Multiparameter 𝓁₁norm waveform fitting: Interpretation of Gulf of Mexico reflection seismograms

Abstract

Estimation of the elastic properties of the crust from surface seismic recordings is of great importance for the understanding of lithology and for the detection of mineral resources. Although in marine reflection experiments only P-waves are recorded, information on shear properties of the medium is contained in multioffset reflection seismograms. Being able to retrieve both dilatational and shear properties gives stronger constraints on the lithology. It is therefore desirable to recover isotropic elastic parameters from multioffset seismograms. Unfortunately, most classical waveform fitting methods used for extracting shear properties of the subsurface are based on a 1-D earth model assumption and on linear approximations of the wave equations. In this paper, a 2.5-D elastic waveform inversion method is used to extract the variations of acoustic impedance and Poisson’s ratio from marine multioffset reflection seismograms collected in the Gulf of Mexico area. A complete seismic profile is interpreted, including complex physical phenomena apparent in the data, such as unconsolidated sediment reflections and seismic refraction events. The amplitude of the reflections cannot be explained by one parameter related to the dilatational properties (P-impedance) only, when trying to minimize the least absolute fit between observed and synthetic seismograms. When adding an additional parameter related to shear properties (Poisson’s ratio), the fit between observed and synthetic seismograms improves. The resulting 2-D models of P-impedance and Poisson’s ratio contrasts are anticorrelated almost everywhere in depth, except where hydrocarbons are present. The estimation of physical P-impedance and Poisson’s ratio models by a full waveform fitting allows lithology characterization and, therefore, the delineation of a shale‐over‐gas sand reservoir.

Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

“…The first numerical tests based on finitedifference simulations of the seismic signal showed promising results (Gauthier et al, 1986). Since then, several full-waveform inversion algorithms, based on Tarantola's pioneering work, have been developed and applied to seismic data (e.g., Mora, 1987;Crase et al, 1990;Djikpéssé and Tarantola, 1999).…”

Valuing recent advances in seismic-while-drilling applications by estimating uncertainty reduction in real-time interpreted velocity measurements

“…matrix (C M ) helps control the smoothness of the inverted model (e.g.,Tarantola, 1987, Djikpesse and Tarantola, 1999, Djikpesse et al, 2006.…”

Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function

“…The normalized zero-lag cross-correlation function relaxes on the amplitude matching, so that it can tolerate wrong or unpredictable amplitude (in the observed data) that cannot be modelled by wavefield extrapolation operator. Thus, in order to compare with the performances both of the L2 norm and the normalized zero-lag cross-correlation function with the performance of the Huber norm as, which is known as its robustness (Djikpéssé & Tarantola 1999;Guitton & Symes 2003;Brossier et al 2009Brossier et al , 2010Ha et al 2009;Pyun et al 2009;Bulcão et al 2013;Jimenez Tejero et al 2014), we also invert all the previously rescaled traces with the Huber norm. As pointed by Brossier et al (2010), the threshold value ε = 0.2 mean(|d obs i |) for the Huber criterion is less sensitive to outliers in the data than the one indicated by Guitton & Symes (2003) based on max(|d obsi |).…”

“…Since the direct amplitude matching of the least-squares (L2) norm is never perfect, it is desirable an objective function with robust performance to deal with this kind of data. To address this problem, some authors have proposed several objective functions (Djikpéssé & Tarantola 1999;Guitton & Symes 2003;Brossier et al 2009Brossier et al , 2010Ha et al 2009;Pyun et al 2009;Bulcão et al 2013;Jimenez Tejero et al 2014). The Huber function (Huber 1973) is highlighted as the most robust norm among all of them.…”