Forward and inversion modelling of the ultrasonic wave in a homogeneous medium using P-wave transducers

Abstract

We use full wave forward and inversion modelling to estimate the elastic properties of rock samples from ultrasonic waveforms. The finite element algorithm (ABAQUS modelling software) is used to model a forward wave propagation within a homogeneous medium. For 19 mm diameter P-wave transducers, the result of the displacement waveform for a uniform source signal is obtained using both a linear and radial (about 2 mm) receiver arrays. Also, the use of a non-uniform source amplitude such as Gaussian distribution improves the displacement waveforms by few percent. The results accuracy is increased with increasing values of Gaussian standard deviation. However, for a nominal frequency of 1MHz, the same error increases with the decreasing frequencies. Additionally, our inversion algorithm (written in Python) searches for the best Young modulus (E) and Poison ratio (ν) of the medium iteratively. Finally, without prior knowledge of any threshold, the elastic parameters are estimated, and the results are consistent with the experimental measurements. These results provide a new modelling workflow to estimate the elastic parameters of the homogeneous and isotropic sample.