# Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography
## 1 Introduction  
Seismic exploration is a fast and intuitive exploration tool before drilling. Almost all oil companies rely on seismic exploration results to determine the location of exploration and development wells. In recent decades, with the development of digital technology, seismic exploration can provide more and more information. Seismic migration is an important part of seismic data processing, which can transform seismic signals into images to intuitively show underground structural information. Moreover, imaging results of true-amplitude migration can provide lithological information. The true amplitude values of the reflectors are of great benefit to seismic attribute inversion, such as AVO (amplitude-versus-offset) inversion. Seismic exploration on land, faces challenges from complex surface conditions, such as severe lateral velocity variation and complex terrain. Seismic imaging in this complex situation has higher requirements for migration algorithms. Among the existing migration algorithms, the ray-based methods [1; 2; 3] are the most widely used. These methods have good adaptability to the topographic surface, and the computation cost is low, but ray-based methods have limitations for complex structure imaging. The one-way wave equation migration [4; 5; 6] performs better than the ray-based method in complex structure imaging. However, the one-way wave equation method is less adaptable to the topographic surface, and it is not as good as the two-way wave equation migration method in terms of imaging accuracy. As a method based on the full wave equation, the reverse time migration (RTM) method is more advantageous in seismic imaging under topographically influenced scenarios [7]. The full-wave-equation migration method not only has advantages in structural imaging, but also has better performance in terms of amplitude preservation. Becauseof these advantages, the RTM method has developed rapidly and has become the research focus of scholars. Many RTM from topography strategies [7; 8; 9] have been proposed. As we all know, the basis of the migration method is to solve the wave equation. RTM solves the full wave equation along the time axis. Because the wavefield extrapolates along the time axis, the calculated wavefield contains multi-scattering waves. This is beneficial for RTM imaging complex structures, but it may also bring more crosstalk artifacts, such as false events under a salt dome caused by internal multiple reflections [10]. Moreover, the RTM method assumes that the wavefield value outside the maximum sampling time is zero [11]. This assumption can affect the amplitude-preserving performance of the method to a certain extent. Unlike RTM algorithms, depth-extrapolation-based full-wave-equation migration methods solve the full wave equation in depth. In 1983, [PERSON] and [PERSON] [12] first introduced a full-wave-equation downward continuation scheme. They used a low-pass filter in the wavenumber domain to suppress evanescent wave energy. However, this strategy loses part of the useful waves, resulting in poor imaging for steep reflectors. [PERSON] and [PERSON] [13] proposed a full-wave-equation depth extrapolation method, which can suppress evanescent waves by using a more advanced method of spectral projection. [PERSON] et al. [14] analyzed the weaknesses of the existing methods and introduced a full-wave-equation depth extrapolation scheme based on the dual-sensor acquisition system. In their experiments, they demonstrated that the full-wave-equation migration method based on depth extrapolation has better amplitude-preserving performance than that of the conventional Kirchhoff and RTM migration methods. [PERSON] and [PERSON] [10] derived a depth-extrapolation-based full-wave-equation migration using matrix multiplication, and applied parallel computing to the core operator to improve computational efficiency. Theoretically the full-wave-equation migration based on depth extrapolation is similar to the imaging accuracy of RTM because they are all derived from the full-wave equation.