TONGJI -- TABLE OF CONTENTS |

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly as the operators involved are dependent on the velocity, and thus are not stationary. We develop an efficient pseudo-spectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We apply -space adjustment to the pseudo-spectral solution to allow for a relatively large extrapolation time-step. The low-rank approximation is, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models show that, our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields, for elastic wave modeling, imaging and inversion.

Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media [pdf 13M]

Wave mode separation and vector decomposition are significantly more expensive than wavefield extrapolation and are the computational bottleneck for elastic reverse-time migration (ERTM) in heterogeneous anisotropic media. We express elastic wave mode separation and vector decomposition for anisotropic media as space-wavenumber-domain operations in the form of Fourier integral operators, and develop fast algorithms for their implementation using their low-rank approximations. Synthetic data generated from 2D and 3D models demonstrate that these methods are accurate and efficient.

Simulating propagation of separated wave modes in general anisotropic media, Part II: qS-wave propagators [pdf 2.9M]

Shear waves, especially converted modes in multicomponent seismic data, provide significant information that allows better delineation of geological structures and characterization of petroleum reservoirs. Seismic imaging and inversion based upon the elastic wave equation involve high computational cost and many challenges in decoupling the wave modes and estimating so many model parameters. For transversely isotropic media, shear waves can be designated as pure SH and quasi-SV modes. Through two different similarity transformations to the Christoffel equation aiming to project the vector displacement wavefields onto the isotropic references of the polarization directions, we derive simplified second-order systems (i.e., pseudo-pure-mode wave equations) for SH- and qSV-waves, respectively. The first system propagates a vector wavefield with two horizontal components, of which the summation produces pure-mode scalar SH-wave data, while the second propagates a vector wavefield with a summed horizontal component and a vertical component, of which the final summation produces a scalar field dominated by qSV-waves in energy. The simulated SH- or qSV-wave has the same kinematics as its counterpart in the elastic wavefield. As explained in our previous paper (part I), we can obtain completely separated scalar qSV-wave fields after spatial filtering the pseudo-pure-mode qSV-wave fields. Synthetic examples demonstrate that these wave propagators provide efficient and flexible tools for qS-wave extrapolation in general transversely isotropic media.

Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators [pdf 2.8M]

Wave propagation in an anisotropic medium is inherently described by elastic wave equations, with P- and S-wave modes intrinsically coupled. We present an approach to simulate propagation of separated wave modes for forward modeling, migration, waveform inversion and other applications in general anisotropic media. The proposed approach consists of two cascaded computational steps. First, we simulate equivalent elastic anisotropic wavefields with a minimal second-order coupled system (that we call here a pseudo-pure-mode wave equation), which describes propagation of all wave modes with a partial wave mode separation. Such a system for qP-wave is derived from the inverse Fourier transform of the Christoffel equation after a similarity transformation, which aims to project the original vector displacement wavefields onto isotropic references of the polarization directions of qP-waves. It accurately describes the kinematics of all wave modes and enhances qP-waves when the pseudo-pure-mode wavefield components are summed. The second step is a filtering to further project the pseudo-pure-mode wavefields onto the polarization directions of qP-waves so that residual qS-wave energy is removed and scalar qP-wave fields are accurately separated at each time step during wavefield extrapolation. As demonstrated in the numerical examples, pseudo-pure-mode wave equation plus correction of projection deviation provides a robust and flexible tool for simulating propagation of separated wave modes in transversely isotropic and orthorhombic media. The synthetic example of Hess VTI model shows that the pseudo-pure-mode qP-wave equation can be used in prestack reverse-time migration (RTM) applications.

TONGJI -- TABLE OF CONTENTS |

2017-07-28