## 3 The 3D Seismic Fine Identification Technology
### Fine Static Correction Processing Technology
#### 3.2.2. OVT Domain Interpolation Processing  
In the presence of complex terrains and buildings, variable observation systems lead to irregular seismic data acquisition: the distribution of offset and azimuth data, as well as the overall data coverage, tend to be uneven, affecting the quality of seismic imaging and resulting in false anomalies when thick seismic data are conventionally processed. In order to eliminate the difference between actual and ideal spatial sampling attributes, the seismic data were regularized in the OVT domain, ensuring that the seismic migration would not be affected by irregular spatial sampling [28; 29]. After processing a Kirchhoff migration in the OVT domain, the COV (Common Offset Vector) gathers in the OVT domain were transformed back to the time-space domain by inverse transformation, obtaining the CRP (Common Reflection Point) gathers after anisotropic processing. The Fourier interpolation algorithm based on orthogonal matching pursuit (OMP) is a relatively effective interpolation method developed in recent years. This method primarily employs Fourier transform as its basis functions. It iteratively selects the largest coefficients from the Fourier transform coefficients and places them into a sparse spectrum. Then, it subtracts these selected coefficients from the input data iteratively until the residual becomes negligible. Finally, it performs an inverse Fourier transform on the resulting sparse spectrum to obtain the interpolated results at the desired locations. The implementation steps are as follows: conduct a discrete Fourier transform (DFT) along the time axis of the input seismic data to acquire the Fourier spectrum in the frequency domain. Compute the energy curves at various angles for the Fourier spectrum and utilize these energy curves as weighting factors applied to the entire Fourier spectrum [30; 31; 32]. Identify the Fourier spectrum component with the highest energy after weighting (effective signal) and integrate this component into the original Fourier spectrum without weighting. Perform an inverse Fourier transform on the Fourier spectrum component obtained in the preceding step and output the result to the corresponding original input positions. Subtract the iterative result from the previous step from the original input data to proceed with the next iteration. These steps delineate the procedure for the Fourier interpolation algorithm employing orthogonal matching pursuit (OMP) for seismic data [33; 34]. Given the seismic data input represented by \(f(x_{j})\), where \(j=0\), \(\ldots\), \(N_{\rm x-1}\), and \(N_{\rm x}\) denotes the total number of seismic traces, with \(0\leq x_{j}\leq x_{\rm max}\) representing the spatial coordinate corresponding to the \(j\)th trace. The Fourier expansion of the input data \(f(x_{j})\) is expressed as:  
\[f(x_{j})\approx\sum_{l}\widetilde{f}(l)\exp(\frac{i2\pi lx_{j}}{x_{\rm max}}) \tag{1}\]  
The inverse Fourier transform is:  
\[\widetilde{f}(l)\approx\sum_{j=0}^{N_{\rm x}-1}f(x_{j})\exp(\frac{-i2\pi lx_{ j}}{x_{\rm max}}) \tag{2}\]  
where \(k_{l}\) represents the spatial wavenumber, and \(k_{l}=2\times pi\times l/x_{\rm max}\), for \(l=-N_{\rm k}/2\),\(\ldots\), \(N_{\rm k}/2\), where \(N_{\rm k}\) is the total number of frequencies. Increasing \(x_{\rm max}\) not only increases  
Figure 6: The selected 3D \(p\)-wave velocity model. the number of traces involved in the calculation but also enhances the sampling in the wavenumber domain, thereby improving interpolation accuracy. Building upon Equation (1), with each addition of a frequency component in the frequency-wavenumber domain, after mm steps, the residual quantity can be expressed as:  
\[R^{m}(x_{j})=f(x_{j})-\sum_{l=0}^{m-1}\widetilde{f}(P_{l})\exp(\frac{i2\pi lx_{ j}}{x_{\max}}) \tag{3}\]  
\(P_{l}\) is the index corresponding to the coefficients selected in the \(l\)-th step.