Conventional Reverse Time Migration Research Articles

Elastic reverse time migration using acoustic propagators

Elastic wave imaging has been a significant challenge in the exploration industry due to the complexities in wave physics and numerical implementation. We have separated the governing equations for P- and S-wave propagation without the assumptions of homogeneous Lamé parameters to capture the mode conversion between the two body waves in an isotropic, constant-density medium. The resulting set of two coupled second-order equations for P- and S-potentials clearly demonstrates that mode conversion only occurs at the discontinuities of the shear modulus. Applying the Born approximation to the new equations, we derive the PP, PS, SP, and SS imaging conditions from the first gradients of waveform matching objective functions. The resulting images are consistent with the physical perturbations of the elastic parameters, and, hence, they are automatically free of the polarity reversal artifacts in the converted images. When implementing elastic reverse time migration (RTM), we find that scalar wave equations can be used to back propagate the recorded P-potential, as well as individual components in the vector field of the S-potential. Compared with conventional elastic RTM, the proposed elastic RTM implementation using acoustic propagators not only simplifies the imaging condition, it but also reduces the computational cost and the artifacts in the images. We have determined the accuracy of our method using 2D and 3D numerical examples.

Frequency-Domain Reverse-Time Migration of Ground Penetrating Radar Based on Layered Medium Green's Functions

A frequency-domain reverse-time migration (RTM) algorithm based on the layered medium dyadic Green's function (DGF) is proposed for high-resolution and efficient subsurface imaging using ground penetrating radar (GPR). Different from the conventional RTM, which is performed by the finite-difference time domain (FDTD) method, both the forward and backward extrapolation wavefields in this frequency-domain RTM are computed by the multiplication between the frequency spectra of the excitation source or the recorded GPR data and the layered medium DGFs. The final image is reconstructed by the direct summation of all the wavefields for all the sampling frequencies in the frequency domain, instead of transforming them back to the time domain and processing them. Two-dimensional (2-D) or 3-D numerical and laboratory experiments show that the proposed frequency-domain RTM algorithm can yield almost the same imaging results as the conventional time domain RTM algorithm but requires less than two orders of magnitude in computational costs. The proposed GPR imaging method is verified to be competent for the fast 3-D imaging of potential larva rocks under the lunar surface, which can provide critical information for the regolith-drilling task of the Chang-E 5 lunar exploration mission of China. Real-time subsurface imaging by RTM could be fulfilled and be widely applied to engineering geophysics, such as urban utility detection, through-wall imaging, and ice monitoring by ground-coupled or air-borne GPR.

One-step data-domain least-squares reverse time migration

Least-squares reverse time migration (LSRTM) is an iterative inversion algorithm for estimating the broadband-wavenumber reflectivity model. Although it produces superior results compared with conventional reverse time migration (RTM), LSRTM is computationally expensive. We have developed a one-step LSRTM method by considering the demigrated and observed data to design a deblurring preconditioner in the data domain using the Wiener filter. For the Wiener filtering, we further use a stabilized division algorithm via the Taylor expansion. The preconditioned observed data are then remigrated to obtain a deblurred image. The total cost of this method is about two RTMs. Through synthetic and real data experiments, we see that one-step LSRTM is able to enhance image resolution and balance source illumination at low computational costs.

Reverse-time migration using multidirectional wavefield decomposition method

Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typically used in conventional reverse-time migration that produces images with strong low-frequency noise. Wavefield decomposition imaging can suppress such noise; however, some residual noise persists in the imaging results. We propose a 2D multidirectional wavefield decomposition method based on the traditional wavefield decomposition method. First, source wavefields and receiver wavefields are separated into eight subwavefields, respectively. Second, cross-correlation imaging is applied to selected subwavefields to produce subimages. Finally, the subimages are stacked to generate the final image. Numerical examples suggest that the proposed method can eliminate the low-frequency noise effectively and produce high-quality imaging profiles.

Microseismic reverse time migration with a multi-cross-correlation staining algorithm for fracture imaging

Accurate characterization of hydraulic fracturing zones is currently becoming increasingly important in production optimization, since hydraulic fracturing may increase the porosity and permeability of the reservoir significantly. Recently, the feasibility of the reverse time migration (RTM) method has been studied for the application in imaging fractures during borehole microseismic monitoring. However, strong low-frequency migration noise, poorly illuminated areas, and the low signal to noise ratio (SNR) data can degrade the imaging results. To improve the quality of the images, we propose a multi-cross-correlation staining algorithm to incorporate into the microseismic reverse time migration for imaging fractures using scattered data. Under the modified RTM method, our results are revealed in two images: one is the improved RTM image using the multi-cross-correlation condition, and the other is an image of the target region using the generalized staining algorithm. The numerical examples show that, compared with the conventional RTM, our method can significantly improve the spatial resolution of images, especially for the image of target region.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

