Xiaolei Song

Seismic Wave Extrapolation Using Lowrank Symbol Approximation

We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media.

Lowrank Finite-differences and Lowrank Fourier Finite-differences for Seismic Wave Extrapolation

We introduce a novel finite-difference approach for seismic wave extrapolation in time. We derive the coefficients of the finite-difference operator from a lowrank approximation of the space-wavenumber, wave-propagator matrix. Numerical examples confirm the validity of the proposed technique. Based on the technique of lowrank finite-differences, we also improve the finite difference scheme of the two-way Fourier finite differences (FFD). We call the new operator: lowrank Fourier finite differences (LFFD). Both the lowrank FD and lowrank FFD method can be applied to enhance accuracy in seismic imaging by reverse-time migration.

Time‐lapse pre‐stack seismic data registration and inversion for CO2 sequestration study at Cranfield

Pre-stack seismic data are indicative of subsurface elastic properties within the amplitude versus offset characteristic and can be used to detect elastic rock property changes caused by CO2 injection. We perform time-lapse pre-stack 3-D seismic data analysis for monitoring CO2 sequestration at Cranfield. The time-lapse amplitude differences of Cranfield datasets are found entangled with time-shifts. To disentangle these two characters, we apply a local-correlation-based warping method to register the time-lapse pre-stack datasets, which can effectively separate the time-shift from the time-lapse seismic amplitude difference without changing the original amplitudes. We demonstrate the effectiveness of our registration method by evaluating the inverted elastic properties. These inverted time-lapse elastic properties can be reliably used for monitoring CO2 plumes.

Lowrank finite-differences for wave extrapolation

We introduce a novel finite-difference approach for seismic wave extrapolation in time. Compared with those of conventional finite-difference (FD) methods, the coefficients of the new method are variables in space. We derive the finitedifference operator from a lowrank approximation of the space-wavenumber, wave-propagator matrix. We present a mathematical derivation of this method. Numerical examples confirm the validity of the proposed technique. The lowrank FD method can be applied to enhancing accuracy and stability in seismic imaging by reverse-time migration.