Data-resolution Matrix and Model-resolution Matrix for Rayleigh-wave Inversion Using a Damped Least-squares Method |
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Authors: | Jianghai Xia Richard D Miller Yixian Xu |
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Institution: | (1) Kansas Geological Survey, The University of Kansas, 1930 Constant Ave, Lawrence, KS 66047, USA;(2) The State Key Laboratory of Mineral Resources and Geological Processes, China University of Geosciences, Wuhan, Hubei, 430074, P.R. China |
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Abstract: | Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface
geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might
match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and
a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (≥2 Hz) Rayleigh-wave phase
velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated
and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there
are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides
insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure.
Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities
within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because
of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that
selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution
matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices
in these examples to show the potential of increasing model resolution with selected surface-wave data. |
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Keywords: | :" target="_blank">: Data-resolution matrix model-resolution matrix multimode Rayleigh-wave data inversion S-wave velocity |
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