A rock physics strategy for quantifying uncertainty in common hydrocarbon indicators

Abstract

We present a strategy for quantifying uncertainties in rock physics interpretations by combining statistical techniques with deterministic rock physics relations derived from the laboratory and theory. A simple example combines Gassmann’s deterministic equation for fluid substitution with statistics inferred from log, core, and seismic data to detect hydrocarbons from observed seismic velocities. The formulation identifies the most likely pore fluid modulus corresponding to each observed seismic attribute and the uncertainty that arises because of natural variability in formation properties, in addition to the measurement uncertainties. We quantify the measure of information in terms of entropy and show the impact of additional data about S-wave velocity on the uncertainty of the hydrocarbon indicator. In some cases, noisy S data along with noisy P data can convey more information than perfect P data alone, while in other cases S data do not reduce the uncertainty. We apply the formulation to a well log example for detecting the most likely pore fluid and quantifying the associated uncertainty from observed sonic and density logs. The formulation offers a convenient way to implement deterministic fluid substitution equations in the realistic case when natural geologic variations cause the reference porosity and velocity to span a range of values.