Seismic simultaneous inversion using a multidamped subspace method

Abstract

Seismic inversion of amplitude variation with offset (AVO) plays a key role in seismic interpretation and reservoir characterization. The AVO inversion should be a simultaneous inversion that inverts for three elastic parameters simultaneously: the P-wave impedance, S-wave impedance, and density. Using only seismic P-wave reflection data with a limited source-receiver offset range, the AVO simultaneous inversion can obtain two elastic parameters reliably, but it is difficult to invert for the third parameter, usually the density term. To address this difficulty in the AVO simultaneous inversion, we used a subspace inversion method in which we partitioned the elastic parameters into different subspaces. We parameterized each single elastic parameter with a truncated Fourier series and inverted for the Fourier coefficients. Because the Fourier coefficients of different wavenumber components have different sensitivities, we grouped the Fourier coefficients of low-, medium-, and high-wavenumber components into different subspaces. We further assigned different damping factors to the Hessian matrix corresponding to different wavenumber components within each subspace. This inversion scheme is referred to as a multidamped subspace method. Synthetic and field seismic data examples confirmed that the AVO simultaneous inversion with this multidamped subspace method is capable of producing reliable estimation of the three elastic parameters simultaneously.

Indifference Computer Experiment for Mathematical Identification of Two Variables

“…This method modifies the Gaussian process prior according to the form of the equation and is used to infer the parameters of linear PDEs from observations. Liu et al proposed the use of deep neural networks to approximate the solutions of high-dimensional partial differential equations; the network is iterated to satisfy differential operators, initial conditions, and boundary conditions; the neural network operates on a randomly sampled set of time and space points, iteratively; the solution is approximated by a neural network [10]. Parise et al by using different neural network structures and different parameterizations improved machine learning algorithms for solving semilinear partial differential equations; the proposed algorithm is compared with several algorithms that utilize deep learning techniques to solve semilinear PDE problems [11].…”