Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Gaussian beam prestack depth migration is an accurate imaging method of subsurface media. Prestack depth migration of multicomponent seismic data improves the accuracy of imaging subsurface complex geological structures. Viscoelastic prestack depth migration is of practical significance because it considers the viscosity of the subsurface media. We use Gaussian beam migration to compensate for the attenuation in multicomponent seismic data. First, we use the Gaussian beam method to simulate the wave propagation in a viscoelastic medium and introduce the complex velocity Q-related and exact viscoelastic Zoeppritz equation. Second, we discuss PP- and PS-wave Gaussian beam prestack depth migration algorithms for common-shot gathers to derive expressions for the attenuation and compensation. The algorithms correct the amplitude attenuation and phase distortion caused by Q, and realize multicomponent Gaussian beam prestack depth migration based on the attenuation compensation and account for the effect of inaccurate Q on migration. Numerical modeling suggests that the imaging resolution of viscoelastic Gaussian beam prestack depth migration is high when the viscosity of the subsurface is considered.

High angle prestack depth migration with absorption compensation

The absorption effect of actual subsurface media can weaken wavefield energy, decrease the dominating frequency, and further lead to reduced resolution. In migration, some actions can be taken to compensate for the absorption effect and enhance the resolution. In this paper, we derive a one-way wave equation with an attenuation term based on the time- space domain high angle one-way wave equation. A complicated geological model is then designed and synthetic shot gathers are simulated with acoustic wave equations without and with an absorbing term. The derived one-way wave equation is applied to the migration of the synthetic gathers without and with attenuation compensation for the simulated shot gathers. Three migration profiles are obtained. The first and second profiles are from the shot gathers without and with attenuation using the migration method without compensation, the third one is from the shot gathers with attenuation using the migration method with compensation. The first and third profiles are almost the same, and the second profile is different from the others below the absorptive layers. The amplitudes of the interfaces below the absorptive layers are weak because of their absorption. This method is also applied to field data. It is concluded from the migration examples that the migration method discussed in this paper is feasible.

Beamlet prestack depth migration and illumination： A test based on the Marmousi model

Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.

Traveltime tomography and prestack depth migration for vertical seismic profiling of an angle-domain walkaway on a complex surface

Walkaway VSP cannot obtain accurate velocity field,as it asymmetrically reflects ray path and provides uneven coverage to underground target,thereby presenting issues related to imaging quality.In this study,we propose combining traveltime tomography and prestack depth migration for VSP of an angle-domain walkaway,in a bid to establish accurate two-dimensional and three-dimensional(3 D)velocity models.First,residual curvature was defined to update velocity,and an accurate velocity field was established.To establish a high-precision velocity model,we deduced the relationship between the residual depth and traveltime of common imaging gathers(CIGs)in walkaway VSP.Solving renewal velocity using the least squares method,a four-parameter tomographic inversion equation was derived comprising formation dip angle,incidence angle,residual depth,and sensitivity matrix.In the angle domain,the reflected wave was divided into up-and down-transmitted waves and their traveltimes were calculated.The systematic cumulative method was employed in prestack depth migration of a complex surface.Through prestack depth migration,the offset-domain CIGs were obtained,and dip angle was established by defining the stack section horizon.Runge–Kutta ray tracing was employed to calculate the ray path from the reflection point to the detection point,to determine the incident angle,and to subsequently calculate the ray path from the reflection point to the irregular surface.The offset-domain residual depths were mapped to the angle domain,and a new tomographic equation was established and solved.Application in the double complex area of the Tarim Basin showed the four-parameter tomographic inversion equation derived in this paper to be both correct and practical and that the migration algorithm was able to adapt to the complex surface.

The Offset-Domain Prestack Depth Migration with Optimal Separable Approximation

The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.

Reverse-Time Prestack Depth Migration of GPR Data from Topography for Amplitude Reconstruction in Complex Environments

With increased computational power, reverse-time prestack depth migration（RT-PSDM） has become a preferred imaging tool in seismic exploration, yet its use has remained relatively limited in ground-penetrating radar（GPR） applications. Complex topography alters the wavefield kinematics making for a challenging imaging problem. Model simulations show that topographic variation can substantially distort reflection amplitudes due to irregular wavefield spreading, attenuation anomalies due to irregular path lengths, and focusing and defocusing effects at the surface. The effects are magnified when the topographic variations are on the same order as the depth of investigation––a situation that is often encountered in GPR investigations. Here, I use a full wave-equation RT-PSDM algorithm to image GPR data in the presence of large topographic variability relative to the depth of investigation. The source and receiver wavefields are propagated directly from the topographic surface and this approach inherently corrects for irregular kinematics, spreading and attenuation. The results show that when GPR data are acquired in areas of extreme topography, RT-PSDM can accurately reconstruct reflector geometry as well as reflection amplitude.

