Zoeppritz equations: from seismology to medical exploration

Abstract

More than a century ago, Karl Bernhard Zoeppritz derived the equations that determine the reflected and transmitted coefficients at a planar interface for an incident seismic wave. The coefficients so obtained are a function of the elastic parameters of the media on each side of the interface and the angle of incidence. Approximations of the equations have been proposed and used in geophysical exploration, however, full use of the equations and their generalization to multiple layers could offer richer information about the properties of the media and be helpful in medical diagnosis via ultrasound. In this work, we investigate how to extract information from the angle-dependent reflection coefficients, including critical angles and the wave distortion at the interface between two and three media. It is shown that it is possible to separate the effect of density from speed of sound mismatch by measuring amplitudes as a function of angle of incidence (AVA). And examining the critical angle and waveform distortion of the reflected waves can reveal the thickness of an intermediate layer, even with subwavelength resolution. These studies could be integrated into medical imaging and also into the training of artificial intelligence systems that assist in diagnosis. In particular, they could help prevent cerebrovascular accidents by early detection of the formation and hardening of plaque in the arteries that irrigate the brain.