**5. Discussion**

## *5.1. Depth Sensitivity*

To evaluate the depth sensitivity of the inversion, we investigate the depth sensitivity kernels of the surface waves based on the inverted shear-wave velocity model. It is constructed by computing partial derivative of the predicted phase velocity with respect to velocity perturbation at different depths.

Figure 11 shows the normalized depth sensitivity kernels for different frequencies of surface waves. It shows that lower-frequency kernels have peak sensitivity at deeper depths while higher-frequency kernels have less sensitivity to deep subsurface structure. It also indicates that deeper layers may be mostly determined by frequencies lower than 1 Hz.

## *5.2. Tomography Resolution*

The ASSA inversions are performed on 1D gathers and then all gathers are used to reconstruct the 3D shear-wave tomographic model. Since we use 30 continuously adjacent sensors (with 50 m spacing) in one cable as a gather and 25 sensors as the overlap between the adjacent gathers, the resolution along the cable is 250 m. The resolution across the cables depends on the spacing between cables, which is 300 m. The thickness of each layer is adaptive during the inversion process. Generally speaking, shallow layers have higher resolution due to the high sensitivity of both high frequencies and low frequencies of surface waves while deeper layers (>1000 m) have lower resolution since they only have some sensitivity to very low frequencies of surface waves.

**Figure 11.** Normalized depth sensitivity kernels for different frequencies of surface waves.

#### *5.3. Non-Uniqueness and Uncertainty*

An important issue should be mentioned is that the non-uniqueness of the solution. Several factors can account for the non-uniqueness of the solution of the shear-wave inversion problem. One factor is that the problem is a highly nonlinear inverse problem and there is no analytical solution available. Numerical methods are used to solve such problems and the uniqueness of the solution to given data are not proven. Another factor is that the given data are usually noisy. In this paper, we assume that the dispersion data uncertainty are independent and Gaussian distributed (Equation (8)). In general, an infinite number of models fitting the noisy data can be found to an acceptable level [32]. The third factor is that, in practice, the dispersion curves are usually cut off to a certain frequency band or sometimes only part of the dispersion curves can be excited by the source, leading to some uncertainties to the solution.

To quantify the uncertainty of the inversion, we have calculated the standard deviation of 100 independent ASSA inversions. Figures 12 and 13 show a vertical and a horizontal slice of the standard deviation of the resolved shear-wave subsurface structure, respectively. Figure 12 indicates an average standard deviation of about 100 m/s. The standard deviation becomes larger at interfaces of layers and zones with a complicated structure (500 to 1500 m). This is because the thickness of each layer is adaptively determined, making slightly different layers for each independent inversion and resulting in larger standard deviation at the interfaces. Figure 13 indicates a generally homogeneous standard deviation on horizontal slices. The uncertainty for deeper layers is not as large as Zhang et al. [37] because our parameterization on number of layers and larger thickness of deeper layers, which constrains the freedom and uncertainty although limiting the resolution at the same time.

**Figure 12.** A vertical slice of the standard deviation of the resolved shear-wave subsurface structure under the 10th cable counted from left to right of the PRMRA in Figure 1.

**Figure 13.** (**<sup>a</sup>**–**d**) show horizontal slices of the standard deviation of the shear-wave subsurface structure at the depth of 150, 300, 600 and 1100 m, respectively. The black line in (**a**) shows the location of Figure 12.
