Reverse Time Migration Imaging Research Articles

Artifact-free reverse time migration

We have derived an improved reverse time migration (RTM) scheme to image the medium without artifacts arising from internal multiple reflections. This is based on a revised implementation of Marchenko redatuming using a new time-truncation operator. Because of the new truncation operator, we can use the time-reversed version of the standard wavefield-extrapolation operator as initial estimate for retrieving the upgoing focusing function. Then, the retrieved upgoing focusing function can be used to directly image the medium by correlating it with the standard wavefield-extrapolation operator. This imaging scheme can be seen as an artifact-free RTM scheme with two terms. The first term gives the conventional RTM image with the wrong amplitude and artifacts due to internal multiple reflections. The second term gives a correction image that can be used to correct the amplitude and remove artifacts in the image generated by the first term. We evaluated the success of the method with a 2D numerical example.

Full-waveform inversion and least-squares reverse-time migration imaging of collimated ultrasonic-beam data for high-resolution wellbore integrity monitoring

Los Alamos National Laboratory (LANL) has recently developed an ultrasonic side-lobe suppressed Bessel collimated beam transducer for low-frequency imaging through highly attenuating materials. We study the effectiveness of using such a collimated ultrasonic-beam transducer for imaging concrete heterogeneities outside borehole casing for high-resolution borehole imaging and wellbore integrity monitoring. We obtain detailed concrete heterogeneities including a low-velocity zone using ultrasound data acquired with a 3D imaging prototype and our recently developed full-waveform inversion and least-squares reverse-time migration methods. Full-waveform inversion fits synthetic ultrasonic waveforms with recorded waveforms to build a high-resolution velocity model. Least-squares reverse-time migration produces a high-resolution structural image showing material discontinuities. Our results demonstrate that LANL's 3D imaging system with a collimated ultrasonic-beam transducer together with full-waveform inversion and least-squares reverse-time migration imaging has great potential for high-resolution single-well borehole imaging and non-destructive evaluation.

Multi-scale high order finite different reverse time migration imaging

At present, the main difficulties in oil and gas exploration are focused on the exploration of the deep region. How to improve the efficiency of imaging on the same accuracy of migration is an urgent problem. The paper puts forward the concept of multi-scale grid for the underground medium based on finite difference time domain (FDTD) of reverse time migration (RTM), which can avoid the oversampling to high speed and hold the sampling density to low-speed layer. The method can shorten the time of RTM with the same accuracy of the traditional RTM imaging. Firstly, devise the multi-scale grid model according to the velocity model; it uses the small-scale grid for the low-speed area and large-scale grid for high-speed area; secondly, calculate the value of each point of the wave field on multi-scale model, especially the points of transition zone; finally, image the underground media according to the RTM imaging condition. The experimental results show that under the condition of the same simulation order, the multi-scale RTM imaging computational efficiency can be promoted by 25.05% average within this paper.

Reverse time migration using phase crosscorrelation

Additional information regarding the continuity and resolution of selected seismic reflectors in reverse time migration (RTM) images can be beneficial for seismic interpretation. We have developed and evaluated new imaging conditions for RTM based on the phase coherence between the forward- and backward-propagated wavefields. These imaging conditions make use of the instantaneous phase and envelope of the analytical signals of the source and receiver wavefields, in addition to their real parts. Once the analytical wavefields are available, these imaging conditions can be calculated simultaneously with conventional conditions at little or no extra cost. The availability of these fields at each image point enables several alternative ways to define imaging conditions. We explore, in addition to pure phase crosscorrelation (PC), two approaches of amplitude-weighted PC. Our numerical experiments, imaging synthetic and field data sets, indicate that these new imaging conditions provide additional images that can highlight some weak reflectors by locally improving the resolution of RTM images. In our examples, this happens particularly in the deep portions of the seismic images. In addition, reflection events produced at discontinuities are enhanced as sharp signals, suggesting that the proposed imaging conditions can help to delineate stratigraphic and structural features that are harder to see in conventional images. These properties of the PC imaging conditions make them an interesting tool to provide additional information that can aid seismic interpretation in complex structural settings.

