Deconvolution Imaging Condition Research Articles

Three‐Dimensional Teleseismic Elastic Reverse‐Time Migration With Deconvolution Imaging Condition and Its Application to Southwest Japan

AbstractWe have developed a novel deconvolution‐based reverse time migration method to image lithospheric structures using teleseismic data recorded by dense seismic arrays. Unlike traditional approaches that rely on the retrieval of Green's functions (or receiver functions), the new method directly utilizes the recorded three‐component (3‐C) seismic waveforms to reconstruct subsurface wavefields, which has the advantage of avoiding the estimation and removal of source time function. Importantly, it enables the asymptotic estimation of P‐to‐S transmission conversion coefficients at the elastic discontinuities and enhances resolving power for the fine‐scale heterogeneities. Taking these improvements, we have obtained a full three‐dimensional (3‐D) high‐resolution image of the subduction zone beneath southwest Japan. This image provides a comprehensive configuration of the severely deformed subducting plate beneath the Kii Channel and Kinki Peninsula.

Ultrasonic imaging of different shaped cracks in an isotropic plate by synthesizing time reversal and reverse time migration methods

The accuracy of reverse time migration (RTM) image of a crack is greatly affected by the position and excitation waveform of PZT transducer as the transmitter. The position of the transmitter is obtained by processing the direct-arrival flexural waves recorded at the receivers using the time reversal method. The excitation waveform generated by the transmitter is represented by the direct-arrival wave recorded at the closest receiver and their position relation, modifying the deconvolution imaging condition of RTM. Three types of cracks with different shapes located on the back of aluminum plates are investigated by employing two linear arrays composed of PZT transducer and laser vibrometer, and their high-resolution images are reconstructed using the modified RTM method. The results show that the obtained positions and shapes of the cracks are consistent with those of the actual cracks, the MRE and RMSE between them are less than 2.06% and 2.82 mm, respectively.

Frequency-Domain Reverse-Time Migration With Attenuation Compensation

Seismic wave suffers from amplitude attenuation and phase distortion when propagating in the attenuating media, thus reverse time migration (RTM) for viscous media should take the attenuation effects into consideration. Compensating for the attenuation effects in RTM may occur numerical instability because of the exponential amplification of the extrapolated wavefields. To obtain stable imaging results, we have developed a stabilized Q-compensated reverse time migration in the frequency domain. This algorithm is implemented by the following steps: first, we use the Kolsky-Futterman model to derive a frequency-domain viscoacoustic wave equation, which can simulate the amplitude loss and phase dispersion effects separately. Then, we calculate the source wavefields in the viscoacoustic media. Next, treating the recorded (viscoacoustic) data as the receiver sources, we can obtain the phase-dispersion-only and viscoacoustic receiver wavefields, which can be used to construct the stabilized Q-compensated receiver wavefields. Finally, we apply the deconvolution imaging condition for obtaining a Q-compensated image. A simple anticline model and gas chimney model are used to verify the effectiveness of the proposed approach. The Q-compensated images for the noise-free data indicate the algorithmic stability and compensation accuracy of the proposed scheme. The noisy data tests for the gas chimney model demonstrate the good anti-noise property of our method. The field data applications further prove its feasibility and practicability.

Log-validated waveform inversion of reflection seismic data with wavelet phase and amplitude updating

We have formulated an inversion approach for near-offset seismic reflection data based on full-waveform inversion (FWI) workflows, in which an element of standard seismic processing takes the place of each of the fundamental components of FWI. A motivation for using reflections in FWI is trying to update the model in deep zones in which the diving waves could not penetrate due to the large-offset limitation. The workflow is an iterative cycle of simulation, depth migration, and impedance inversion, and it is an outgrowth of an approach referred to as iterative modeling, migration, and inversion. Two-way wave operators (similar to those used in reverse time migration), which are part of the gradient calculation, are replaced with one-way wave operators; pseudo-Hessian preconditioning of the gradient is replaced with a deconvolution imaging condition; and well-log information to calibrate the update direction (i.e., model validation) replaces the standard line search (i.e., data validation). For land data applications, variations in the source wavelet are anticipated to be a large issue. To address this, we update the amplitude and phase of the simulated source wavelet during the inversion. The alternative workflow is referred to as log-validated waveform inversion (LVWI). The stabilization of LVWI is analyzed in a synthetic environment in which we examine the sensitivity to geologic complexity, well location, and log interval, each of which can impact the usefulness of local well-log information. Data from the Hussar experiment, a 2D land survey carried out in 2011 specifically to test waveform inversion procedures, are used to validate the approach. The Hussar data set is the framework for several experiments designed to analyze the effect of the wavelet update and the well-log calibration procedures. The results suggest that the implementation of wavelet updates and well calibration may provide an opportunity to mitigate cycle skipping and overcome potential local minima.

