Receiver Wavefields Research Articles

Numerical modeling of wind waves affected the marine structures in the Kola Bay

In this study of the evaluation of wave impacts on a gravity base structure (GBS) which is moored to berth No. 5 of the Centre of construction of large-capacity marine structures (CCLMS). It was identified five main wind directions that can be dangerous for the construction of CCLMS: East direction (E) South-East (SE) South direction (S), Southwest (SW), West (W) and Northwest (NW). According to the results of statistical processing of extreme storms of the 30-year period, two most dangerous directions of unrest were chosen-the Eastern direction (B) and the South-Eastern (SE) direction. Using a numerical model ARTEMIS, it was received wave field in the waters CCLMS near GBS reading for different sea levels. The simulation results showed that the wave heights affected the structure can reach 2.4 m.

Higher-order source-wavefield reconstruction for reverse time migration from stored values in a boundary strip just one point wide

One way to deal with the storage problem for the forward source wavefield in reverse time migration and full-waveform inversion is the reconstruction of that wavefield during reverse time stepping along with the receiver wavefield. Apart from the final states of the source wavefield, this requires a strip of boundary values for the whole time range in the presence of absorbing boundaries. The width of the stored boundary strip, positioned in between the interior domain of interest and the absorbing boundary region, usually equals about half that of the finite-difference stencil. The required storage in 3D with high frequencies can still lead to a decrease in computational efficiency, despite the substantial reduction in data volume compared with storing the source wavefields at all or at appropriately subsampled time steps. We have developed a method that requires a boundary strip with a width of just one point and has a negligible loss of accuracy. Stored boundary values over time enable the computation of the second and higher even spatial derivatives normal to the boundary, which together with extrapolation from the interior provides stability and accuracy. Numerical tests show that the use of only the boundary values provides at most fourth-order accuracy for the reconstruction error in the source wavefield. The use of higher even normal derivatives, reconstructed from the stored boundary values, allows for higher orders as numerical examples up to order 26 demonstrate. Subsampling in time is feasible with high-order interpolation and provides even more storage reduction but at a higher computational cost.

Vector-based excitation amplitude imaging condition for elastic RTM

In recent years, many studies have focused on elastic reverse time migration (RTM). In response to the problems associated with elastic RTM, we propose a new procedure for 2D elastic multicomponent RTM. In this new method, decomposed P- and S-wave components are obtained from the decoupled propagation of the source and receiver wavefields, which allows the expedient calculation of the Poynting vectors and the incident and reflection angles of the P- and S-waves. In addition, we deduce the vector-based excitation amplitude imaging condition. This process automatically accounts for the particle vibration directions when determining the angle-dependent signed reflection coefficients, and does not require the sign to be determined apart from the value of the reflection coefficients. This concept was further extended to the source-normalized crosscorrelation imaging condition. The reflection coefficient of the layered model test was in agreement with the Zoeppritz theory, the PP and PS wave images of the Marmousi II model were clear, and the PS wave images had higher resolution and richer details. In addition, since the calculated reflection coefficients are angle-dependent, they can be easily used for the extraction of angle-domain common-image gathers. Moreover, the imaging condition avoids the polarization reversal in PS wave images and does not require all of the source wavefield data. Consequently, the computation and storage requirements are significantly reduced, which will facilitate the use of the elastic RTM in practice.

Converted-wave guided imaging condition for elastic reverse time migration with wavefield separation

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.

ELASTIC REVERSE TIME MIGRATION BASED ON WAVEFIELD SEPARATION

AbstractCompared with other imaging algorithms (e.g., ray‐based, one‐way wave equation), reverse time migration (RTM) based on the two‐way wave equation exhibits greater superiority, especially in handling steeply dipping structures. However, imaging with conventional single‐component seismic data is unsuited for some complicated structures (e.g., gas clouds). Elastic RTM, which is based on the elastodynamic equation and uses multi‐component seismic data to extract PP and PS reflectivity and subsurface information, can more consistently reproduce the characteristics of elastic wave propagation in real Earth media, resulting in seismic images that more accurately characterize the subsurface. To begin with, we exploit the first order stress‐velocity equations to extrapolate the elastic vector wavefield, then the P‐ and S‐wavefields are separated by computing the divergence and curl operator of the extrapolated particle‐velocity wavefield. Then, imaging profiles with pure wave modes are computed by applying the source normalized cross‐correlation imaging condition, thus avoiding crosstalk between unseparated wave modes. To address the polarity reversal problem of the converted image, we propose an alternative method in the common‐shot domain. We also develop an efficient method that reconstructs the source wavefield in the reverse time direction to save storage in the GPU and to avoid large input/output in the elastic reverse time migration. During the forward modeling, the method only saves the particle‐velocity wavefield of all time intervals within an efficient absorbing boundary and the total wavefields in the final time interval. When we extrapolate the receiver wavefield in the reverse time direction, we simultaneously reconstruct the total source wavefields via the saved wavefields. Numerical examples performed with the graben and Marmousi2 models have shown that the polarity reversal correction method works, and elastic reverse time migration can accurately characterize complicated structures.