Prism waves for imaging steep geologic features and sediment terminations against salt flanks: Examples from the Gulf of Mexico

Subsalt imaging in the Gulf of Mexico often suffers from illumination problems where various steep geologic features are not captured with conventional imaging techniques due to the lack of a direct wave path from the source to the steep reflector and back to the receiver. The exact geometry of these invisible salt flanks or salt welds is of great interest to interpreters during salt model building and prospect mapping. This paper discusses a suite of technologies that uses prism waves for imaging geologic interfaces with reverse time migration (RTM). Prism wave RTM imaging represents an example of imaging with multiples, Due to its specific geometric setup, it is often complementary to traditional RTMs. Specifically, the prism wave reflections can illuminate steep features that are invisible otherwise. Furthermore, by utilizing prism wave RTM in “reverse,” one can specify the steep event as the input prism wave generator (often a well-constrained salt boundary) and obtain an alternative (and perhaps cleaner) image of the sediment geometries next to this input event. In the industry, a lot of resources are spent on trying to improve illumination for the geologic features of interest by acquiring additional seismic surveys. With prism wave imaging, one can instead leverage the seismic signal that has already been recorded. We believe that even with moderate prism wave illumination uplift, the interpretive value gained can be quite large. To give the reader a glimpse of what is possible, we present several real data examples highlighting the utility of prism waves in interpretation.

Anisotropic Reverse-Time Migration of Ground-Penetrating Radar Data Collected on the Sand Dunes in the Badain Jaran Desert

Ground-penetrating radar (GPR) profiling is the primary tool to provide detail information of the internal structure and characteristics inside a sand dune in the desert area. However, with the severe elevation change in a short horizontal distance and on the rugged and complex surface topography of the sand dunes, getting clear imaging of the internal structure of sand dunes from the GPR profiling is still a big challenge. The classic imaging technique such as the Kirchhoff migration has been applied to process GPR data on sand dunes, with limited success. The reverse-time migration (RTM) technique is the most advanced imaging technique that can handles GPR data acquired on rugged surface with severe topographic relief to generate subsurface structural images with high fidelity and has been tried to process GPR data on sand dunes. The results are encouraging, and the imaging quality is significantly improved. The finite-difference time-domain (FDTD) method is the major numerical tool for forward and backward continuations of the wave field during the RTM process. There are two aspects for using FDTD in RTM of GPR data on sand dunes still need improvement: the numerical scattering caused by the staircase approximation of the ground surface by using gridding in the Cartesian coordinate, and the negligence of the possible anisotropy of the electromagnetic material properties due to the calcareous cementation bedding inside a sand dune. In this paper, we develop the RTM algorithm based on the staggered grid FDTD that handles the rugged topographic surface by using the curvilinear coordinate, and the possible anisotropic radar wave velocity of the sand dune media. We first demonstrate the equivalency of the nonuniform, isotropic medium and the uniform, anisotropic medium for justifying using the uniform, anisotropic velocity in the RTM by synthetic modeling. Next, we validate our approach of using the synthetic data with the comparison of using the Cartesian coordinate and the curvilinear coordinate in an isotropic medium. The results indicate that the RTM algorithm using the curvilinear coordinate can efficiently eliminate the adverse effect of the staircase approximated boundary of the topography surface. Finally, we processed the real GPR data collected on a sand dune in the Badain Jaran desert by using the curvilinear coordinate and the uniform, anisotropic velocity in FDTD forward and backward wave field continuation. Comparison of the results indicates that the RTM imaging using the boundary-conforming curvilinear coordinate and anisotropic velocity gains more coherent and higher resolution images for the calcareous cementation layers and the water table.

Effective modeling and reverse-time migration for novel pure acoustic wave in arbitrary orthorhombic anisotropic media

The conventional pseudo-acoustic wave equations (PWEs) in arbitrary orthorhombic anisotropic (OA) media usually have coupled P- and SV-wave modes. These coupled equations may introduce strong SV-wave artifacts and numerical instabilities in P-wave simulation results and reverse-time migration (RTM) profiles. However, pure acoustic wave equations (PAWEs) completely decouple the P-wave component from the full elastic wavefield and naturally solve all the aforementioned problems. In this article, we present a novel PAWE in arbitrary OA media and compare it with the conventional coupled PWEs. Through decomposing the solution of the corresponding eigenvalue equation for the original PWE into an ellipsoidal differential operator (EDO) and an ellipsoidal scalar operator (ESO), the new PAWE in time-space domain is constructed by applying the combination of these two solvable operators and can effectively describe P-wave features in arbitrary OA media. Furthermore, we adopt the optimal finite-difference method (FDM) to solve the newly derived PAWE. In addition, the three-dimensional (3D) hybrid absorbing boundary condition (HABC) with some reasonable modifications is developed for reducing artificial edge reflections in anisotropic media. To improve computational efficiency in 3D case, we adopt graphic processing unit (GPU) with Compute Unified Device Architecture (CUDA) instead of traditional central processing unit (CPU) architecture. Several numerical experiments for arbitrary OA models confirm that the proposed schemes can produce pure, stable and accurate P-wave modeling results and RTM images with higher computational efficiency. Moreover, the 3D numerical simulations can provide us with a comprehensive and real description of wave propagation.

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.

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.

