Estimation of elastic anisotropy from three-component ultrasonic measurements using laser Doppler interferometry

Abstract

Ultrasonic measurements using laser Doppler interferometry (LDI) have been reported to provide robust estimates of elastic anisotropy of rock samples. In this approach, an ultrasonic wave is emitted by a piezo-electric source and detected by the LDI, which can be configured to measure three components of the particle velocity in a very small area (~1 mm2) of the sample. Repeating these measurements for a dense array of points on the sample’s surface gives a distribution of traveltimes and polarisation fields on the surface. Anisotropy is then obtained by inverting these fields using analytical expressions or numerical algorithms for computing phase and group velocities. The existing implementation of this approach involves the inversion of direct compressional (P) and shear (S) wave arrivals only. A previous study showed that this approach produces stable results if only a small range of source–receiver offsets is included in the inversion. This limitation resulted in a relatively large uncertainty of the result. This uncertainty can be reduced by inverting the entire traveltime field. To this end, we numerically simulate the wavefield in the sample. Analysis of the computed wavefield reveals the presence of P- and S-waves as well as a critically refracted converted PS-wave. Hence, the inversion of the entire traveltime field must include these three waves. We implement this inversion using global minimisation of the traveltime misfit function, coupled with numerical computation of ray velocities. Application of this algorithm to laboratory LDI measurements on a transversely isotropic phenolic sample provides stable anisotropy estimates consistent with previous studies.