Acoustic VTI reverse time migration based on an improved source wavefield storage strategy

Acoustic VTI modeling and pre-stack reverse-time migration based on the time–space domain staggered-grid finite-difference method

Summary In this abstract, we discuss some practical issues related to the implementation of reverse time migration (RTM) in a tilted transversely isotropic (TTI) medium. We have proposed a methodology to effectively reduce the cost. Through optimization of the coefficients of high-order difference scheme on the variable grid, larger depth steps at greater depth can be used instead of fixed step size. Synthetic data examples are used to demonstrate the effectiveness of the methodology. Introduction Reverse time migration (RTM) based on solving a two-way wave equation has been one of the most accurate imaging tools available in dealing with large lateral velocity variations and complicated geology such as large dips. RTM for isotropic and vertical transversely isotropic (VTI) medium has been routinely in use in the industry, but the application of RTM in TTI medium is still in the early stage. This lag results from the difficulties in numerical formulations for non-vertical symmetric axes and the subsequent instabilities. The TTI implementation also leads to higher computational costs compared with its isotropic or VTI counterparts. Instead of solving the original anisotropic wave equation, several modified quasi-P wave equations were derived by different authors, that can be used to perform anisotropic RTM for P-waves imaging without cause significant S wave scattering. Alkhalifah (2000) derived a 4th-order partial differential equation (PDE) in time to describe TTI propagation. To avoid solving a high order PDE, Zhou et al. (2006) split Alkhaifah's equation into two coupled 2nd-order PDEs. However it has been observed that their equations cause instability in practice when large dip is at presence. To circumvent this stability issue, Zhang et al. (2009) pursue an equivalent TTI formulation that preserves physical energy with the kinematics retained. Fletcher et al. (2009) proposed adding non-zero shear wave velocity terms to mitigate the instability problem. Unfortunately, their solution adds numerical complexity. In our implementation, to deal with both the stability and accuracy issues in TTI environment, we have to cut the cost dramatically to run it in production environment. To reduce the computational cost of TTI RTM, we use the least-square-root method in the Fourier domain to construct optimized finite difference (FD) schemes of variable grid in depth to approximate the first and second order derivatives. With larger steps in space in deep layers of higher velocity while keeping the same criteria for controlling the numerical dispersion, the total number of grid point is reduced. We analyzed the stability condition for this proposed FD scheme to determine the size of time step, which is related to minimum grid space, maximum velocity as well as the coefficients of FD scheme. With this implementation our RTM has been enhanced greatly in efficiency, and gained success in numerous 3D land imaging projects. Here we will demonstrate the effectiveness of this method using the 2D BP TTI model as a test case.

In real strata anisotropy and viscosity extensively exists. They degraded waveforms in amplitude, resulting in which reducing of image resolution. To obtain high-precision imaging of deep reservoirs, we extended the separated viscous and anisotropic reverse time migration (RTM) to a stable viscoacoustic anisotropic RTM for vertical transverse isotropic (VTI) media, based on single generalized standard and linear solid (GSLS) media theory.. We used a pseudo-spectral method to develop the numerical simulation. By introducing a regularization operator to eliminate the high-frequency instability problem, we built a stable inverse propagator and achieved viscoacoustic VTI media RTM. High-resolution imaging results were obtained after correcting for the effects of anisotropy and viscosity. Synthetic tests verify the validity and accuracy of algorithm.

To improve the computational efficiency of reverse-time migration (RTM) for vertically transverse isotropic (VTI) media, various acoustic approximations of the elastic wave equations have been presented. Among these, the pseudo-acoustic wave equation, which combines differential and scalar operators, has the advantage that it does not produce shear wave artefacts. In this study, we investigate the feasibility of pseudo-acoustic anisotropic RTM (PA-RTM) for the analysis of synthetic and observed ocean-bottom cable (OBC) datasets of the Volve oil field in the North Sea. To analyse the influence of anisotropic parameters on RTM images and the sensitivity of data components to seismic anisotropy, we perform PA-RTM using synthetic data by incorporating various background models, as well as pressure wavefields and vertical particle acceleration. The synthetic experiments demonstrate that the anisotropic parameter ε plays an important role, whereas δ is negligible in PA-RTM for VTI media, and that vertical particle acceleration is less affected by seismic anisotropy than the pressure wavefields. Our experiments using observed data show that reflectors are better imaged by PA-RTM than by isotropic-RTM, particularly near the reservoir below the strongly anisotropic region, which is supported by angle-domain common image gathers. These results indicate that PA-RTM using only the vertical component is a suitable option for VTI media when insufficient seismic anisotropy data are available.

