Multidimensional scaling for the evaluation of a geostatistical seismic elastic inversion methodology

Abstract

Due to the nature of seismic inversion problems, there are multiple possible solutions that can equally fit the observed seismic data while diverging from the real subsurface model. Consequently, it is important to assess how inverse-impedance models are converging toward the real subsurface model. For this purpose, we evaluated a new methodology to combine the multidimensional scaling (MDS) technique with an iterative geostatistical elastic seismic inversion algorithm. The geostatistical inversion algorithm inverted partial angle stacks directly for acoustic and elastic impedance (AI and EI) models. It was based on a genetic algorithm in which the model perturbation at each iteration was performed recurring to stochastic sequential simulation. To assess the reliability and convergence of the inverted models at each step, the simulated models can be projected in a metric space computed by MDS. This projection allowed distinguishing similar from variable models and assessing the convergence of inverted models toward the real impedance ones. The geostatistical inversion results of a synthetic data set, in which the real AI and EI models are known, were plotted in this metric space along with the known impedance models. We applied the same principle to a real data set using a crossvalidation technique. These examples revealed that the MDS is a valuable tool to evaluate the convergence of the inverse methodology and the impedance model variability among each iteration of the inversion process. Particularly for the geostatistical inversion algorithm we evaluated, it retrieves reliable impedance models while still producing a set of simulated models with considerable variability.

Geostatistics for Seismic Characterization of Oil Reservoirs

“…Detailed application examples of this method can be found in the following studies: Nunes et al (2012), Azevedo et al (2013b), Azevedo and Soares (2017). For illustrative purpose, here we show the application of this methodology to the same case study shown in the previous section.…”

“…The acoustic inversion algorithm was extended for the inversion of partial angle stacks directly, and simultaneously, for acoustic and elastic impedance (Is) models (Nunes et al 2012;Azevedo et al 2013b). The main purpose of this development was the integration of more information, related with the elastic domain (Is), to enrich the final elastic reservoir models allowing better lithofacies prediction.…”

Geostatistical seismic inversion for non‐stationary patterns using direct sequential simulation and co‐simulation

“…However, they are normally incapable of providing an uncertainty analysis of the inverse solution as they are normally limited by a linearisation problem around the best‐fit solution (Azevedo et al . ).…”

Exploring seismic inversion methodologies for non‐stationary geological environments: a benchmark study between deterministic and geostatistical seismic inversion

“…This work also includes the assessment of how the model parameter space is explored by each inversion technique individually and how different initial guesses for deterministic inversion solutions impact these results (Azevedo et al . ).…”

“…In this work, we present a new highly non-stationary and realistic three-dimensional synthetic dataset (CERENA-IV), built exclusively to assess the performance of different seismic inversion methodologies (both deterministic and stochastic) in reproducing the real elastic models. This work also includes the assessment of how the model parameter space is explored by each inversion technique individually and how different initial guesses for deterministic inversion solutions impact these results (Azevedo et al 2013a).…”