# Two-Dimensional Full-Waveform Joint Inversion of Surface Waves Using Phases and Z/H Ratios
## 5 Discussion  
As the extension of 2D surface-wave adjoint tomography method [32], the computing of 2D joint inversion also kept the efficiency. Taking the small-scale inversion as an example, the model was 600 m in length and 100 m in depth with 100 \(\times\) 20 elements, and the simulation contained 20,000 time steps with a 0.0003 s time interval. As shown in Table 2, the phase inversion included 50 forward-modellings and calculations of kernels; the number of processors for each source was 4, leading to a total cost of 200 CPU hours. The computation time was 6.25 h for 46 iterations. For joint inversion, the CPU hours cost was doubled (400 CPU hours total) due to the addition of the Z/H-ratio kernel calculation. However, the actual computation also showed relative efficiency, and 38 iterations could be completed in just 5.8 h, which was acceptable compared with the computational cost in the 3D case. On the basis of the time cost, the 2D joint inversion can be very efficient when computational resources are limited. Figure 12: Waveform fitting for three traces of stations at X = 150, 300, and 450 m from one shot gather located at X = 50 m after inversion. Comparison of the target, initial, and final seismic traces obtained via (**a**) phase inversion; (**b**) joint inversion. Left: H-component. Right: Z-component. The synthetic examples above provided us with two actual situations for the application of joint inversion. For large-scale inversion, we could use earthquake surface waves recorded by linear seismic arrays. In reality, it is difficult to find enough earthquakes along the profile. Fortunately, the approach has been developed over decades, in which the Z/H ratio can be extracted from ambient-noise cross-correlation data [7], which makes it the most suitable situation for applying the joint-inversion method. The tomographic experiment in Section 4.1 shows that both Rayleigh wave phase and Z/H ratio had sensitivity to S-wave velocity in the crustal structure, but their sensitivity patterns were different. Rayleigh wave phase velocity dispersion was sensitive to the average velocity of the depth range sampled. The Z/H ratio was more sensitive to the shallower structure compared to the Rayleigh wave phase velocity dispersion at the same frequency; thus, the Z/H ratio was more helpful to constrain the shallow structure, such as the sedimentary basin. The joint inversion combined the complementary sensitivities of the phases and Z/H ratio and was capable of building a more unified crustal structure. For small-scale inversion, this method could be used effectively in retrieving model parameters and characterizing the near-surface region using active-source surface waves for engineering applications, geotechnical studies, and physical modeling tests. The tomographic experiment in Section 4.2 indicated that joint inversion has another important advantage; that is, it can deal with the cycle-skipping problem, which easily occurs in FWI of surface waves in near-surface cases. This contributes to envelope-information usage in the Z/H ratio calculation, which avoids incorrect vs. model updates, leading to a secondary minimum. Due to limited sensitivity to the P-wave velocity model, it was found that the P-wave model also seemed to be not well constrained by the joint inversion. This can be improved by inclusion of body-wave data sets, such as the receiver function for large-scale inversions and seismic refractions for small-scale inversions, which is sensitive to the P-wave velocity. Before application to real data, there are some issues that require more study. One is the difficulty of extracting stable Z/H-ratio measurements from a single source-station pair. Similarly, using amplitude information from an ambient-noise cross-correlation is not always reliable. Another issue is the 3D structural effect on both phase and Z/H-ratio kernels, which were not properly modeled in the 2D case. For example, the ray path may not follow the profile.