Anisotropic elastic wavefield imaging using the energy norm

Based on the energy conservation principle, we derive a scalar imaging condition for anisotropic elastic wavefield migration. Compared with conventional imaging conditions that correlate displacement components or potentials from source and receiver wavefields, the proposed imaging condition does not suffer from polarity reversal, which degrades the image quality after stacking over shots. Our imaging condition also accounts for the directionality of the wavefields in space and time, leading to the attenuation of backscattering artifacts, which commonly appear in elastic reverse time migration images in the presence of strong model contrasts. In addition, our new imaging condition does not require wave-mode decomposition, which demands significant additional cost for elastic wavefields in anisotropic media. To properly image structures, we rely on the anisotropy parameters used in migration, as one would do for any other imaging condition. Our imaging condition is suitable for arbitrary anisotropy. We show the successful application of the anisotropic energy imaging condition by performing numerical experiments on simple and complex geologic models. We compare its quality with conventional counterparts by simulating complex geologic settings with vertical or tilted transverse isotropy.

Elastic least-squares reverse time migration

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM will produce migration noise stronger than that seen in the RTM images.

Elastic wavefield separation based on the Helmholtz decomposition

Divergence and curl operators used for the decomposition of P- and S-wave modes in elastic reverse time migration (RTM) change the amplitudes, units, and phases of extrapolated wavefields. I separate the P- and S-waves in elastic media based on the Helmholtz decomposition. The decomposed wavefields based on this approach have the same amplitudes, units, and phases as the extrapolated wavefields. To avoid expensive multidimensional integrals in the Helmholtz decomposition, I introduce a fast Poisson solver to efficiently solve the vector Poisson’s equation. This fast algorithm allows us to reduce computational complexity from [Formula: see text] to [Formula: see text], where [Formula: see text] is the total number of grid points. Because the decomposed P- and S-waves are vector fields, I use vector imaging conditions to construct PP-, PS-, SS-, and SP-images. Several 2D numerical examples demonstrate that this approach allows us to accurately and efficiently decompose P- and S-waves in elastic media. In addition, elastic RTM images based on the vector imaging conditions have better quality and avoid polarity reversal in comparison with images based on the divergence and curl separation or direct component-by-component crosscorrelation.

From classical reflectivity-to-velocity inversion to full-waveform inversion using phase-modified and deconvolved reverse time migration images

To obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity update is a phase-modified and deconvolved RTM image obtained with the residual data. Consistent with the deconvolution, the multiscale approach applies a gradually widening low-pass frequency filter to the deconvolved wavelet at early iterations, and then it uses the unfiltered deconvolved wavelet for the final iterations. Our numerical testing determined that the new method makes a significant improvement to the quality of the inversion result.

无人机载探地雷达数据消除地面影响的正反向延拓方法研究

随着全球气候的变化，青藏高原冻土区热融湖塘的大小、形状和冰层厚度在区域内存在明显的变化，热融湖塘的变化与区域内富冰冻土层和气候变化息息相关。高原区热融湖塘分布广，覆盖面大，现有的地面探地雷达技术很难快速准确地监测冰层厚度的变化。机载探地雷达能在复杂的地形区域实现快速、重复监测，但由于强反射地表面产生的多次波的干扰，严重影响冰层厚度的识别。本篇文章基于机载探地雷达数据中普遍存在地表面问题，应用正反向延拓方法压制地表面引起的多次波，消除地表面对地下构造识别的影响。通过比较正反向延拓前后的零偏移距逆时偏移剖面，论证了正反向延拓方法在消除地表面影响方面的优势；应用不同飞行高度的模型分析正反向延拓方法对不同飞行高度机载探地雷达数据的效果。零偏移距逆时偏移成像结果显示，正反向延拓方法能有效地去除地表面的影响，但随着飞行高度的增加，偏移成像的分辨率会降低。模型数据的正演模拟和零偏移距逆时偏移成像分析认为，正反向延拓方法能有效地压制多次波干扰，清晰地反映平界面特征，但对倾斜界面成像较差。延拓计算和飞行高度会影响偏移成像的分辨率，不利于高分辨率探测，还需要进一步改善。 The size, shape, and ice thickness of thermokarst lakes have obviously changed in the Tibetan Plateau permafrost region due to global climate changing. These changes have strong correlation with ice-permafrost and climate changing. Since thermokarst lakes have widely appeared and covered large area in Tibetan Plateau, it’s difficult to quickly monitor the change of ice thickness using ground-penetrating radar (GPR). Unmanned aerial vehicles (UAV) GPR can adapt to the complex area and realize the quickly and more times monitor, however, the ground surface as a strong reflection interface can generate the multiple waves, which will seriously impact on identification of ice thickness. In this paper, the researchers used the forward and reverse continuation method to eliminate the ground surface’s effect based on the widely appeared the ground surface’s effect for the UAV GPR data. Through comparison with the forward continuation and reverse continuation (FCRC) of zero-offset reverse time migration (RTM) and raw zero-offset RTM profile, the researchers demonstrate the FCRC method can eliminate the ground surface’s effect. From the zero-offset RTM profile of different elevation’s model, the researchers analyze the effectiveness of FCRC method for UAV GPR data with different flight altitude. The results of zero-offset RTM imaging show that the FCRC method can effectively eliminate the surface’s effect, however, with the increase of flight altitude, the resolution of migration imaging will decrease. From the result of forward modeling and zero-offset RTM imaging for models data, the researchers consider that the FCRC method can effectively eliminate multiple waves, better reflect the flat interface information, but cannot image the dip interface. The process of FCRC and flight altitude can decrease the UAV GPR resolution which will go against the high resolution detection; we still need make new progress for the process of UAV GPR data.