Combining multidirectional source vector with antitruncation-artifact Fourier transform to calculate angle gathers from reverse time migration in two steps

Because receiver wavefields reconstructed from observed data are not as stable as synthetic source wavefields, the source-propagation vector and the reflector normal have often been used to calculate angle-domain common-image gathers (ADCIGs) from reverse time migration. However, the existing data flows have three main limitations: (1) Calculating the propagation direction only at the wavefields with maximum amplitudes ignores multiarrivals; using the crosscorrelation imaging condition at each time step can include the multiarrivals but will result in backscattering artifacts. (2) Neither amplitude picking nor Poynting-vector calculations are accurate for overlapping wavefields. (3) Calculating the reflector normal in space is not accurate for a structurally complicated reflection image, and calculating it in the wavenumber ([Formula: see text]) domain may give Fourier truncation artifacts. We address these three limitations in an improved data flow with two steps: During imaging, we use a multidirectional Poynting vector (MPV) to calculate the propagation vectors of the source wavefield at each time step and output intermediate source-angle-domain CIGs (SACIGs). After imaging, we use an antitruncation-artifact Fourier transform (ATFT) to convert SACIGs to ADCIGs in the [Formula: see text]-domain. To achieve the new flow, another three innovative aspects are included. In the first step, we develop an angle-tapering scheme to remove the Fourier truncation artifacts during the wave decomposition (of MPV) while preserving the amplitudes, and we use a wavefield decomposition plus angle-filter imaging condition to remove the backscattering artifacts in the SACIGs. In the second step, we compare two algorithms to remove the Fourier truncation artifacts that are caused by the plane-wave assumption. One uses an antileakage FT (ALFT) in local windows; the other uses an antitruncation-artifact FT, which relaxes the plane-wave assumption and thus can be done for the global space. The second algorithm is preferred. Numerical tests indicate that this new flow (source-side MPV plus ATFT) gives high-quality ADCIGs.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition

In the implementation of migration of multiples, reverse time migration (RTM) is superior to other migration algorithms because it can handle steeply dipping structures and offer high-resolution images of the complex subsurface. However, the RTM results using two-way wave equation contain high-amplitude, low-frequency noise and false images generated by improper wave paths in migration velocity model with sharp velocity interfaces or strong velocity gradients. To improve the imaging quality in RTM of multiples, we separate the upgoing and downgoing waves in the propagation of source and receiver wavefields. A complex function involved with the Hilbert transform is used in wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots required by the conventional wavefield separation technique. We applied migration of multiples with wavefield decomposition on a simple two-layer model and the Sigsbee 2B synthetic data set. Our results demonstrate that the proposed approach can improve the image generated by migration of multiples significantly.

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.

Reverse time migration of multiples based on different-order multiple separation

Multiples are traditionally treated as undesired noise, but they are also real reflections from the subsurface as primaries. Smaller reflection angles and longer travel paths usually make them provide more structural information and more balanced illumination than primaries. Instead of multiple elimination in conventional seismic data processing, the migration of multiples has drawn great attention in recent years. The most commonly used method is performed by replacing the source wavelet with the observed data and using separated multiples as the receiver wavefield to apply traditional migration algorithms. However, crosstalk artifacts caused by crosscorrelation of unrelated events severely degrade the image quality of multiples. We have analyzed the cause of artifacts followed by a novel proposal of migrating the multiples by separating surface-related multiples into different orders. First, we combine surface-related multiple elimination and the focal transform to do the separation of multiples in order. Then, crosstalk can be well-eliminated by migrating different-order multiples separately and stacking the separated images together. Taking advantage of reverse time migration, imaging of multiples can be greatly improved. Theoretical analysis shows that crosstalk artifacts can be well-eliminated by our method. Numerical and field data examples determined that our method can provide a greater amount of correct information for subsurface structures.