Vector elastic deconvolution migration with dual wavefield decomposition

Elastic-wave imaging using multicomponent data can provide more useful subsurface information than acoustic-wave imaging, but it is usually algorithmically challenging. We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media. Our new method uses a vector deconvolution imaging condition based on dual wavefield decomposition, including an explicit directional wavefield separation using the Hilbert transform and a P/S vector wavefield decomposition using the low-rank decomposition method. Using three elastic models, we numerically determine that our new method produces notably higher resolution and more amplitude-balanced elastic images compared with a crosscorrelation-based vector elastic reverse time migration method.

Addressing the crosstalk issue in imaging using seismic multiple wavefields

Surface-related-multiple wavefields constitute redundant information in conventional migration and can often be difficult to attenuate. However, when used for migration, multiple wavefields can improve subsurface illumination. Unfortunately, the process of imaging using multiples involves the management of crosstalk, which largely restricts its application. Crosstalk causes phantom images formed by spurious correlation of unrelated events in a migration process. These events can be unrelated orders of multiples in the source and receiver wavefields; they can also be one event associated with a reflector in the source wavefield and another event generated by a different reflector in the receiver wavefield. We have first examined crosstalk by explicitly investigating its generation mechanisms in a migration process and classifying it into different categories based on causality. Following this analysis, crosstalk can be predicted in a migration process and subtracted in the image domain; however, this method is usually difficult to apply due to the complexity of wavefield separation and adaptive subtraction. Furthermore, we develop different algorithms to attenuate the crosstalk, including a deconvolution imaging condition, a least-squares migration (LSM) method, and an advanced algorithm combining LSM with a deconvolution imaging condition. We evaluate these different strategies with synthetic examples. A deconvolution imaging condition can attenuate some crosstalk, but it is less effective at suppressing strong coherent crosstalk events. However, the LSM method can fundamentally address the crosstalk issue, and this approach is further optimized when combined with a deconvolution imaging condition.

Amplitude-Versus-Angle Analysis of Local Angle-Domain Common Image Gathers With Prestack Gaussian-Beam Migration of Seismic Data

The analysis of seismic reflection amplitude versus angle/amplitude versus offset (AVA/AVO) is an important tool for investigating the physical properties of subsurface rocks and/or reservoirs. We propose to generate local angle-domain common image gathers (ADCIGs) from the surface-recorded seismic data for AVA analysis via Gaussian-beam migration (GBM) using a deconvolution imaging condition. The traditional seismic reflection amplitude analysis is often based on the AVO response from common middle point (CMP) gathers. However, the AVO analysis based on the horizontally layered medium assumption can achieve success only in simple geological cases. Our approach provides an AVA response during the migration process that reveals true local physical properties in the image domain even if the image point is at a tilted interface or has a complicated overburden geological structure. We test our approach with a two-layer velocity model with a tilted interface, and with the benchmark Marmousi2 model that has a complicated geological structure. From these two numerical examples, we demonstrate that our method faithfully provides the AVA response that can be used to further interpret the rock/reservoir physical properties.

Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach

We have developed an explicit inverse approach with a Hessian matrix for the least-squares (LS) implementation of prestack time migration (PSTM). A full Hessian matrix is divided into a series of computationally tractable small-sized matrices using a localized approach, thus significantly reducing the size of the inversion. The scheme is implemented by dividing the imaging volume into a series of subvolumes related to the blockwise Hessian matrices that govern the mapping relationship between the migrated result and corresponding reflectivity. The proposed blockwise LS-PSTM can be implemented in a target-oriented fashion. The localized approach that we use to modify the Hessian matrix can eliminate the boundary effects originating from the blockwise implementation. We derive the explicit formula of the offset-dependent Hessian matrix using the deconvolution imaging condition with an analytical Green’s function of PSTM. This avoids the challenging task of estimating the source wavelet. Moreover, migrated gathers can be generated with the proposed scheme. The smaller size of the blockwise Hessian matrix makes it possible to incorporate the total-variation regularization into the inversion, thus attenuating noises significantly. We revealed the proposed blockwise LS-PSTM with synthetic and field data sets. Higher quality common-reflection-point gathers of the field data are obtained.

Reflection full waveform inversion

Because of the combination of optimization algorithms and full wave equations, full-waveform inversion (FWI) has become the frontier of the study of seismic exploration and is gradually becoming one of the essential tools for obtaining the Earth interior information. However, the application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Compared to other types of seismic waves, reflections carry the information of the deep part of the subsurface. Reflection FWI, therefore, is able to improve the accuracy of imaging the Earth interior further. Here, we demonstrate a means of achieving this successfully by interleaving least-squares RTM with a version of reflection FWI in which the tomographic gradient that is required to update the background macro-model is separated from the reflectivity gradient using the Born approximation during forward modeling. This provides a good update to the macro-model. This approach is then followed by conventional FWI to obtain a final high-fidelity high-resolution result from a poor starting model using only reflection data. Further analysis reveals the high-resolution result is achieved due to a deconvolution imaging condition implicitly used by FWI.

