SENSITIVITY OF INVERSION ALGORITHMS FOR RECOVERING ELASTIC-CONSTANTS OF ANISOTROPIC SOLIDS FROM LONGITUDINAL WAVESPEED DATA

This paper discusses the sensitivity of inversion algorithms for recovering the elastic constants of moderately anisotropic solids using only ultrasonic longitudinal wavespeed data measured for various directions in a medium. This investigation is motivated, in part, by experience with the recently developed point source/point receiver technique, in which longitudinal wave arrivals are clearer and easier to measure accurately than the later transverse wave arrivals. A perturbation method is presented which shows that for a medium of triclinic symmetry, the longitudinal wavespeeds are most sensitive to the partial set of elastic constants C-11, C22, C33, (C-12 + 2C66), (C23 + 2C44) and (C-13 + 2C55), and it is these constants which can therefore be most accurately recovered from longitudinal wavespeed data. A number of illustrative numerical examples are presented which demonstrate the lack of sensitivity to certain constants and illustrate the recovery of elastic constants from simulated longitudinal mode data. These show that there is good convergence for the partial set of elastic constants, whereas the remaining elastic constants are much less accurately recovered.