a product of an angle-domain operator and the partial images. The new angle-domain imaging condition substantially reduces the artifacts in the PP image and produces the PS image with correct polarizations. However, the imaging procedure involves intensive computations. A numerical algorithm, which can greatly reduce the calculation, is proposed to improve the efficiency.

Summary Borehole dipole shear reflection imaging has attracted widespread attention in the evaluation of heterogeneous reservoirs in recent years due to its good performance in reflection amplitude, detecting depth and directivity. However, the conventional migration method based on oneway acoustic equation has been proved to be improper for the wave excited by dipole source in this paper. An elastic wave reverse time migration (RTM) is developed for more exactly imaging of dipole reflected wave to find the location of effective reservoir. The problem of storage in RTM is solved by a boundary storage strategy improved for borehole environment in our research, which has been proved to be very effective by the simulated data. The processing of 2D simulated data of formation models with cave, crack and formation interface indicate the good performance of this migration method. The migration results of the field data with this method agree well with the borehole electric imaging logging data. Furthermore, our researches reveal that the effects of the unknown formation parameters, shielding interface of former reflector, would make the interpretation of the migration image difficult.