Introduction
Porosity and saturation are the two flow parameters often required in reservoir characterization. The estimation of these parameters from seismic data is not a trivial task since most seismic models ignore poro-elasticity. A sequential method first estimates porosity and then predicts saturation by keeping the porosity fixed - this may be subject to error. Estimation of porosity and saturation from inverted elastic parameters , and density will also lead to error due to propagation of previous inversion errors. To overcome these difficulties, we have developed a stochastic inversion method to jointly estimate porosity and saturation by combining a rock physics model and pre-stack seismic waveform inversion. The model parameters in our inversion are porosity and saturation that are converted to elastic parameters using a rock physics model or a statistical petrophysical relationship, at every iteration of the inversion. At each CMP location. we generate synthetic seismograms using a reflectivity method and employ a global optimization method based on very fast simulated annealing (VFSA) to search for the optimal model parameters. One novel aspect of our algorithm is the use of wavelets in model descriptions that helps in constraining the high as well as low frequency variations of the elastic models. Further a direct search over porosity and saturation results in a much reduced model space resulting in a better constrained solution. We demonstrate our technique using a synthetic case study based on a well log from the Gulf of Mexico. The optimization algorithm is very general in that it allows for the use of statistical prior and nonlinear uncertainty estimation. v p vs
Seismic data contain invaluable sources of information for reservoir characterization as it provides extensive spatial coverage with dense and regular lateral sampling, especially when compared to the sparse well locations. However, estimation of reservoir parameters from reflection seismic data is a challenging task and subject to much uncertainty. Over the years, there have been many studies on how to infer reservoir parameters from seismic data. Initially, only post-stack seismic data were used; for example, Maureau et al. (1979) employed a direct linear impedance-porosity relationship to recover porosity. A similar approach was also used by Angeleri (1982). Geostatistical techniques are now applied to model porosity maps as demonstrated by Doyen (1988, 1996). The objective of this method is to improve resolution and implement uncertainty analysis. Hampson (2001) proposed predicting porosity by using a multi-attribute transform and neural network approach. Pre-stack seismic inversion provides more elastic parameters for reservoir characterization, such as acoustic and shear impedance, compressional and shear velocity, and density (Sen and Stoffa 1991; Pendrel 2000; Ma 2001a, 2001b; Sen and Roy 2003; Hampson 2005). From the rock physics model and statistical analysis, it is known that the compressional velocity is sensitive to saturation but shear velocity is not. Both compressional and shear velocity are, however, sensitive to porosity. This is the physical basis for separating porosity and saturation from elastic parameters and therefore, pre-stack inversion is ideally suited for this purpose.