Strategies for imaging with Marchenko-retrieved Green’s functions

Recent papers show that imaging with the retrieved Green’s function constructed by the Marchenko equations, called Marchenko imaging, reduces artifacts from internal and free-surface multiples compared with standard imaging techniques. Even though artifacts are reduced, they can still be present in the image, depending on the imaging condition used. We have found that when imaging with the up- and downgoing Green’s functions, the multidimensional deconvolution (MDD) imaging condition yields better images than correlation and deconvolution. “Better” in this case means improved resolution, fewer artifacts, and a closer match with the true reflection coefficient of the model. We have determined that the MDD imaging condition only uses primaries to construct the image, whereas multiples are implicitly subtracted in the imaging step. Consequently, combining the first arrival of the downgoing Green’s function with the complete upgoing Green’s function produces superior (or at least equivalent) images than using the one-way Green’s functions because the first arrival of the downgoing Green’s function excludes all the downgoing multiply reflected waves. We also find that standard imaging algorithms which use the redatumed reflection response, constructed with the one-way Green’s functions, produce images with reduced artifacts from multiples compared with standard imaging conditions, which use surface reflection data. All imaging methods that rely on the Marchenko equations require the same inputs as standard imaging techniques: the reflection response at the surface and a smooth estimate of the subsurface velocities.

Subsurface reflectivity estimation from imaging of primaries and multiples using amplitude-normalized separated wavefields

Several studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors. However, to characterize the reflector properties, there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples. From this perspective and based on the wave equation and Rayleigh’s reciprocity theorem, recent works have suggested computing the subsurface image from the Green’s function reflection response (or reflectivity) by inverting a Fredholm integral equation in the frequency-space domain. By following Claerbout’s imaging principle and assuming locally reacting media, the integral equation may be reduced to a trace-by-trace deconvolution imaging condition. For a complex overburden and considering that the structure of the subsurface is angle-dependent, this trace-by-trace deconvolution does not properly solve the Fredholm integral equation. We have inverted for the subsurface reflectivity by solving the matrix version of the Fredholm integral equation at every subsurface level, based on a multidimensional deconvolution of the receiver wavefields with the source wavefields. The total upgoing pressure and the total filtered downgoing vertical velocity were used as receiver and source wavefields, respectively. By selecting appropriate subsets of the inverted reflectivity matrix and by performing an inverse Fourier transform over the frequencies, the process allowed us to obtain wavefields corresponding to virtual sources and receivers located in the subsurface, at a given level. The method has been applied on two synthetic examples showing that the computed reflectivity wavefields are free of propagation effects from the overburden and thus are suited to extract information of the image point location in the angular and spatial domains. To get the computational cost down, our approach is target-oriented; i.e., the reflectivity may only be computed in the area of most interest.

Least‐squares reverse‐time migration in a matrix‐based formulation

ABSTRACTThis paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful.

An amplitude-preserved adaptive focused beam seismic migration method

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

A stabilized least-squares imaging condition with structure constraints

Conventional shot-gather migration uses a cross-correlation imaging condition proposed by Clarebout (1971), which cannot preserve imaging amplitudes. The deconvolution imaging condition can improve the imaging amplitude and compensate for illumination. However, the deconvolution imaging condition introduces instability issues. The least-squares imaging condition first computes the sum of the cross-correlation of the forward and backward wavefields over all frequencies and sources, and then divides the result by the total energy of the forward wavefield. Therefore, the least-squares imaging condition is more stable than the classic imaging condition. However, the least-squares imaging condition cannot provide accurate results in areas where the illumination is very poor and unbalanced. To stabilize the least-squares imaging condition and balance the imaging amplitude, we propose a novel imaging condition with structure constraints that is based on the least-squares imaging condition. Our novel imaging condition uses a plane wave construction that constrains the imaging result to be smooth along geological structure boundaries in the inversion frame. The proposed imaging condition improves the stability of the imaging condition and balances the imaging amplitude. The proposed condition is applied to two examples, the horizontal layered model and the Sigsbee 2A model. These tests show that, in comparison to the damped least-squares imaging condition, the stabilized least-squares imaging condition with structure constraints improves illumination stability and balance, makes events more consecutive, adjusts the amplitude of the depth layers where the illumination is poor and unbalanced, suppresses imaging artifacts, and is conducive to amplitude preserving imaging of deep layers.

