Orthotropic anisotropy analysis and parameter estimation from 3-D vertical seismic profile data

Orthotropic velocity models are commonly considered as to have the lowest complexity (or highest symmetry) that can realistically describe the combined effect of Earth's velocity heterogeneity in the vertical and in the horizontal (radial) directions. Velocity heterogeneity in the vertical direction is commonly caused by horizontal stratification of subsurface rock layers with different elastic properties or caused intrinsically by microlayered rocks such as shales. In the horizontal direction, azimuthal variation of the Earth's stress field can initially lead to preferential deformation of pore space in the rocks and eventual development of aligned (vertical) fractures that are commonly regarded as the main cause for seismic azimuthal anisotropy. Building an appropriate orthotropic velocity model that can explain seismic velocity variations in vertical planes and along any azimuthal direction can therefore enhance the quality of seismic data processing and imaging. This, however, requires knowledge of several anisotropy parameters defined in the three symmetry planes of the orthotropic model and also the orientation of these planes. A combination of P- and S-wave slowness and polarization data derived from vertical seismic profile (VSP) measurements has been routinely used to estimate parameters of less complex anisotropic media such as transverse isotropy with vertical axes of symmetry (VTI). The accuracy of anisotropy parameter estimation by these methods depends primarily on the availability of data that are used in the inversion and the size of anisotropy parameters. In this study, we develop a benchmark for the accuracy of orthotropic parameters that are estimated from 3-D VSP measurements using P-wave slowness only method. Through numerical analysis, we model a wide range of fracture-induced orthotropic symmetries by adding vertical fractures to a background VTI media and show that the accuracy of our orthotropic parameter estimation method is dependent on anisotropy in the host media, intensity of fracturing, noise level in slowness data and slowness data coverage in both the dip and azimuthal planes. We then expand our accuracy analysis work to multilayer media by examining the accuracy of P-wave slowness method for orthotropic anisotropy parameter estimation by inverting finite-difference data generated in a pseudo 3-D VSP experiment. We show that, for a typical 3-D VSP experiment, reasonable estimates of orthotropic parameters in the model can only be obtained with slowness data taken from X-max/Z >= 1 and line azimuth interval phi <= 10 degrees where X-max is the maximum source to receiver offset and Z is the receiver depth. We finally describe how field VSP measurements can be inverted for orthotropic anisotropy parameters.

Automated summary

Orthotropic velocity models play an important role in seismic data processing and imaging by explaining velocity variations in both vertical and horizontal directions. The accuracy of estimating orthotropic parameters depends on factors such as fracture-induced symmetries, noise level, and data coverage. This study also examines the accuracy of estimating orthotropic anisotropy parameters in multilayer media and presents a method for inverting field VSP measurements.