Elastic waves are affected by viscoelasticity during the propagation through the Earth, resulting in energy attenuation and phase distortion, in turn resulting in low seismic imaging accuracy. Therefore, viscoelasticity should be considered in seismic migration imaging. We propose a Q compensated multi-component elastic Gaussian beam migration (Q-EGBM) method to (1) separate the elastic-wave data into longitudinal (P) and transverse (S) waves to perform PP-wave and PS-wave imaging; (2) recover the amplitude loss caused by attenuation; (3) correct phase distortions caused by dispersion; (4) improve the resolution of migration imaging. In this paper, to accomplish (2), (3), and (4), we derive complex-valued traveltimes in viscoelastic media. The results of numerical experiments using a simple five-layer model and a sophisticated BP gas model show that the method presented here has significant advantages in recovering energy decay and correcting phase distortion, as well as significantly improving imaging resolution.
Summary The fault-karst reservoir is a type of hydrocarbon-enriched carbonate reservoirs in the Tarim Basin. It is a combination of small-scale caves, vugs and fractures developing near deep-seated faults, which makes it difficult to delineate using traditional seismic imaging methods. Recent researches on the characteristics of paleokarst reservoirs facilitate hydrocarbon exploration and exploitation in western China. To interpret karstic fault systems and reservoirs, the seismic image is an effective tool. A high-quality velocity model is essential for high-resolution imaging. In order to image the complicated and irregular fractured-cavity reservoirs accurately, we applied multi-scale FWI method accelerated on graphics processing unit (GPU) devices to models containing fault-controlled paleokarst reservoirs. According to numerical test results, FWI shows high performance of delineating boundaries of fault-controlled karstic reservoirs. The proposed method also has the potential to characterize inner structures. Based on the high-precision velocity model provided by FWI, the seismic image obtained by reverse time migration (RTM) is also improved. These seismic results will show the location, width and shape of the fault-karst structure, which gives detailed information for reservoir interpretation.
The constant-Q viscoelastic wave equation, which includes decoupled amplitude attenuation and phase dispersion terms, is commonly used for attenuation-compensated reverse time migration (RTM). However, this equation involves fractional Laplacian operators and typically requires computationally intensive spectral methods. Efficient implementation is crucial for practical applications. To address this, we derive a new isotropic viscoelastic wave equation based on the standard linear solid model, which also contains decoupled amplitude attenuation and phase dispersion terms. This new equation can be solved using an efficient finite-difference method in the time domain. Consequently, we develop a viscoelastic RTM with attenuation compensation. Numerical simulations demonstrate that this equation accurately and efficiently simulates the decoupled amplitude loss and phase dispersion characteristics.
Conventional vertical transverse isotropic (VTI) least-squares reverse time migration (LSRTM) method does not account for the distortion caused by the anisotropy tilted angle, which can lead to defocusing of migration images in highly tilted anisotropic geologic environments. In addition, the wavefield simulated by the traditional coupled pseudo-acoustic equation is not only affected by SV-wave artifacts but also limited by the model parameters (ϵ>δ). Therefore, we propose a least-squares reverse time migration (LSRTM) method based on the pure qP-wave equation in tilted transverse isotropic (TTI) media. First, a finite-difference (FD) method, which could be improve the efficiency of numerical simulation, is used to solve the pure qP-wave quasi-differential equations in TTI media. Then, we implement a TTI LSRTM by deriving a demigration operator, migration operator, and gradient formula for TTI media. Numerical tests on the synthetic data show that the new method can correct the deviation due to the media's anisotropy, suppress imaging noise and improve the imaging resolution. Presentation Date: Wednesday, September 18, 2019 Session Start Time: 8:30 AM Presentation Start Time: 11:25 AM Location: 214C Presentation Type: Oral
The pseudoviscoacoustic anisotropic wave equation is widely used in the oil and gas industry for modeling wavefields in attenuating anisotropic media. Compared to the full viscoelastic anisotropic wave equation, it can greatly reduce the computational cost of wavefield modeling while maintaining the visco-qP-wave kinematics very well. However, even if we place the source in a thin isotropic layer, there will be some unwanted S-wave artifacts in the qP wavefield simulated by the pseudoviscoacoustic anisotropic wave equation due to the stepped approximation of inclined layer interfaces. Furthermore, the wavefield simulated by the pseudoviscoacoustic anisotropic wave equation may suffer from numerical instabilities when the anisotropy parameter epsilon is less than delta. To overcome these problems, we derive a pure-viscoacoustic tilted transversely isotropic (TTI) wave equation in media with anisotropy in velocity and attenuation based on the exact complex-valued phase velocity formula. The pure-viscoacoustic TTI wave equation has decoupled amplitude dissipation and phase dispersion terms, which is suitable for further reverse time migration with Q compensation. For numerical simulations, we adopt the second-order Taylor series expansion to replace the mixed-domain spatially variable fractional Laplacian operator, which guarantees the decoupling of the wavenumber from the space-related fractional order. Then, we use an efficient and stable hybrid finite-difference and pseudospectral method (HFDPSM) to solve the pure-viscoacoustic TTI wave equation. Numerical tests indicate that the simulation results of the newly derived pure-viscoacoustic TTI wave equation are stable, free from S-wave artifacts, and accurate. We further demonstrate that HFDPSM outperforms the pseudospectral method in terms of numerical simulation stability and computing efficiency.
