Analysis of prior models for a blocky inversion of seismic AVA data

Abstract

Resolving thinner layers and focusing layer boundaries better in inverted seismic sections are important challenges in exploration and production seismology to better identify a potential drilling target. Many seismic inversion methods are based on a least-squares optimization approach that can intrinsically lead to unfocused transitions between adjacent layers. A Bayesian seismic amplitude variation with angle (AVA) inversion algorithm forms sharper boundaries between layers when enforcing sparseness in the vertical gradients of the inversion results. The underlying principle is similar to high-resolution processing algorithms and has been adapted from digital-image-sharpening algorithms. We have investigated the Cauchy and Laplace statistical distributions for their potential to improve contrasts betweenlayers. An inversion algorithm is derived statistically from Bayes’ theorem and results in a nonlinear problem that requires an iterative solution approach. Bayesian inversions require knowledge of certain statistical properties of the model we want to invert for. The blocky inversion method requires an additional parameter besides the usual properties for a multivariate covariance matrix, which we can estimate from borehole data. Tests on synthetic and field data show that the blocky inversion algorithm can detect and enhance layer boundaries in seismic inversions by effectively suppressing side lobes. The analysis of the synthetic data suggests that the Laplace constraint performs more reliably, whereas the Cauchy constraint may not find the optimum solution by converging to a local minimum of the cost function and thereby introducing some numerical artifacts.

Exploitation of data-information content in elastic-waveform inversions

“…To take advantage of this feature, it could be useful to modify the smoothness constraints in the GaussNewton algorithm, such that an L 1 norm regularization would be applied. Several studies have demonstrated that L 1 norm regularization better reconstructs model edges (e.g., Theune, 2010). This could be implemented using the approach proposed by Farquharson and Oldenburg (1998).…”

Support Vector Machine (SVM) based prestack AVO inversion and its applications

“…To constrain and stabilize the AVO inversion problem, however, some scholars have endeavored to adopt different prior probabilistic constraints following a Bayesian framework. Based on the classical work on geophysical probabilistic inverse theory (e.g., Tarantola, 1987;Menke, 1989), they employ the Bayesian statistical method to formulate the AVO inversion problem successfully (Gouveia, 1996;Sen and Stoffa, 1996;Gouveia and Scales, 1998;Buland and Omre, 2003;Riedel et al, 2003;Downton, 2005;Rabben et al, 2008;Karimi et al, 2010;Theune et al, 2010;Alemie and Sacchi, 2011;Zong et al, 2013). In the literature listed above, some are using the linearized approximations (see Aki and Richards, 1980;Shuey, 1985;Smith and Gidlow, 1987;Gray et al, 1999;Ursin and Dahl, 1992;Wang, 1999;Ursenbach, 2002) and some are employing the accurate Zeoppritz equations (Simmons and Backus, 1996).…”

“…Since the occurrence of AVO analysis proposed by Ostrander (1984), it has received considerable attention in the field of seismic exploration (Aki and Richards, 1980;Smith and Gidlow, 1987;Swan, 1993;Simmons and Backus, 1996;Buland and Omre, 2003;Riedel et al, 2003;Downton, 2005;Rabben et al, 2008;Theune et al, 2010;Alemie and Sacchi, 2011;Zhang et al, 2013;Zong et al, 2013).…”

Three‐term inversion of prestack seismic data using a weighted l2, 1 mixed norm

“…In general, the coefficients of such approximations can be related to physical parameters associated to lithology, fluid, and porosity, key issues for the characterisation of hydrocarbon reservoirs (Ostrander ; Castagna, Swan and Foster ; Smith and Gidlow ; Chopra and Castagna ). Beyond the AVA/AVO analysis, AVA/AVO data inversion provides a more direct means to obtain estimates of the physical parameters of interest, such as the P‐ and S‐wave velocities and density (Buland and Omre ; Theune, Jensås and Eidsvik ).…”