Joint inversion of Rayleigh-wave dispersion data and vertical electric sounding data: synthetic tests on characteristic sub-surface models

In the traditional inversion of the Rayleigh dispersion curve, layer thickness, which is the second most sensitive parameter of modelling the Rayleigh dispersion curve, is usually assumed as correct and is used as fixed a priori information. Because the knowledge of the layer thickness is typically not precise, the use of such a priori information may result in the traditional Rayleigh dispersion curve inversions getting trapped in some local minima and may show results that are far from the real solution. In this study, we try to avoid this issue by using a joint inversion of the Rayleigh dispersion curve data with vertical electric sounding data, where we use the common-layer thickness to couple the two methods. The key idea of the proposed joint inversion scheme is to combine methods in one joint Jacobian matrix and to invert for layer S-wave velocity, resistivity, and layer thickness as an additional parameter, in contrast with a traditional Rayleigh dispersion curve inversion. The proposed joint inversion approach is tested with noise-free and Gaussian noise data on six characteristic, synthetic sub-surface models: a model with a typical dispersion; a low-velocity, half-space model; a model with particularly stiff and soft layers, respectively; and a model reproduced from the stiff and soft layers for different layer-resistivity propagation. In the joint inversion process, the non-linear damped least squares method is used together with the singular value decomposition approach to find a proper damping value for each iteration. The proposed joint inversion scheme tests many damping values, and it chooses the one that best approximates the observed data in the current iteration. The quality of the joint inversion is checked with the relative distance measure. In addition, a sensitivity analysis is performed for the typical dispersive sub-surface model to illustrate the benefits of the proposed joint scheme. The results of synthetic models revealed that the combination of the Rayleigh dispersion curve and vertical electric sounding methods in a joint scheme allows to provide reliable sub-surface models even in complex and challenging situations and without using any a priori information.