A strategy for nonlinear elastic inversion of seismic reflection data

Abstract

The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of obtaining the Earth model for which the predicted data best fit the observed data. If an adequate forward model is used, this best model will give the best images of the Earth's interior.

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

“…An isotropic and elastic medium is univocally described by a spatial distribution of three independent parameters (Aki & Richards, 2002), most commonly density and the Lamè coefficients (Tarantola, 1986); although equivalent in a forward modelling sense, different parametrisations have different convergence properties and parameters' resolution. The most desirable parametrisation guarantees the minimum crosstalk among the unknowns of the inversion (Tarantola, 1986;Kormendi & Dietrich, 1991); ideally, the partial derivative wavefield of one parameter should be uncorrelated with the residual wavefield produced by each other independent parameter (Tarantola, 1986;Operto et al, 2013).…”

“…The most desirable parametrisation guarantees the minimum crosstalk among the unknowns of the inversion (Tarantola, 1986;Kormendi & Dietrich, 1991); ideally, the partial derivative wavefield of one parameter should be uncorrelated with the residual wavefield produced by each other independent parameter (Tarantola, 1986;Operto et al, 2013). In marine reflection seismic data, the presence of only one propagation mode impedes the opportunity to obtain independent estimates of P-wave (Vp) and S-wave velocity (Vs) (Jin et al, 1992;Igel et al, 1996); on the other hand, density is strongly coupled with P-wave velocity at narrow reflection angle; the two parameters can't be effectively resolved and in fact yield a posterior reconstruction of the P-impedance model (Tarantola, 1986;Operto et al, 2013). Here we choose to parametrise the reflectivity of the earth model as a distribution of P-impedance, Poisson's ratio and density (Debski & Tarantola, 1995;Igel et al, 1996), super-imposed to a long-wavelength P-wave velocity model that controls the wavefield kinematic (Tarantola, 1986;Jannane, 1989).…”

“…The limited offset, limited bandwidth, lack of diving waves and multi-component data of UHF data produce a highly hierarchical dependancy on the multi-parameter space as a function of the reflection angle range (Tarantola, 1986). P-impedance is the dominant parameter over the whole angle range, and it is sufficient to explain the reflected energy at near-zero reflection angle (Tarantola, 1986).…”

“…Although such properties can be retrieved through the inversion of the reflections' AVO, a full waveform approach has the advantage to account for all the wave phenomena (Tarantola, 1984(Tarantola, , 1986Fichtner, 2011), within the required resolution and modelling approximation. By exploiting the information contained in the complete waveform, FWI outperforms AVO inversion in most realistic reservoir geophysics application (Mallick & Adhikari, 2015), especially when complicated layer interference and velocity gradients are present (Xu et al, 1993;Igel et al, 1996), which is likely to be a factor in UHF near-surface seismic data.…”

A local adaptive method for the numerical approximation in seismic wave modelling

“…Nowadays, in seismic exploration, it is common to formulate the problem of estimation of a high-resolution subsurface model as an optimization problem in which the difference between the observed and the predicted seismograms is minimized applying optimization algorithms (e.g., [1,2]). The predicted data can be obtained by the numerical solution of the wave equation using suitable numerical schemes, with the aim of improving either the approximation error or reducing the computation cost.…”