Effective medium modeling: How to efficiently infer porosity from seismic data?

Many geophysical studies in reservoir characterization focus on the variations in the elastic properties of rocks. They commonly involve seismic data, which are processed in terms of seismic attributes. These processed data still have to be related to the physical properties of the rock mass and the fluids saturating the pore space. This need motivated the development of research projects based upon the effective medium theory (EMT). We have used the EMT to infer porosity and also fracture data from seismic impedances in part of the Fort Worth Basin, Texas. The main idea was to take advantage of the available impedances to characterize porosity in terms of equant pores and cracks. We then focused on the volume fraction of spherical pores and crack density. Shortly thereafter, we developed an effective medium (EM) model that provided numerical responses for seismic impedances. These responses were then compared to the impedances obtained from stratigraphic inversion. The overall procedure consisted in adjusting the input parameters of the EMT model, which were the spherical porosity and the crack density, to minimize the impedance mismatch. Our case study involved two limestone formations of the Fort Worth Basin (the Marble Falls and Ellenburger Formations) and one shaly formation (the Barnett Shale). The results are promising - The EMT turns out to be a very useful tool to explain reservoir and geophysical data in terms of microstructural properties, in particular, for fractured reservoirs.