f Moving point mechanism representation for low frewuency monopole borehole sensors

In this paper we derive the equivalent line mechanism for the case of low frequency monopole sources and receivers in boreholes. This line mechanism is equal to a point mechanism which propagates at the speed of tube waves. This was first recognized and treated in White and Sengbush (Geophysics, 28, p. 1001-1019). The resulting far-field radiation (or receptivity) pattern is a generalization of that published by Lee and Balch (Geophysics, 47, p 1308-1314) in that it addresses the case where the shear velocity is close to or slower than the tube wave speed. The equivalent moving point representation can be incorporated into existing modeling codes, thereby avoiding the need to directly model the borehole. Furthermore, realistic borehole environments (such as casing, caliper logs, curved welk, anisotropic formations, etc) can be incorporated into the equivalent representation.