**1. Introduction**

Establishing the initial model is one of the necessary and key steps of the modelbased inversion method, which has a great impact on the inversion effect. Traditionally, the method of generating the initial model is to extrapolate the inversion parameters observed from the wells or vertical seismic profile (VSP) along the interfaces picked from seismic profiles [1,2] or to extrapolate the seismic attributes [3–7]. In these methods, seismic horizons are necessary and manual interpretations are required. Horizon picking is one of the most time-consuming and labor-intensive steps [8]. Automatic horizon interpretation technology has been developing. Many geophysicists have proposed a variety of algorithms to improve the efficiency and accuracy of automatic horizons tracking [9–14], but these methods still need some prior information, such as manually setting up seed points or carrying out manual interpretation of large sets of strata. It is difficult to establish the initial model directly without manual interpretation. In addition, seismic inversion usually requires the initial model to cover the entire 3D region, but in practice, the automatic interpretation of the entire data volume is difficult to achieve. Therefore, there is a need for an efficient and accurate seismic extrapolation method to establish an initial model with the condition of lack of horizons.

Neidall et al. [15] presented the concept of velocity spectrum. The seismic gathers are automatically scanned with equal velocity intervals, and the velocity spectra are generated by stacking energy or similarity coefficient. Compared with artificial horizon interpretation, the velocity spectra are easier to generate. In conventional seismic data processing, stacking or migration velocity is obtained by velocity analysis on velocity spectra. The hyperbolas in the prestack seismic gathers reflect the characteristics of the interfaces, and the velocity

**Citation:** Sun, L.; Ding, L.; Wang, X. Research on Initial Model Construction of Seismic Inversion Based on Velocity Spectrum and Siamese Network. *Appl. Sci.* **2022**, *12*, 10593. https://doi.org/10.3390/ app122010593

Academic Editor: José A. Peláez

Received: 31 August 2022 Accepted: 19 October 2022 Published: 20 October 2022

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spectrum contains the position and velocity information of each hyperbola in prestack gathers. Compared with the gathers, the features on velocity spectrum are more focused. The velocity spectrum is a 2D image, which can be used to identify the changes of the lateral characteristics of the formation.

Deep learning technology has shown much better performance than traditional neural network methods in speech and visual tasks, such as image classification [16], semantic segmentation [17], and image segmentation [18]. This is mainly due to the strong feature expression ability of deep networks such as convolutional neural network (CNN). In the field of exploration geophysics, deep learning has been successfully applied to seismic processing and interpretation [19,20]. However, most of the current applications need to manually make and label samples first, and then extract the corresponding type of feature information from the seismic images. For the establishment of the initial inversion model, it is still unable to get rid of the dependence on horizons. Deep learning has the potential to provide more global information. As an important part of computer vision, visual target tracking technology has been developed rapidly. The Siamese network uses the idea of similarity learning, describes the tracking problem as an object matching problem, and judges the position of objects by comparing the similarity of objects [21,22].

In this paper, we transformed the parameter extrapolation problem in constructing the initial inversion model into a 2D image tracking problem and proposed a method for constructing the initial model based on velocity spectrum and Siamese network. Firstly, the velocity spectra generated by CDP gathers were used to track the lateral variation of formation characteristics. Then, the target tracking results at different CDP positions were obtained by combining the similarity of the triple Siamese network analog velocity spectrum. Finally, the discrete inversion parameters were extrapolated along the tracking path to obtain the initial model. We proposed an improved triple Siamese structure, which adds an update branch to solve the lateral variation of velocity spectrum characteristics during target tracking. This improvement takes dynamic update into tracking. In order to verify the applicability of the method, we carried out tests on theoretical and practical data. The results show that it can automatically obtain the extrapolation paths and can be used to establish the initial model of seismic inversion.
