Study on the radiation and reception of the wave field in a single-well imaging system with an eccentric source

The far-field asymptotic solutions to the wave field excited by an eccentric point source in a fluid-filled borehole are derived by the steepest descent integration method. When there is a reflector outside the borehole, the asymptotic solution to the reflected wave field received by eccentric receivers in the borehole is obtained using reciprocity. The asymptotic results are in good agreement with those from the finite difference method. The effects of frequency and eccentric distance on the wave field are analyzed. Simulations show that frequency is the dominant factor affecting the wave field outside the borehole. When the frequency is low, the far-field wave field excited by the eccentric source is independent of eccentric distance, and the eccentric source can be regarded as a central source. When the frequency is high, the difference between the farfield wave field excited by the eccentric point source and the central source cannot be neglected. The higher the frequency and the greater the eccentric distance, the greater the difference is. Simulations also show that the amplitude of the radiated wave field and the received wave field are both azimuth-dependent when using the eccentric source and eccentric receivers. Finally, an example is given to show the elimination of the 180 degrees uncertainty of azimuth angle of the reflector by using the variation of reflected wave amplitude.