Amplitude-preserved pre-stack time migration in 3D VTI media

We present a new method of amplitude-preserved pre-stack time migration in 3D vertical transversely isotropic (VTI) media. The travel time and amplitude of a wave propagating in VTI media are calculated by using one-way wave operators and the stationary-phase theory. An imaging weight from the deconvolution imaging condition is introduced to produce amplitude-preserved image gathers for hydrocarbon and fluid detection. Velocities and stacking anisotropic parameters are estimated by a semblance scanning method. A time-dependent migration aperture corresponding to the dip of subsurface structure is then obtained to balance imaging quality and imaging noises. Numerical examples demonstrate that our method is accurate, robust and easy to implement.

A new stabilized least-squares imaging condition

The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where the energy of the downgoing wave field is small. To stabilize the least-squares imaging condition, the energy of the downgoing wave field is replaced by its average value computed in a horizontal plane in poorly illuminated regions. Applications to the Marmousi and Sigsbee2A data sets show that the stabilized least-squares imaging condition produces better images than the least-squares and cross-correlation imaging conditions.

True-amplitude Gaussian-beam migration

Gaussian-beam depth migration and related beam migration methods can image multiple arrivals, so they provide an accurate, flexible alternative to conventional single-arrival Kirchhoff migration. Also, they are not subject to the steep-dip limitations of many (so-called wave-equation) methods that use a one-way wave equation in depth to downward-continue wavefields. Previous presentations of Gaussian-beam migration have emphasized its kinematic imaging capabilities without addressing its amplitude fidelity. We offer two true-amplitude versions of Gaussian-beam migration. The first version combines aspects of the classic derivation of prestack Gaussian-beam migration with recent results on true-amplitude wave-equation migration, yields an expression involving a crosscorrelation imaging condition. To provide amplitude-versus-angle (AVA) information, true-amplitude wave-equation migration requires postmigration mapping from lateral distance (between image location and source location) to subsurface opening angle. However, Gaussian-beam migration does not require postmigration mapping to provide AVA data. Instead, the amplitudes and directions of the Gaussian beams provide information that the migration can use to produce AVA gathers as part of the migration process. The second version of true-amplitude Gaussian-beam migration is an expression involving a deconvolution imaging condition, yielding amplitude-variation-with-offset (AVO) information on migrated shot-domain common-image gathers.

Preserved amplitude migration based on the one way wave equation in the angle domain

Traditional pre-stack depth migration can only provide subsurface structural information. However, simple structure information is insufficient for petroleum exploration which also needs amplitude information proportional to reflection coefficients. In recent years, pre-stack depth migration algorithms which preserve amplitudes and based on the one-way wave equation have been developed. Using the method in the shot domain requires a deconvolution imaging condition which produces some instability in areas with complicated structure and dramatic lateral variation in velocity. Depth migration with preserved amplitude based on the angle domain can overcome the instability of the one-way wave migration imaging condition with preserved amplitude. It can also offer provide velocity analysis in the angle domain of common imaging point gathers. In this paper, based on the foundation of the one-way wave continuation operator with preserved amplitude, we realized the preserved amplitude prestack depth migration in the angle domain. Models and real data validate the accuracy of the method.

A comparison of imaging conditions for wave-equation shot-profile migration

The application of a deconvolution imaging condition in wave-equation shot-profile migration is important to provide illumination compensation and amplitude recovery. Particularly if the aim is to successfully recover a measure of the medium reflectivity, an imaging condition that destroys amplitudes is unacceptable. We study a set of imaging conditions with illumination compensation. The imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced. In numerical experiments using a vertically inhomogeneous velocity model, the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield, also known as the illumination map. In an application to Marmousi data, unconditional division by autocorrelation turned out to be unstable. Effective stabilization was achieved by smoothing the illumination map.

Prestack depth migration of primary and surface-related multiple reflections: Part I — Imaging

Surface-related multiples (i.e., all seismic waves reflected at the free surface at least once) often severely contaminate seismic recordings. Because conventional imaging techniques require input data that consist of primary reflections only, significant processing effort is commonly dedicated to attenuating multiples prior to migration. On the other hand, surface-related multiples provide additional illumination of the subsurface and, therefore, should not be considered as noise. We present a prestack depth-migration method that allows primary and multiple reflections to be imaged simultaneously. Depth imaging using primary and multiple reflections (DIPMR) involves decomposing the datainto upgoing and downgoing wave constituents, followed by downward extrapolation. Artifacts generated by interference of upgoing and downgoing events not associated with the same subsurface reflection points (crosstalk) are attenuated by using a 2D deconvolution imaging condition. In contrast to existing methods, DIPMR does not require a priori information about the source signature or directivity, because the illuminating source wavefield is extracted directly from the data themselves via the up/down separation. Moreover, there is no need for elimination nor identification of multiples prior to migration. By including surface-related multiples in the imaging procedure, the effective source wavefield is stronger, the spatial aperture is wider, and a higher vertical resolution is enabled through the application of a deconvolution-based imaging condition.