ALBERT

Description: A three dimensional, second order finite difference method was used to create synthetic seismograms for elastic wave propagation in heterogeneous media. These synthetic seismograms are used to model rough seafloor, the shallow crust, or complex structural and stratigraphic settings with strong lateral heterogeneities. The finite difference method is preferred because it allows models of any complexity to be generated and includes all multiple scattering, wave conversion and diffraction effects. The method uses a fully staggered grid as developed by Virieux (1986). Wavefront snapshots and time series output allow the scattering and focussing of different wave modes with direction to be visualized. The extensive calculations required for realistic size models stretches the resources of serial computers like the VAX 8800. On the Connection Machine, a massively parallel computer, the finite difference grid can be directly mapped onto the virtual processors, reducing the nested time and space loops in the serial code to a single time loop. As a result, the computation time is reduced dramatically.

Description: Funding provided by Office of Naval Research under Contract Numbers: N00014-87-K-0007 and N00014-89-J-1012.

Description: We describe a methodology for quantitatively characterizing the fractured nature of a hydrocarbon or geothermal reservoir from surface seismic data under a Bayesian inference framework. The method combines different kinds of measurements of fracture properties to find a best-fitting model while providing estimates of the uncertainty of model parameters. Fractures provide pathways for fluid flow in a reservoir, and hence, knowledge about a reservoir's fractured nature can be used to enhance production from the reservoir. The fracture properties of interest in this study (to be inferred) are fracture orientation and excess compliance, where each of these properties are assumed to vary spatially over a 2-D horizontal grid which is assumed to represent the top of a reservoir. The Bayesian framework in which the inference problem is cast has the key benefits of (1) utilization of a prior model that allows geological information to be incorporated, (2) providing a straightforward means of incorporating all measurements (across the 2-D spatial grid) into the estimates at each gridpoint, (3) allowing different types of measurements to be combined under a single inference procedure and (4) providing a measure of uncertainty in the estimates. The observed data are taken from a 2-D array of surface seismic receivers responding to an array of surface sources. Well understood features from the seismic traces are extracted and treated as the observed data, namely the P -wave reflection amplitude variation with acquisition azimuth and offset (amplitude versus azimuth data) and fracture transfer function (FTF) data. Amplitude versus azimuth data are known to be more sensitive to fracture properties when the fracture spacing is significantly smaller than the seismic wavelength, whereas FTF data are more sensitive to fracture properties when the fracture spacing is on the order of the seismic wavelength. Combining these two measurements has the benefit of allowing inferences to be made about fracture properties over a larger range of fracture spacing than otherwise attainable. Geophysical forward models for the measurements are used to arrive at likelihood models for the data. The prior distribution for the fracture variables is obtained by defining a Markov random field over the lateral 2-D grid where we wish to obtain fracture properties, where this method for defining the prior has the added benefit of allowing for non-stationarity in the resulting model covariance. The fracture variables are then inferred by application of loopy belief propagation to yield approximations for the posterior marginal distributions of the fracture properties, as well as the maximum a posteriori and Bayes least-squares (posterior mean) estimates of these properties. Verification of the inference procedure is performed using a synthetic data set, where the estimates obtained are shown to be at or near ground truth for the full range of fracture spacings for fracture orientation and at low fracture spacings for excess compliance estimates.