Reverse time migration angle gathers using Poynting vectors

Angle-domain common-image gathers provide much useful data about the subsurface, such as seismic velocities and amplitude-versus-angle (AVA) information, and they can be manipulated to provide high-quality stacked images. However, the computation of angle gathers for reverse time migration (RTM), the most physically accurate migration algorithm, has proven to be costly in terms of computer time and memory usage. We have developed an algorithm for computing RTM angle gathers in a relatively efficient manner. Our method is based on the construction of the directions of propagation of the source and receiver wavefields, given by the direction of energy flux, known as the Poynting vector. The computation is carried out in the space-time domain, avoiding the need to transform the wavefield to, for example, frequency-wavenumber space, as is needed for methods based on wavefront projection. Given accurate Poynting vectors for source and receiver wavefields, one may compute the local reflection angle and azimuth, as well as the reflector dip and azimuth. An important advantage of our method is that it is based on local direction information at the reflection point, and thus it avoids the loss of resolution and smearing that can occur with some other techniques. A simple implementation of the Poynting-vector method can lead to noisy gathers, with leakage between angle bins, caused by unstable division of the local wavefields. We have developed an efficient technique to mitigate this noise and evaluated examples illustrating the aforementioned smearing issues of the subsurface-offset-based gathers and the improvements in the Poynting-vector gathers arising from our algorithm enhancement. Finally, the use of angle gathers for AVA analysis requires that (relative) amplitudes as a function of angle be correct. To this end, we derive weight functions for computing gathers with the correct AVA behavior. We determine the correctness of these weights by testing them with synthetic data.

Imaging diffractors using wave-equation migration

We have developed a fast and practical wave-equation-based migration method to image subsurface diffractors. The method is composed of three steps in our implementation. First, it decomposes extrapolated receiver wavefields at every imaging point into local plane waves by a linear Radon transform; the transform is realized by a novel computationally efficient recursive algorithm. Second, the decomposed plane waves are zero lag-correlated with the incident source wavefields, where the incident angles are computed via the structure tensor approach. The resulting prestack images are binned into dip-angle gathers according to the directions of the decomposed plane waves and the calculated incident angles. Third, a windowed median filter is applied to the dip-angle gathers to suppress the focused reflection energy, and it produces the desired diffraction images. This method is tested on synthetic and field data. The results demonstrate that it is resistant to random noise, computationally efficient, and applicable to field data in practice. The results also indicate that the diffraction images are able to provide important discontinuous geologic features, such as scattering and faulting zones, and thus are helpful for seismic interpretation.

Comparison of two viscoacoustic propagators for Q-compensated reverse time migration

Without considering intrinsic attenuation, reverse time migration (RTM) of data from lossy media produces smeared migration images because of the [Formula: see text] effects (amplitude loss and velocity dispersion). To mitigate the [Formula: see text] effects during RTM, amplitudes need to be compensated and the propagation velocity of the compensated wavefield needs to be the same as in the attenuating wavefield. We have compared the decoupled constant [Formula: see text] (DCQ) viscoacoustic equation with the viscoacoustic equation based on the generalized standard linear solids (GSLS), for modeling and for [Formula: see text] compensation. The DCQ propagator separates amplitude loss and velocity dispersion operators; for the GSLS propagator, memory variables are used to introduce the [Formula: see text] effects. Amplitude loss and velocity dispersion are decoupled in the DCQ equation, whereas they are coupled in the GSLS equation. Viscoacoustic modeling by the two viscoacoustic propagators produces visually identical seismograms. To compensate for the [Formula: see text] effects, for the DCQ equation, we reverse the sign of the amplitude loss operator and keep the sign of the velocity dispersion operator unchanged. For the GSLS equation, the sign of the memory variables is reversed. Both approaches can compensate for the amplitude loss. Propagation velocities in the attenuating and [Formula: see text]-compensated wavefields are the same for the DCQ equation and are different for the GSLS equation. The [Formula: see text]-compensated wavefield propagates faster than the attenuating wavefield for the GSLS equation. Viscoacoustic RTM is implemented with the source normalized crosscorrelation imaging condition; the source wavefield is attenuated, and [Formula: see text] compensation is applied during receiver wavefield extrapolation. Results of [Formula: see text]-compensated migration on a three-layer model, a salt model, and the BP 2004 model using the DCQ equation are more consistent with the acoustic (nonviscous) RTM results, but they have a wider wavelet and a different [Formula: see text]-dependent amplitude behavior; there is a phase shift in the migration results when using the GSLS equation.

