Asymptotic solution to a 3D dipole single-well imaging system with combined monopole and dipole receivers with an application in elimination of azimuth ambiguity

Abstract

Single-well imaging (SWI) is a borehole measurement technique aimed at detecting geologic interfaces or structures tens of meters away from the borehole. In SWI, acoustic signals generated by a monopole or a dipole source in the borehole are reflected by geologic interfaces and received by arrays of receivers of the same type. Current SWI cannot determine the azimuth angle of the geologic interfaces uniquely. We have developed a new SWI system with combined dipole and monopole receivers for a dipole source. This system can be used to determine the azimuth angle uniquely. The other difficult issue is to quickly simulate the wavefield of SWI to meet the needs of real-time data processing in field logging. We derive asymptotic solutions of the horizontal displacement and the fluid pressure for the reflected wave from the geologic interfaces in this nonaxisymmetric system. The radiation fields of a monopole and a dipole are computed using the steepest-descent integration method. The wave reflected from a reflector outside the borehole is proved to be equivalent to the radiation of a virtual source outside the borehole. We use the reciprocity relation between the virtual source and a monopole or a dipole source to obtain the asymptotic solutions of fluid pressure or horizontal displacement for the reflected wave. The asymptotic results agree well with those from 3D finite-difference simulation. The asymptotic solution demonstrates the polarity of fluid pressure changes when the azimuth angle changes by 180°. Based on the characteristics of asymptotic solutions, we evaluate a scheme to determine the azimuth uniquely.