Summary
Traditional seismic inversion approaches have focused on reducing error between data and model within a fixed geological scenario. The problem with this approach is that either uncertainty related to geological interpretation is ignored or that inversion needs to be repeated for each scenario. In this paper we propose to first assess the consistency of all available geologic scenarios with the observed data by defining a pattern similarity between seismic data and forward simulated data. The considered scenarios include geologic variables (such as facies proportions, geobody size, and stacking patterns), as well as rock physics relationships relating rock properties to seismic data. We develop a pattern-based procedure to estimate the probability of each scenario given seismic data. Low probability scenarios are rejected. To estimate this probability, we generate a set of models from each scenario, and calculate distances between forward modeled seismic data and actual data. The distance between two seismic responses is defined as the difference in frequency of patterns found in the images. We use two different patternbased techniques, namely Multiple Points Histogram (MPH) and Discrete Wavelet Transform (DWT). Next we apply the Jensen-Shannon (JS) divergence to evaluate the distance between the frequency distributions of two images (MPH frequencies and wavelet coefficients frequencies in each sub-band). The resulting distance matrix can be projected in multi-dimensional scaling (MDS) space to estimate the likelihood distributions of each scenario given the data. The likelihood is evaluated using an adaptive kernel smoothing technique. The proposed workflow is applied on 2D seismic section with 16 geologic scenarios, and verified by success rates of a Bayesian confusion matrix and a comparison with rejection sampler.
