Data Resolution Matrix Of High-Frequency Rayleigh-Wave Phase Velocities

Abstract

High-frequency (≥ 2 Hz) Rayleigh-wave phase velocities have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. For a given nearsurface geophysical problem, it is essential to understand how well the data, calculated according to a layered earth model, might match the observed data. It is also important to recognize that the match may only be possible for data in a certain frequency range because the sensitivity of Rayleigh-wave phase velocities due to changes in S-wave velocities varies with frequency. The data resolution matrix is not a function of the data, but only of the data kernel (the Jacobian matrix, determined by a geophysical model and a priori information applied to the problem). The data resolution matrix of high-frequency Rayleigh-wave phase velocities, therefore, offers a quantitative tool for design of field surveys and prediction of the match between calculated and observed data. We employ the data resolution matrix to discuss the resolving power of phase velocities at different frequencies and the advantages of higher modes. Our discussion provides insights into the inversion of Rayleigh-wave phase velocities. Because of restrictions of the data kernel of the inversion system, each near-surface geophysical problem can be resolved only with Rayleigh-wave phase velocities in a specific frequency range and higher modes normally possess higher resolving power than the fundamental mode.