Surface wave dispersion inversion using an energy likelihood function

Seismic surface wave dispersion inversion is used widely to study the subsurface structure of the Earth. The dispersion property is usually measured by using frequency–phase velocity (f–c) analysis of data recorded on a local array of receivers. The apparent phase velocity at each frequency of the surface waves travelling across the array is that at which the f–c spectrum has maximum amplitude. However, because of potential contamination by other wave arrivals or due to complexities in the velocity structure the f–c spectrum often has multiple maxima at each frequency for each mode. These introduce errors and ambiguity in the picked phase velocities, and consequently the estimated shear velocity structure can be biased, or may not account for the full uncertainty in the data. To overcome this issue we introduce a new method which directly uses the spectrum as the data to be inverted. We achieve this by solving the inverse problem in a Bayesian framework and define a new likelihood function, the energy likelihood function, which uses the spectrum energy to define data fit. We apply the new method to a land data set recorded by a dense receiver array, and compare the results to those obtained using the traditional method. The results show that the new method produces more accurate results since they better match independent data from refraction tomography. This real-data application also shows that it can be applied with relatively little adjustment to current practice since it uses standard f–c panels to define the likelihood, and efficiently since it removes the need to pick phase velocities. We therefore conclude that the energy likelihood function can be a valuable tool for surface wave dispersion inversion in practice.