**4. Real Data Applications**

In the real data test, we used the land seismic data from eastern China. The CRP gathers after prestack time migration were used to generate velocity spectra. The number of CRP gathers was 500. The maximum offset was 2200 m. The longitudinal time was 2.5 s. The sampling interval was 2 ms. The stack section is shown in Figure 12a. Figure 12b is the CRP gather at CDP 203, and Figure 12c is the velocity spectrum at CDP 203.

**Figure 12.** (**a**) Stack section; (**b**) CRP gather at CDP 203; (**c**) velocity spectrum at CDP 203.

The velocity spectrum at CDP 203 was used as the tracking target of the training data set. Since there was no obvious boundary between the energy clusters in the velocity spectrum in Figure 12, we used the sliding window to realize the target tracking. The time window length is given as 250 ms. The tracking windows are shown in Figure 13a. The real data samples were made in the same way as the theoretical data. The training process had 500 iterations, and the learning rate was set to 0.0001. The position of the window was changed and the same training process repeated until the tracking of the target in the whole time range was completed. The tracking results of all CDP points were connected to form the final tracking paths as shown in Figure 13b. Comparing Figure 13b with Figure 12a, the tracking paths are consistent with the interfaces. The faults between CDP 200–CDP 350 and 1.3–1.8 s can be correctly identified on the tracking results. Along the tracking path, the parameter to be inversed can be extrapolated from the well, and the initial inversion model consistent with the structure can be obtained.

**Figure 13.** (**a**) Tracking windows; (**b**) the result of tracking paths.

### **5. Discussions**

This method also has some application limitations. Because the characteristics of the energy clusters in the velocity spectrum are closely related to the reflection characteristics of the formation, the method can obtain ideal tracking results when the reflection characteristics from the same formation interface are relatively stable in lateral. In contrast, if the reflection characteristics of the formation change dramatically in lateral, the velocity spectrum tracking will be unstable and the results may be multi-solution. This requires manual intervention or adding constraints to obtain reliable tracking results, such as limiting the trend of the tracking path within a certain range or limit the maximum change of the tracking results of adjacent traces. In addition, if the signal-to-noise ratio of real seismic data is very low, the velocity spectrum features will not be significant, and it will be difficult to extract features and track targets.

In the velocity spectrum tracking of real seismic data, there may be difficulties such as unclear clusters features or background interference. In these cases, the accuracy of target tracking can be improved by changing the window length. The tracking task can be carried out with different window lengths, and the corresponding similarity results will be output for each window length. The results with the highest similarity can be extracted and combined as the final target tracking result.

The extrapolation path of geophysical parameters can be obtained by lateral tracking of velocity spectrum, which can be used as a constraint framework to construct the initial model. The essence of the method is the similarity of the characteristics of velocity spectrum in lateral, that is, the invariable part of the velocity spectrum. In fact, the characteristics of the velocity spectrum have certain changes in lateral, and this change also represents the lateral changes of geophysical parameters to a certain extent. In the absence of gooddata, how to make full use of the characteristics of velocity spectrum to provide more geophysical information will be the next possible research direction.

### **6. Conclusions**

A lateral tracking method of velocity spectrum based on a triple Siamese network structure is proposed in this paper. With this method, the positions of the target image on the velocity spectrum of each CDP can be tracked. The results of the tracking paths can constrain the lateral extrapolation of seismic parameter to establish an initial inversion model, for example, an initial velocity model for prestack depth migration or P-wave, Swave and density models for elastic parameters inversion. The method does not depend on the interpretation horizons and manual annotation samples. The theoretical and practical results show that the method can efficiently generate the initial model that conforms to the seismic structure and stratigraphic characteristics without the constraint of interpreted horizon data.

**Author Contributions:** Methodology, L.S.; validation, L.S. and L.D.; writing—original draft preparation, L.S.; writing—review and editing, L.D. and X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (grantno. 42204128).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