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.

Kirchhoff PSDM angle-gather generation based on the traveltime gradient

Angle-domain common-image gathers（ADCIGs） are the basic data in migration velocity analysis（MVA） and amplitude variation with angle（AVA） analysis. We propose a common-angle gather-generating scheme using Kirchhoff PSDM based on the traveltime gradient field. The scheme includes three major operations：（1） to calculate the traveltime field of the source and the receiver based on the dynamic programming approach;（2） to obtain the refl ection angle according to the traveltime gradient field in the image space; and（3） to generate the ADCIGs during the migration process. Because of the computation approach, the method for generating ADCIGs is superior to conventional ray-based methods. We use the proposed ADCIGs generation method in 3D large-scale seismic data. The key points of the method are the following.（1） We use common-shot datasets for migration,（2） we load traveltimes based on the shot aperture, and（3） we use the MPI and Open Mp memory sharing to decrease the amount of input and output（I/O）. Numerical examples using synthetic data suggest that the ADCIGs improve the quality of the velocity and the effectiveness of the 3D angle-gather generation scheme.

Plane wave shot PSDM and controlled illumination techniques

The Pre-Stack Depth Migration （PSDM） method based on wavefield continuation is the most reliable method for imaging complex structure in the subsurface, although there are large computational costs and poorly adaptive geometry. Plane wave shot migration is another method to perform exact wave equation prestack imaging with high computational efficiency and without the migration aperture problem. Moreover, wavefield energy can be compensated at the target zone by controlled illumination. In this paper, plane wave shot PSDM was implemented by the control of the plane down-going wavefield and selection of number and range of the raypaths in order to optimize the imaging effect. In addition, controlled illumination techniques are applied to enhance the imaging precision of interesting areas at different depths. Numerical calculation indicates that plane wave shot imaging is a rapid and efficient method with less computational cost and easy parallel computation compared to the single-square-root operator imaging for common shot gathers and double- square-root operator imaging for common midpoint gathers.

A self-adaptive algorithm for choosing reference velocities in the presence of lateral velocity variations

Based on perturbation theory, the wave equation extrapolation operator with mixed domains has the ability to deal with lateral velocity variations. It is the image method that has undergone much research in seismology. All extrapolation operators face the problem of choosing the reference velocity due to continuation in depth. The wavefield extrapolation operator with a single reference velocity is suitable for media with weak lateral variation. The multi-reference velocity extrapolation operator can cope with severe lateral velocity variations and improve image accuracy. However, the calculation cost is large. We present a self-adaptive approach to automatically determine the number of selected reference velocities according to the complexity of structure and the given velocity threshold value. The approach can be used to construct the SSF, FFD, WXFD, and GSP multi-reference velocity wavefield extrapolation image algorithms. The result of a salt-dome model data test demonstrates that the self-adoptive multi-reference wavefield extrapolation algorithm has the ability to deal with severe lateral velocity variations and can also be used for structure edge detection. The method is flexible and computationally cost-effective.

3D wavefield extrapolation with optimal separable approximation

An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.

Geological Guided Tomography Inversion Based on Fault Constraint and Its Application

Fault block reservoirs are one of the main types of hydrocarbon reservoirs found in offshore basins,and they are widely distributed within the Mesozoic and Cenozoic basins of the northern South China Sea.Conventional seismic profiles of complex fault areas often contain obvious fragmentation and distortion of seismic events that is corresponding to geological structure under the fault.This phenomenon is known as a fault shadow;it occurs in relation to rapid changes in velocity near the fault that deviate the ray path of waves,and it seriously affects the ability to determine the geological structure and subsequently evaluate the reserves of fault reservoirs.In the current conventional tomography inversion method,the velocity model is over-smoothed,which results in distortion of the reflection layer under the fault.Based on the velocity tomography inversion of imaging gathers method and the concept of regularization,this paper first introduces the anisotropy Gauss regularization operator.A high-resolution tomography inversion method is then developed,and the fault-controlled geological guidance is constrained.This technology is then applied to a complex fault block reservoir basin in the South China Sea,and the results show that it can significantly solve the problem of fault shadow imaging and determine the geological structures in the target area.The newly developed method thus has very good application prospects.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.