Analysis of up/down decomposed acoustic reverse time migration images

With the up/down separation of propagating wavefields using complex traces, (forward time extrapolated) source and (reverse time extrapolated) receiver wavefields are decomposed into up- and downgoing parts in acoustic reverse time migration (RTM). Together with the crosscorrelation imaging condition, four images (down-up, up-down, up-up, and down-down) are generated, which facilitate the analysis of artifacts and the imaging ability of the four images. Artifacts may exist in all of the decomposed images, but their positions and types are different. We have explained and illustrated the causes of artifacts in different images with sketches and numerical tests. The up-down image better images subsalt turned waves than does the down-up image; thus, decomposed images have advantages over a single composite image for target interpretation.

Polarized wavefield magnitudes with optical flow for elastic angle-domain common-image gathers

We have developed a polarized wavefield magnitude (PWM) approach to determine the polarity of an elastic vector wavefield magnitude, for elastic prestack reverse time migration imaging and common-image gather generation. Explicit decomposition of the coupled elastic wavefield into separate P-waves and converted S-waves is performed by using decoupled elastodynamic wavefield propagation. Stable source and receiver wavefield propagation angles are determined by an optical flow method for elastic media. The sign ambiguity in the propagation directions for incident P- and reflected P- and S-wavefield vector magnitudes is resolved by establishing a relation between the propagation and particle velocity vectors. From the computed propagation angles, PP- and PS-wavefields are imaged using source-normalized crosscorrelation followed by sorting into common-image gathers. Modeling of amplitude variations with angle (AVA) from single-shot migrations and from elastic angle-domain common-image gathers demonstrates that the amplitude fidelity is maintained. Mode-converted PS reflectivities also give an independent set of accurate AVA information. Numerical results for the elastic Marmousi2 model confirm PWM as a physically valid and robust method for elastic wavefield imaging in arbitrarily complicated media.

Isotropic elastic wavefield imaging using the energy norm

From the elastic-wave equation and the energy conservation principle, we have derived an energy norm that is applicable to imaging with elastic wavefields. Extending the concept of the norm to an inner product enables us to compare two related wavefields. For example, the inner product of source and receiver wavefields at each spatial location leads to an imaging condition. This new imaging condition outputs a single image representing the total reflection energy, and it contains individual terms related to the kinetic and potential energy (strain energy) from both extrapolated wavefields. An advantage of the proposed imaging condition compared with alternatives is that it does not suffer from polarity reversal at normal incidence, as do conventional images obtained using converted waves. Our imaging condition also accounted for the directionality of the wavefields in space and time. Based on this information, we have modified the imaging condition for attenuation of backscattering artifacts in elastic reverse time migration images. We performed numerical experiments that revealed the improved quality of the energy images compared with their conventional counterparts and the effectiveness of the imaging condition in attenuating backscattering artifacts even in media characterized by high spatial variability.

Reverse-Time Migration Based Optical Imaging.

We theoretically demonstrated a new optical imaging technique based on reverse-time migration (RTM) for reconstructing optical structures in homogeneous media for the first time. RTM is a powerful wave-equation-based method to reconstruct the image of the structure by modeling the wave propagation inside the media with both forward modeling and reverse-time extrapolation. While RTM is commonly used with acoustic seismic waves, this paper represents the first effort to develop optical RTM imaging method for biomedical research. To refine the image quality, we further developed new methods to suppress the low-wavenumber artifact (LWA). When compared with the conventional means for LWA suppression such as Laplacian filtering, illumination normalization, and the ratio method, our new derivative-based and power-image methods are able to significantly reduce LWA, resulting in high-quality reconstructed images with sufficient contrasts and spatial resolutions for structure identification. The optical RTM imaging technique may provide a new platform for non-invasive optical imaging of structures in deep layers of tissues for biomedical applications.

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.

Internal multiple prediction and removal using Marchenko autofocusing and seismic interferometry

Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.