A memory-efficient staining algorithm in 3D seismic modelling and imaging

The staining algorithm has been proven to generate high signal-to-noise ratio (S/N) images in poorly illuminated areas in two-dimensional cases. In the staining algorithm, the stained wavefield relevant to the target area and the regular source wavefield forward propagate synchronously. Cross-correlating these two wavefields with the backward propagated receiver wavefield separately, we obtain two images: the local image of the target area and the conventional reverse time migration (RTM) image. This imaging process costs massive computer memory for wavefield storage, especially in large scale three-dimensional cases. To make the staining algorithm applicable to three-dimensional RTM, we develop a method to implement the staining algorithm in three-dimensional acoustic modelling in a standard staggered grid finite difference (FD) scheme. The implementation is adaptive to the order of spatial accuracy of the FD operator. The method can be applied to elastic, electromagnetic, and other wave equations. Taking the memory requirement into account, we adopt a random boundary condition (RBC) to backward extrapolate the receiver wavefield and reconstruct it by reverse propagation using the final wavefield snapshot only. Meanwhile, we forward simulate the stained wavefield and source wavefield simultaneously using the nearly perfectly matched layer (NPML) boundary condition. Experiments on a complex geologic model indicate that the RBC-NPML collaborative strategy not only minimizes the memory consumption but also guarantees high quality imaging results. We apply the staining algorithm to three-dimensional RTM via the proposed strategy. Numerical results show that our staining algorithm can produce high S/N images in the target areas with other structures effectively muted.

First-Order Acoustic Wave Equation Reverse Time Migration Based on the Dual-Sensor Seismic Acquisition System

We analyze the mathematical requirements for conventional reverse time migration (RTM) and summarize their rationale. The known information provided by current acquisition system is inadequate for the second-order acoustic wave equations. Therefore, we introduce a dual-sensor seismic acquisition system into the coupled first-order acoustic wave equations. We propose a new dual-sensor reverse time migration called dual-sensor RTM, which includes two input variables, the pressure and vertical particle velocity data. We focus on the performance of dual-sensor RTM in estimating reflection coefficients compared with conventional RTM. Synthetic examples are used for the study of estimating coefficients of reflectors with both dual-sensor RTM and conventional RTM. The results indicate that dual-sensor RTM with two inputs calculates amplitude information more accurately and images structural positions of complex substructures, such as the Marmousi model, more clearly than that of conventional RTM. This shows that the dual-sensor RTM has better accuracy in backpropagation and carries more information in the directivity because of particle velocity injection. Through a simple point-shape model, we demonstrate that dual-sensor RTM decreases the effect of multi-pathing of propagating waves, which is helpful for focusing the energy. In addition, compared to conventional RTM, dual-sensor RTM does not cause extra memory costs. Dual-sensor RTM is, therefore, promising for the computation of multi-component seismic data.

Acoustic-elastic coupled equation for ocean bottom seismic data elastic reverse time migration

Conventionally, multicomponent geophones used to record the elastic wavefields in the solid seabed are necessary for ocean bottom seismic (OBS) data elastic reverse time migration (RTM). Particle velocity components are usually injected directly as boundary conditions in the elastic-wave equation in the receiver-side wavefield extrapolation step, which causes artifacts in the resulting elastic images. We have deduced a first-order acoustic-elastic coupled equation (AECE) by substituting pressure fields into the elastic velocity-stress equation (EVSE). AECE has three advantages for OBS data over EVSE when performing elastic RTM. First, the new equation unifies wave propagation in acoustic and elastic media. Second, the new equation separates P-waves directly during wavefield propagation. Third, three approaches are identified when using the receiver-side multicomponent particle velocity records and pressure records in elastic RTM processing: (1) particle velocity components are set as boundary conditions in receiver-side vectorial extrapolation with the AECE, which is equal to the elastic RTM using the conventional EVSE; (2) the pressure component may also be used for receiver-side scalar extrapolation with the AECE, and with which we can accomplish PP and PS images using only the pressure records and suppress most of the artifacts in the PP image with vectorial extrapolation; and (3) ocean-bottom 4C data can be simultaneously used for elastic images with receiver-side tensorial extrapolation using the AECE. Thus, the AECE may be used for conventional elastic RTM, but it also offers the flexibility to obtain PP and PS images using only pressure records.

