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

ABSTRACT Geostatistical seismic inversion methods are routinely used in reservoir characterisation studies because of their potential to infer the spatial distribution of the petro‐elastic properties of interest (e.g., density, elastic, and acoustic impedance) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and a global spatial continuity model as estimated from the available well‐log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous, and, in many cases, non‐stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, the application of a single distribution function and a spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a three‐dimensional geostatistical inversion technique that is able to incorporate the reservoir's heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi‐distribution functions and spatial continuity models under non‐stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non‐stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques.