Time domain Gauss-Newton seismic waveform inversion in elastic media

Abstract

S U M M A R YWe present a seismic waveform inversion methodology based on the Gauss-Newton method from pre-stack seismic data. The inversion employs a staggered-grid finite difference solution of the 2-D elastic wave equation in the time domain, allowing accurate simulation of all possible waves in elastic media. The partial derivatives for the Gauss-Newton method are obtained from the differential equation of the wave equation in terms of model parameters. The resulting wave equation and virtual sources from the reciprocity principle allow us to apply the Gauss-Newton method to seismic waveform inversion. The partial derivative wavefields are explicitly computed by convolution of forward wavefields propagated from each source with reciprocal wavefields from each receiver. The Gauss-Newton method for seismic waveform inversion was proposed in the 1980s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties which are addressed in this work. We used different sizes of grids for the inversion, temporal windowing, approximation of virtual sources, and parallelizing computations. With numerical experiments, we show that the Gauss-Newton method has significantly higher resolving power and convergence rate over the gradient method, and demonstrate potential applications to real seismic data.

Sinkholes and the Engineering and Environmental Impacts of Karst: Proceedings of the Fourteenth Multidisciplinary Conference

“…Where these data can be integrated into the design process, they offer lifecycle cost benefits, improvements to the safety of the traveling public, and protection of the environment, particularly in groundwater-sensitive karst terranes. (Shipp and Singh, 2002;Ravaut et al, 2004;Sheen et al, 2006;Cheong et al 2006;Brenders and Pratt, 2007;Choi and Alkhalifah, 2011;and others). In larger scale experiments surface waves can clearly separate from body waves and be removed in the inversion process.…”

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

“…Quasi-newton methods, such as the lBFGS (Malinkowski et al, 2011;Gholami et al, 2013;Dagnino et al, 2014), are now a commonplace implementation of Hessian-based FWI, in which the inverse Hessian is recursively estimated from the evolution of the gradient and model update over a number of previous iterations (Nocedal & Wright, 2006;Virieux & Operto, 2009). Sheen et al (2006) and Shin et al (2001), on the other hand, propose to reduce the computational burden of the partial derivative wavefield by exploiting the source-receiver reciprocity.…”

“…In the Gauss-Newton method, a locally linear misfit functional is assumed (Kormendi & Dietrich, 1991;Menke, 1989;Aster et al, 2005), which allows the second order term of the Hessian to be dropped (Virieux & Operto, 2009). We obtain explicitly the sensitivity matrix J by perturbing each model parameter at each layer depth; the resulting partial derivative wavefield is propagated from the secondary virtual sources to the receivers' position (Rodi, 1976;Sheen et al, 2006;Operto et al, 2013). The effectiveness of this approach in scaling and weighting the gradient is higher than the steepest-descent and quasi-Newton methods, because the approximate Hessian J T J is computed rather than statistically estimated.…”

Time-lapse walkaway vertical seismic profile monitoring for CO2 injection at the SACROC enhanced oil recovery field: A case study

“…The objective function can be minimized via, e.g., the Gauss-Newton or conjugate gradient methods. Because of the computation and memory cost of calculating the Hessian matrix (Sheen et al, 2006), we use the nonlinear conjugate gradient method because it does not require the Hessian matrix, and it has a better convergence rate than the steepest descent method (Rodi and Mackie, 2001). The model parameters are updated in each iteration according to…”