Least-squares RTM with L1 norm regularisation

Reverse time migration (RTM), for imaging complex Earth models, is a reversal procedure of the forward modelling of seismic wavefields, and hence can be formulated as an inverse problem. The least-squares RTM method attempts to minimise the difference between the observed field data and the synthetic data generated by the migration image. It can reduce the artefacts in the images of a conventional RTM which uses an adjoint operator, instead of an inverse operator, for the migration. However, as the least-squares inversion provides an average solution with minimal variation, the resolution of the reflectivity image is compromised. This paper presents the least-squares RTM method with a model constraint defined by an L1-norm of the reflectivity image. For solving the least-squares RTM with L1 norm regularisation, the inversion is reformulated as a 'basis pursuit de-noise (BPDN)' problem, and is solved directly using an algorithm called 'spectral projected gradient for L1 minimisation (SPGL1)'. Three numerical examples demonstrate the effectiveness of the method which can mitigate artefacts and produce clean images with significantly higher resolution than the least-squares RTM without such a constraint.

Efficient amplitude encoding least‐squares reverse time migration using cosine basis

ABSTRACTLeast‐squares reverse time migration provides better imaging result than conventional reverse time migration by reducing the migration artefacts, improving the resolution of the image and balancing the amplitudes of the reflectors. However, it is computationally intensive. To reduce its computational cost, we propose an efficient amplitude encoding least‐squares reverse time migration scheme in the time domain. Although the encoding scheme is effective in increasing the computational efficiency, it also introduces the well‐known crosstalk noise in the gradient that degrades the quality of the imaging result. We analyse the cause of the crosstalk noise using an encoding correlation matrix and then develop two numerical schemes to suppress the crosstalk noise during the inversion process. We test the proposed method with synthetic and field data. Numerical examples show that the proposed scheme can provide better imaging result than reverse time migration, and it also generates images comparable with those from common shot least‐squares reverse time migration but with less computational cost.

Removing false images in reverse time migration: The concept of de-primary

Primary reflections, like multiples, can generate false images when reverse time migration (RTM) algorithms are used. The false images are formed by the zero-lag correlation of the source wavefields and primary reflections, which are propagated by the migration algorithm along nonphysical paths. These paths are generated by strong velocity gradients or reflection interfaces when the two-way wave equation is used. Conceptually, this type of artifact can be removed by separating up- and downgoing waves, but such separation may be impractical because it often requires storing the entire wavefields at all time steps. We have developed a de-primary RTM method in which such separation can be accomplished without saving the wavefields. The computational cost of the proposed method was only approximately 33% higher than that of conventional RTM algorithms. Using field and synthetic data sets, we have demonstrated the existence of this endemic RTM problem and verified the effectiveness of the de-primary RTM technique for removing the false events.

Least-squares reverse-time migration for reflectivity imaging

A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zero-phase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration.

An illustration of adaptive Marchenko imaging

In Marchenko imaging, wavefields are retrieved at specified focal points in the subsurface through an iterative scheme derived from the multidimensional Marchenko equation. The method requires seismic-reflection data at the earth's surface (after free-surface multiple elimination) and an estimate of the direct wavefield from the surface to each focal point, which can be computed, for instance, in a macrovelocity model. In the first iteration, the direct wavefield is crosscorrelated with the reflection data. This operation is identical to inverse-wavefield extrapolation as is applied commonly in various imaging schemes, for instance, in reverse time migration (RTM). At each succeeding iteration, the result of the previous iteration is truncated in time and crosscorrelated with the reflection data again. To obtain a seismic image, a multidimensional deconvolution-based imaging condition can be applied to the retrieved wavefields. By this approach, both primary reflections and internal multiples contribute to the construction of the image. Alternatively, a crosscorrelation-based imaging condition can be used in which only the primary reflections are imaged and the contributions of internal multiples are subtracted. The latter strategy offers more flexibility because the subtraction of redatumed internal multiples can be implemented adaptively. Through this approach, the artifacts from internal multiples can be removed effectively from a conventional RTM image.

Compensating for source and receiver ghost effects in full waveform inversion and reverse time migration for marine streamer data

In conventional marine seismic surveys, due to the time-delayed reflections from the sea surface on both source and receiver sides, ghosts present in recorded seismograms and lead to both phase and spectrum distortions (especially near certain frequency notches). To achieve a high-quality broad-band image/velocity model with conventional reverse time migration (RTM)/full waveform inversion (FWI) that adopts a synthetic zero-phase source wavelet and absorbing surface condition during wavefield modelling, marine seismic data have to be pre-processed to remove ghost effects. However, seismic deghosting is not a trivial task. Instead of employing an external deghosting process, we propose a strategy to compensate for ghost effects during FWI and RTM, which consists of two parts: first, to address phase distortions due to ghost effects by means of obtaining an accurate source wavelet estimation and adopting an appropriate surface boundary condition in both forward and backward wave propagation to appropriately generate ghosts; secondly, to build a compensation operator in the adjoint state computation to mitigate spectrum distortions caused by dominant ghost effects. To demonstrate the success and robustness of the proposed strategy, we present both synthetic experiments and field examples, which suggest that this strategy can lead to successful applications of FWI/RTM directly on marine seismic data without an extra deghosting process.

Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as [Formula: see text]-LSRTM. During the least-squares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that [Formula: see text]-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of [Formula: see text]-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and [Formula: see text] errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

Migration of multiples from the South China Sea

The South China Sea where water depth is up to 5000 m is the most promising oil and gas exploration area in China in the future. The seismic data acquired in the South China Sea contain various types of multiples that need to be removed before imaging can be developed. However, compared with the conventional reflection migration, multiples carry more information of the underground structure that helps provide better subsurface imaging. This paper presents a method to modify the conventional reverse time migration so that multiple reflections can migrate to their correct locations in the subsurface. This approach replaces the numerical impulsive source with the recorded data including primaries and multiples on the surface, and replaces the recorded primary reflection data with multiples. In the reverse time migration process, multiples recorded on the surface are extrapolated backward in time to each depth level, while primaries and multiples recorded on the surface are extrapolated forward in time to the same depth levels. By matching the difference between the primary and multiple images using an objective function, this algorithm improves the primary resultant image. Synthetic tests on Sigsbee2B show that the proposed method can obtain a greater range and better underground illumination. Images of deep water in the South China Sea are obtained using multiples and their matching with primaries. They demonstrate that multiples can make up for the reflection illumination and the migration of multiples is an important research direction in the future.

Least-squares reverse-time migration with a wavefield-separation imaging condition and updated source wavefields

Directly imaging steeply dipping fault zones is difficult for conventional migration, including reverse-time migration (RTM). We developed a new least-squares RTM (LSRTM) method to directly image steeply dipping fault zones. The method uses a wavefield-separation imaging condition and updated source wavefields during each iteration. Our new imaging method produces horizontal-looking images that show mostly steeply dipping fault zones. Conventional least-squares RTM does not update source wavefields and cannot directly image vertical fault zones. We numerically determined that it is crucial to update source wavefields to image steeply dipping fault zones. Using synthetic seismic data, we proved that our new LSRTM method can directly image steeply dipping fault zones with dipping angles up to 90°. Compared with conventional LSRTM, our LSRTM method was less sensitive to the smoothness and the velocity error of the initial migration velocity model.

Reducing the computer memory requirement for 3D reverse-time migration with a boundary-wavefield extrapolation method

Reverse-time migration (RTM) using the crosscorrelation imaging condition requires that the forward-propagated source wavefield and the backward-propagated receiver wavefield be accessible within the imaging domain at the same time step. There are two categories of methods to balance the computer memory requirement and the computational complexity of RTM: checkpointing methods and source-wavefield reconstruction methods. We have developed a new source-wavefield reconstruction method to improve the balance between the computer memory requirement and the computational complexity of RTM. During the forward simulation of the source wavefield, we stored boundary wavefields only at one or two layers of spatial grid points and reconstructed the back-propagated source wavefield at the same time step as that of the back-propagated receiver wavefield, using a high-order wave-equation extrapolation scheme. One conventional RTM method uses boundary wavefields stored at multiple layers of spatial grid points and a high-order finite-difference (FD) scheme to reconstruct the back-propagated source wavefield. For an FD scheme with the eighth or sixteenth order of accuracy in space, our new method used only 37.5% of the computer memory required by this conventional method to store the boundary wavefields. This reduction of computer memory usage is significant because storing the boundary wavefields consumes most of the computer memory required for 3D migration using reconstructed source wavefields. Moreover, our method maintained the spatial order of accuracy of the FD scheme for the entire imaging domain, whereas some conventional methods reduce the spatial-order accuracy of the FD scheme near the boundaries to back-propagate the source wavefield to decrease the computer memory requirement. We validated our method using synthetic seismic data. Our method produced 2D and 3D migration images of complex subsurface structures as accurate as those yielded using an RTM method without reducing the spatial order of accuracy near the boundaries.

Staining algorithm for seismic modeling and migration

In seismic migration, some structures such as those in subsalt shadow zones are not imaged well. The signal in these areas may be even weaker than the artifacts elsewhere. We evaluated a method to significantly improve the signal-to-noise ratio (S/N) in poorly illuminated areas of the model. We constructed a “phantom” wavefield: an extension of the wavefield to the complex domain. The imaginary wavefield was synchronized with the real wavefield, but it contained only the events relevant to a target region of the model, which was specified using a staining algorithm. The real wavefield interacted with the entire model. However, all structures except for the target were transparent to the imaginary wavefield, which is excited only when the real wavefront arrives at the target structure. The real and the imaginary source wavefields were crosscorrelated with the regular receiver wavefield. The results were revealed in two images: the conventional reverse time migration image and an image of the target region only. Synthetic experiments showed that the S/N of the target structures was improved significantly, with other structures effectively muted.