Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions

Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation.

[1]  A. Koesoemadinata,et al.  Seismic Reservoir Characterization In Marcellus Shale , 2011 .

[2]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[3]  Amilcar Soares,et al.  Stochastic Inversion with a Global Perturbation Method , 2007 .

[4]  Tapan Mukerji,et al.  Seismic inversion combining rock physics and multiple-point geostatistics , 2008 .

[5]  Luís,et al.  Geostatistical Inversion of Prestack Seismic Data , 2012 .

[6]  A. Soares Direct Sequential Simulation and Cosimulation , 2001 .

[7]  Rúben Nunes,et al.  Parallelization of sequential Gaussian, indicator and direct simulation algorithms , 2010, Comput. Geosci..

[8]  Alexandre Boucher,et al.  A SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM , 2008, Comput. Geosci..

[9]  Andre G. Journel,et al.  Constraining Stochastic Images to Seismic Data , 1993 .

[10]  Amilcar Soares,et al.  Direct Sequential Co-simulation with Joint Probability Distributions , 2010 .

[11]  Amilcar Soares,et al.  Simulation of continuous variables at meander structures: application to contaminated sediments of a lagoon , 2010 .

[12]  C. Burns Seismic Reservoir Characterization , 1999 .

[13]  O. Dubrule,et al.  Geostatistical inversion - a sequential method of stochastic reservoir modelling constrained by seismic data , 1994 .

[14]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[15]  Guenther Schwedersky Neto,et al.  Integration of well data into geostatistical seismic amplitude variation with angle inversion for facies estimation , 2015 .

[16]  Gregoire Mariethoz,et al.  The Direct Sampling method to perform multiple‐point geostatistical simulations , 2010 .