A Bayesian framework for fracture characterization from surface seismic data

作者：Zamanian S Ahmad^*; Fehler Michael C; Fang Xinding; Burns Daniel R

来源：Geophysical Journal International, 2014, 199(2): 1230-1244.

DOI：10.1093/gji/ggu321

• Probability distributions
• Fracture and flow
• Seismic anisotropy
• Computational seismology
• Statistical seismology
• Wave scattering and diffraction

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 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.

• 出版日期2014-11
• 单位MIT