Viscoacoustic VTI media reverse time migration method in the complex-domain based on the staining algorithm

Seismic waves propagating in anisotropic earth media suffer from waveform distortion, which leads to degraded resolution in seismic data imaging if this adverse effect is not corrected. Additionally, the wavefields simulated by the traditional coupled pseudo‐acoustic wave equations contain undesired shear wave artefacts and are unstable when Thomsen's anisotropy parameter ε is less than δ. To address these issues, many pure qP‐wave equations are proposed to describe wave propagation in anisotropic media. However, these equations are either low precision or high accuracy but computationally expensive. Considering the trade‐off between the computation efficiency and simulation accuracy, we derive a pure qP‐wave equation from the exact dispersion formula in tilted transverse isotropic media. The newly derived equation has only two higher order partial derivatives, which can better balance the accuracy and efficiency than the previous pure qP‐wave equations. The least‐squares reverse time migration method can balance amplitudes, suppress migration artefacts and improve imaging resolution. Then, based on the newly derived pure qP‐wave equation, we derive the Born modelling operator and adjoint migration operator and develop an anisotropic least‐squares reverse time migration method. To achieve the accelerated convergence, we introduce a generalized minimum residual algorithm to implement the anisotropic least‐squares reverse time migration method. Numerical simulation results show that the proposed pure qP‐wave equation outperforms the previous equations in balancing the trade‐off between accuracy and efficiency. In addition, synthetic examples demonstrate the effectiveness and robustness of our proposed anisotropic least‐squares reverse time migration method in correcting the deviations due to anisotropic effects.

The time period from the early 1990s through to the early 2010s saw a consistent and steady increase in the (1) depth of data imaged, (2) level of seismic detail revealed, and (3) complexity of tectonic and salt structures resolved. To achieve this remarkable increase in data quality, the seismic industry made parallel advances in seismic acquisition techniques, data processing algorithms, and computer processing speed. The resulting high quality imagery has allowed interpreters, modelers, and research scientists to advance the science of salt tectonics from a relatively basic level in the early 1990s to a robust and highly integrated science in 2019. State-of-the-art marine seismic data acquisition in 1990 involved a single vessel towing a single cable 4 km long collecting time data in a 1-2 km spaced 2-D grid. By the early 1990s, narrow azimuth 3-D time acquisition evolved. Initially this started with a single vessel towing two streamers of 4 km length and recording 8 second records. It grew to involve multiple vessels towing 3-6 streamers of 6 km length and recording 14 second records. Kirchhoff was standard advancing from post-stack time to pre-stack time migration. In the early 2000s, time processing and depth processing existed side by side, but exploration needs were pushing for better depth data. Kirchhoff pre-stack depth volume quality was replaced by Wave Equation pre-stack depth data in areas of greater structural complexity. Depth processing now included one or two top salt-base salt pairs to image the subsalt stratigraphy. By the mid-2000s, wide-azimuth acquisition was the procedure of choice. Vessels were towing 8-10 streamers of 7-8 km in length. Maximum offsets were reaching 8-9 km and receiver location systems were being employed. Velocity analysis employed multi-azimuth sediment tomography incorporating seismic anisotropy and later vertical transverse isotropy. Around 2009-2010, reverse time migration became the processing algorithm of choice. Velocity fields were calibrated to subsalt well ties. Velocity analysis incorporated full waveform inversion with vertical transverse isotropy and then tilted transverse isotropy. Running multiple iterations of intrasalt and subsalt full waveform inversion would become standard practice. In the early 2010s, WesternGeco introduced full azimuth and multi-vessel full azimuth acquisition. Proper acquisition and processing of full azimuth data required streamer steering capabilities, precise receiver positioning, advanced noise attenuation algorithms, and state-of-the-art computing facilities. Full azimuth acquisition produced maximum offsets of 14-16 km. Eventually, full azimuth and wide-azimuth data sets were merged to reduce noise and maximize the efficiency of tried and tested wide-azimuth processing routines. Seismic examples over the same location shot from 1990s to 2015 illustrate the incremental gains made in imaging the subsurface in response to these technical advances.

