Experimental And Finite Difference Modelling Of Borehole Mach Waves

Abstract

A series of model experiments are done in the ultrasonic laboratory to study the radiation of downhole sources in a variety of formations. Three models are used in the experiments. They are a lucite model, a lucite model with free glass pipe in the center, and a glass cased soil model. In addition, the finite difference modelling technique is used to simulate the wave propagation in these models and the results of the laboratory and numerical experiments are compared. In the lucite borehole model the waveforms recorded in the experiment agree very well with the finite difference synthetics. The snapshots of the wavefield from finite difference simulation show the radiation pattern of the P and S wave in the lucite formation. These patterns are consistent with the theoretical calculations. In the lucite model with the free glass pipe, the finite difference synthetics are also in good agreement with the experimental observations, especially for the conical P-wave arrival. The angle between the wavefront of the conical P wave and the borehole axis observed from the snapshot agrees with the theory. In the cased soil model the arrival time of the finite difference synthetics is in good agreement with the lab measurements. The relative amplitudes of the P wave and Mach wave are not correctly modelled because of no intrinsic attenuation in the finite difference calculation. The Mach cone angle from the snapshot agrees with the theoretical prediction. Finally the finite difference method is used to simulate the Mach wave propagation in the formation with two horizontal layers. In the two slow formation layers case, Mach wave generated in the first layer reflected back from and transmitted through the boundary and another Mach wave is generated at the second layer when the Stoneley wave travels into the second layer. In the one slow and the one fast formation layer case, the Mach wave generated in the slow formation is reflected back at the boundary and leaked into the fast formation layer. There is no Mach wave in the fast formation layer.