Abstract Seismic waves propagating through attenuating media induce amplitude loss and phase dispersion. Neglecting the attenuation effects during seismic processing results in the imaging profiles with weakened energy, mispositioned interfaces and reduced resolution. To obtain high‐quality imaging results, Q ‐compensated reverse time migration is developed. The kernel of the Q ‐compensated reverse time migration algorithm is a viscoacoustic wave equation with decoupled amplitude loss and phase dispersion terms. However, the majority of current decoupled viscoacoustic wave equations are solved using the computationally expensive pseudo‐spectral method. To enhance computational efficiency, we initiate our approach from the dispersion relation of a single standard linear solid model. Subsequently, we derive a novel decoupled viscoacoustic wave equation by separating the amplitude loss and phase dispersion terms, previously coupled in the memory variable. The newly derived decoupled viscoacoustic wave equation can be efficiently solved using the finite‐difference method. Then, we reverse the sign of the amplitude loss term of the newly derived viscoacoustic wave equation to implement high‐efficient Q ‐compensated reverse time migration based on the finite‐difference method. In addition, we design a regularization term to suppress the high‐frequency noise for stabilizing the wavefield extrapolation. Forward modelling tests validate the decoupled amplitude loss and phase dispersion characteristics of the newly derived viscoacoustic wave equation. Numerical examples in both two‐dimensional and three‐dimensional confirm the effectiveness of the Q ‐compensated reverse time migration based on the finite‐difference algorithm in mitigating the attenuation effects in subsurface media and providing high‐quality imaging results.
Subsurface anisotropy is commonly induced by shale layers, aligned cracks, and fine bedding and has a significant impact on seismic wave propagation. Ignoring anisotropic effects during seismic migration degrades image quality. Therefore, we derive a pure qP-wave equation with high accuracy for modeling seismic wave propagation in tilted transversely isotropic (TTI) media. However, the derived pure qP-wave equation requires a computationally expensive spectral-based method for performing numerical simulations. This is unsuitable for large-scale industrial applications, particularly 3D applications. For numerical efficiency, we first decompose the newly derived wave equation into some fractional differential operators and spatial derivatives. The spatial derivatives can be directly solved by conventional finite-difference (FD) approaches. Then, we use an asymptotic approximation to find an equivalent form of fractional differential operators, obtaining scalar operators that we can discretize with the FD method. Numerical tests show that our TTI pure qP-wave equation with an FD discretization can produce accurate and highly efficient wavefield simulations in TTI media. We also use our TTI pure qP-wave equation with an FD discretization as a forward engine to implement TTI reverse time migration (RTM). Synthetic examples and a field data test demonstrate that our TTI RTM can effectively correct the anisotropic effects, providing high-quality imaging results while maintaining good computational efficiency.
Abstract Based on the elastic wave equation, a pseudoelastic pure P‐mode wave equation has been recently derived by projecting the wavefield along the wavefront normal direction. This pseudoelastic pure P‐mode wave equation offers an accurate simulation of P‐wave fields with accurate elastic phase and amplitude characteristics. Moreover, considering no S‐waves are involved, it is computationally more efficient than the elastic wave equation, making it an excellent choice as a forward simulation engine for P‐wave exploration. Here, we propose a new pseudoelastic pure P‐mode wave equation and apply the stress image method to it to implement the free surface boundary condition. The new pseudoelastic wave equation offers significantly improved computational efficiency compared to the previous pseudoelastic wave equation. Additionally, the wavefields simulated by this new pseudoelastic wave equation exhibit clear physical interpretations. We evaluate the accuracy of the new wave equation in simulating elastic P‐waves by employing a model with high‐velocity contrasts. We find that this new equation, which purely admits P‐waves, though having exact amplitude and phase behaviour as the elastic waves for transmission components, the amplitudes slightly suffer in the scattering scenario. The difference in amplitude between the elastic and our pseudoelastic increases as the contrast in velocity at the interface (interlayer velocity ratio) increases, especially the S‐wave velocities. This has negative implications on scattering from the free surface boundary condition or the sea bottom interface, especially if the shear wave velocity below the surface or the sea bottom is high. However, in cases where, like for land data in the Middle East, the transition to a free surface is smoother, the accuracy of the pseudoelastic equation is high. In all cases, regardless of the interlayer velocity ratio, the accuracy of the pseudoelastic wave equation in simulating the elastic case, for scattered waves, exceeds that of the acoustic wave equation in phase and amplitude.
'/%3e%3cuse xlink:href='%23a' transform='rotate(23.036 .093 25.536)'/%3e%3cuse xlink:href='%23a' transform='rotate(45.87 1.273 16.18)'/%3e%3cuse xlink:href='%23a' transform='rotate(69.945 .996 12.078)'/%3e%3cuse xlink:href='%23a' transform='rotate(20.66 -19.689 31.932)'/%3e%3c/svg%3e)