EXPERIMENTAL AND FINITE-DIFFERENCE MODELING OF BOREHOLE MACH WAVES

A series of model experiments was performed in an ultrasonic laborator y to study the radiation of downhole sources in a variety of formation s. Three models were used in the experiments. They were a Lucite model , a Lucite model with a free glass pipe in the centre, and a glass-cas ed soil model. In addition, a finite-difference modelling technique wa s used to simulate the wave propagation in these models and the result s of the laboratory and numerical experiments are compared. In the Luc ite borehole model the waveforms recorded in the experiment agree very well with the finite-difference synthetics. The snapshots of the wave field from the finite-difference simulation show the radiation pattern of the P- and S-waves in the Lucite formation. These patterns are con sistent with the theoretical calculations. In the Lucite model with th e free glass pipe, the finite-difference synthetics are also in good a greement with the experimental observations, especially for the conica l P-wave arrival. The angle between the wavefront of the conical P-wav e and the borehole axis, observed from the snapshot, agrees with the t heory. In the cased soil model, the arrival time of the finite-differe nce synthetics is in good agreement with the laboratory measurements. The relative amplitudes of the P-wave and the Mach wave are not correc tly modelled because intrinsic attenuation is not included in the fini te-difference calculation. The Mach cone angle from the snapshot agree s with the theoretical prediction. Finally, a finite-difference method was used to simulate Mach-wave propagation in a formation with two ho rizontal layers. In the case of two slow layers, the Mach-wave generat ed in the first layer is reflected back from and transmitted through t he boundary and another Mach wave is generated at the second layer whe n the Stoneley wave travels into the second layer. In the case of a fo rmation having one slow and one fast layer, the Mach wave generated in the slow layer is reflected back at the boundary and leaked into the fast layer. There is no Mach wave in the fast layer.