Spatial categorical inversion: Seismic inversion into lithology/fluid classes
Seminar Room 1, Newton Institute
Modeling of discrete variables in a three-dimensional reference space is a challenging problem. Constraints on the model expressed as invalid local combinations and as indirect measurements of spatial averages add even more complexity.
Evaluation of offshore petroleum reservoirs covering many square kilometers and buried at several kilometers depth contain problems of this type. Foc us is on identification of hydrocarbon (gas or oil) pockets in the subsurface - these appear as rare events. The reservoir is classified into lithology (rock) cla sses - shale and sandstone - and the latter contains fluids - either gas, oil or brine (salt water). It is known that these classes are vertically thin with large horizontal continuity. The reservoir is considered to be in equilibrium - hence fixed vertical sequences of fluids - gas/oil/brine - occur due to gravitational sorting. Seismic surveys covering the reservoir is made and through processing of the data, angle-dependent amplitudes of reflections are available. Moreover, a few wells are drilled through the reservoir and exact obse rvations of the reservoir properties are collected along the well trace.
The inversion is phrased in a hierarchical Bayesian inversion framework. The prior model, capturing the geometry and ordering of the classes, is of Markov random field type. A particular parameterization coined Profile Markov random field is def ined. The likelihood model linking lithology/fluids and seismic data captures maj or characteristics of rock physics models and the wave equation. Several parameters in this likelihood model are considered to be stochastic and they are inferred from seismic data and observations along the well trace. The posterior model is explored by an extremely efficient MCMC-algorithm.
The methodology is defined and demonstrated on observations from a real North Sea reservoir.