Reverse time migration: A prospect of seismic imaging methodology

<p>Acoustic wave equations are widely employed in wavefield extrapolation and inversion due to their simplicity compared to the elastic wave equations. In anisotropic media, qP- and qSV-waves are coupled. Multiple acoustic approximations in the vertical transversely isotropic (VTI) media have been proposed during the last decades. A classic way is to set the vertical S-wave velocity zero. As such, the S-wave artefacts still exist, whose amplitude increases with anisotropy. Setting S-wave velocity zero in all propagating directions tackles the issue. However, the higher-order spatial derivatives in the pure qP-wave equation make it hard to solve in the space domain. The spatial derivatives in the denominator of the pure qP-wave equation make the solution by the spatial-domain finite-difference unstable.  In this study, we employed the time-domain pseudospectral method to solve both the classic acoustic wave equation and the pure qP-wave equation in VTI media. Hybrid absorbing boundary conditions are used. Both equations are applied to reverse time migration (RTM) for the anisotropic Marmousi model. The new qP-wave equation outperformed the classic qP-wave equation regarding the computational time. Further work can be extended to waveform inversion with the pure qP-wave equation.</p>

Reverse time migration (RTM) exhibits great advantages over other imaging methods because it is based on computing numerical solutions to a two-way wave equation. It does not suffer from dip limitation like one-way downward continuation techniques do, thus enabling overturned reflections to be imaged. As well as correctly handling multipathing, RTM has the potential to image internal multiples when the boundaries responsible for generating the multiples are present in the model. In isotropic media, one can use a scalar acoustic wave equation for RTM of pressure data. In anisotropic media, P- and SV-waves are coupled together so, formally, elastic wave equations must be used for RTM. A new wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing. If the shear velocity along the axis of symmetry is set to zero, stable numerical solutions can be computed for media with a vertical axis of symmetry and ε not less than δ. In TTI media with rapid variations in the direction of the axis of symmetry, setting the shear velocity along the axis of symmetry to zero can cause numerical solutions to become unstable. A solution to this problem is proposed that involves using a small amount of nonzero shear velocity. The amount of shear velocity added is chosen to remove triplications from the SV wavefront and to minimize the anisotropic term of the SV reflection coefficient. We show modeling and high-quality RTM results in complex TTI media using this equation.

Advances in marine seismic acquisition allow for the recording of four-component (4C) data from dual-source configurations, i.e., using monopole and dipole sources. Here, we describe a novel method for multicomponent reverse-time migration that is based on an adjoint-state formulation using the full vector-acoustic wave equations for pressure and displacement fields. This method takes advantage of the directional dynamic information contained in 4C acoustic fields by using source and receiver weights operators incorporated into the adjoint-state scheme. With this method, we show that the source and receiver radiation properties of the vector-acoustic(VA) depth image can be custom-designed by choosing specific weighting operators. In the examples presented, weights are chosen so that both the source- and receiver-side ghosts are jointly migrated with primary energy. Because the dipole field components (e.g., particle acceleration) are proportional to the spatial gradient components of pressure, our method is a formulation of reverse-time map migration because it images pressure fields while jointly using directional information from its recorded 3C gradient. Thus, our reverse-time 4C map migration yields less aperture- and sampling-related artifacts than migration of pressure-only or 2C seismic data. Finally, our method sets a framework for full-waveform inversion using dual-source 4C seismic data.

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

Recent seismic acquisition and anisotropic velocity modeling has resulted in improved salt definition and sub‐salt imaging at Puma and Mad Dog Fields in the Gulf of Mexico. For these fields, wide‐azimuth towed‐streamer (WATS) surveys, isotropic imaging, vertical transverse isotropy (VTI) imaging, and tilted transverse isotropy (TTI) imaging were carried out sequentially. This series offers a great opportunity to understand the impact of different levels of anisotropy approximation and why TTI reverse time migration (RTM) should be used for future WATS imaging.

Nowadays, benefiting from its strong capability of non-destructive detection, the ground penetrating radar (GPR) has been applied to detect and reconstruct underground targets and has drawn lots of attention both in military and civilian fields. However, in the processing of GPR imaging, due to the dispersion errors caused by random distribution of various particles in soil, conventional imaging methods have disadvantages of low signal-noise ratio (SNR), low resolution and unbalanced amplitude. In this paper, in order to achieve high resolution and high veracity on underground targets 3-D reconstruction, we improved the conventional reverse time migration (RTM) algorithm in perspective of medium constitutive relationship. Besides, we extended the improved RTM method in 3-D environments and reconstructed the 3-D structure of several underground targets. To make RTM algorithm suitable for stepped frequency continuous wave (SFCW) GPR system, we generated three excitation signal models and analyzed the effect of different excitation signals on imaging performance. Finally, through the quantitative analysis of simulation and on-vehicle experimental results, we found that the 3-D images generated by improved RTM method had higher resolution, smaller measurement error, and higher veracity than those of conventional RTM method.

Acceleration of stable TTI P-wave reverse-time migration with GPUs