Analysis and processing of received signals in boreholes

This study is a part of a project to develop a borehole sonar for acoustic imaging of the geological structure of the rock formation near to a deviate d or horizontal borehole performed while drilling. The purpose of the sonar is to provide a direct measure of the distance and the direction to bed bo undaries parallel to the borehole. This paper gives a theoretical analysis of the effect of the borehole and the drillstring on the received response on sensors positioned on the drillstring and proposes a method for processi ng the received signal to enable the determination of the direction of an i ncoming plane wave and time of arrival. In the first part of this paper, th e response at any position in a fluid filled borehole is determined for an incoming plane P-wave. It is shown that the response is quite complicated a nd consists of several vibrating modes with resonance structure. Secondly, the paper presents how the received signals can be decomposed and the indiv idual modes can be resolved by utilizing the orthogonal properties of the m ode functions. The individual mode functions are resolved by performing a s patial Fourier transform of the sensor signals. A requirement is that the s ensors are uniformly distributed around the circumference of the drillstrin g and that the number of sensors is at least two times the number of signif icant modes. It is demonstrated that the spatial and temporal characteristi cs of the resolved modes can then be exploited to determine the time of arr ival and the angle of direction of the incoming reflected waves.