Enabling affordable omnidirectional subsurface extended image volumes via probing

ABSTRACTImage gathers as a function of subsurface offset are an important tool for the inference of rock properties and velocity analysis in areas of complex geology. Traditionally, these gathers are thought of as multidimensional correlations of the source and receiver wavefields. The bottleneck in computing these gathers lies in the fact that one needs to store, compute, and correlate these wavefields for all shots in order to obtain the desired image gathers. Therefore, the image gathers are typically only computed for a limited number of subsurface points and for a limited range of subsurface offsets, which may cause problems in complex geological areas with large geologic dips. We overcome increasing computational and storage costs of extended image volumes by introducing a formulation that avoids explicit storage and removes the customary and expensive loop over shots found in conventional extended imaging. As a result, we end up with a matrix–vector formulation from which different image gathers can be formed and with which amplitude‐versus‐angle and wave‐equation migration velocity analysis can be performed without requiring prior information on the geologic dips. Aside from demonstrating the formation of two‐way extended image gathers for different purposes and at greatly reduced costs, we also present a new approach to conduct automatic wave‐equation‐based migration‐velocity analysis. Instead of focusing in particular offset directions and preselected subsets of subsurface points, our method focuses every subsurface point for all subsurface offset directions using a randomized probing technique. As a consequence, we obtain good velocity models at low cost for complex models without the need to provide information on the geologic dips.

Multipathing in three‐parameter common‐image gathers from reverse‐time migration

ABSTRACTReverse‐time migration gives high‐quality, complete images by using full‐wave extrapolations. It is thus not subject to important limitations of other migrations that are based on high‐frequency or one‐way approximations. The cross‐correlation imaging condition in two‐dimensional pre‐stack reverse‐time migration of common‐source data explicitly sums the product of the (forward‐propagating) source and (backward‐propagating) receiver wavefields over all image times. The primary contribution at any image point travels a minimum‐time path that has only one (specular) reflection, and it usually corresponds to a local maximum amplitude. All other contributions at the same image point are various types of multipaths, including prismatic multi‐arrivals, free‐surface and internal multiples, converted waves, and all crosstalk noise, which are imaged at later times, and potentially create migration artefacts. A solution that facilitates inclusion of correctly imaged, non‐primary arrivals and removal of the related artefacts, is to save the depth versus incident angle slice at each image time (rather than automatically summing them). This results in a three‐parameter (incident angle, depth, and image time) common‐image volume that integrates, into a single unified representation, attributes that were previously computed by separate processes. The volume can be post‐processed by selecting any desired combination of primary and/or multipath data before stacking over image time. Separate images (with or without artifacts) and various projections can then be produced without having to remigrate the data, providing an efficient tool for optimization of migration images. A numerical example for a simple model shows how primary and prismatic multipath contributions merge into a single incident angle versus image time trajectory. A second example, using synthetic data from the Sigsbee2 model, shows that the contributions to subsalt images of primary and multipath (in this case, turning wave) reflections are different. The primary reflections contain most of the information in regions away from the salt, but both primary and multipath data contribute in the subsalt region.

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.

Acoustic wavefield imaging using the energy norm

Wavefield energy can be measured by the so-called energy norm. We have extended the concept of “norm” to obtain the energy inner product between two related wavefields. Considering an imaging condition as an inner product between the source and receiver wavefields at each spatial location, we have developed a new imaging condition that represents the total reflection energy. Investigating this imaging condition further, we have found that it accounts for wavefield directionality in space time. Based on the directionality discrimination provided by this imaging condition, we have applied it to attenuate backscattering artifacts in reverse time migration (RTM). This imaging condition can be designed not only to attenuate backscattering artifacts, but also to attenuate any selected reflection angle. By exploiting the flexibility of this imaging condition for attenuating certain angles, we have developed a procedure to preserve the type of events that propagate along the same path, i.e., backscattered, diving, and head waves, leading to a suitable application for full-waveform- inversion (FWI). This application involves filtering the FWI gradient to preserve the tomographic term (waves propagating in the same path) and attenuate the migration term (reflections) of the gradient. We have developed the energy imaging condition applications for RTM and FWI using numerical experiments in simple (horizontal reflector) and complex models (Sigsbee and Marmousi).

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.

Accelerating extended least-squares migration with weighted conjugate gradient iteration

Least-squares migration (LSM) iteratively achieves a mean-square best fit to seismic reflection data, provided that a kinematically accurate velocity model is available. The subsurface offset extension adds extra degrees of freedom to the model, thereby allowing LSM to fit the data even in the event of significant velocity error. This type of extension also implies additional computational expense per iteration from crosscorrelating source and receiver wavefields over the subsurface offset, and therefore places a premium on rapid convergence. We have accelerated the convergence of extended least-squares migration by combining the conjugate gradient algorithm with weighted norms in range (data) and domain (model) spaces that render the extended Born modeling operator approximately unitary. We have developed numerical examples that demonstrate that the proposed algorithm dramatically reduces the number of iterations required to achieve a given level of fit or gradient reduction compared with conjugate gradient iteration with Euclidean (unweighted) norms.

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.