Explicit imaging expressions for weak horizontal transverse isotropy

Abstract

SUMMARY Despite the recognized prevalence of vertical parallel cracks in reservoir rocks, the necessary imaging expressions for the weak HTI (horizontal transverse isotropy) system have not been studied in sufficient generality. With the exception of the P-wave phase velocity formula, the existing first-order HTI expressions are restricted to certain regimes of applicability. The HTI and VTI (vertical TI) systems are distinguished from one another merely by the way they are configured in relation to the acquisition coordinate system. In this paper, using coordinate transformation rules connecting the two systems, we first map all the coordinate dependent physical quantities appearing in the imaging VTI expressions, to their HTI counterparts - the mapped quantities are accurate to first-order. Then, by a simple substitution into the VTI expressions, we develop a complete suite of imaging expressions for systems with weak HTI. Our P- and S-wave phase velocity, polarization, and group velocity expressions are entirely general, in that they account for wave propagation in arbitrary directions within the HTI media. Thus, they can be readily incorporated into the multi-component production processing algorithms.