ALBERT

Description: The Cartesian-based least squares reverse time migration (LSRTM) aims to obtain a relatively high-resolution amplitude preserving imaging by calculating and solving the Hessian matrix. In addition, conjugate gradient algorithm is proved to be an efficient iterative method, which makes the traditional LSRTM feasible in practical data processing applications. Each iteration process of LSRTM includes two main parts; The first part is the forward simulation of wavefield, and the second part is the back propagation of wavefield. However, the calculation of these two parts takes a lot of time, and oversampling effects will occur in the calculation process. The thesis develops a smooth understanding of the LSRTM scheme in pseudodepth domain and gives information about this type of wavefield extrapolation method to achieve amplitude-preserved image with low computational costs in terms of memory and time. The underground media faced by seismic exploration usually include low velocity bodies, high steep structures and pore fracture units. When simulating the seismic wavefield in these media, in order to ensure the simulation accuracy and computational stability by finite difference methods, the grid spacing needs to be very small, which leads to the oversampling problem of the traditional finite difference forward simulation method in Cartesian coordinate system. In order to overcome this problem, the pseudo depth domain algorithm is applied to the least-squares reverse time migration to improve its computational efficiency. The problem of stabilizing this Pseudodepth wavefield arises from the introduction of the mapping function and velocity and also the vertical axis operator that converts the finite difference solution partially from time into frequency domains. Stability and convergence analysis suggests that the spatial derivatives of Riemannian axis should be approximated by a mixed Fourier pseudo-spectral and ordinary finite-difference schemes methods using a special Gaussian-like impulse function to generate the vector-matrix of the complex source term within the finite-difference operator, in addition to the mapping velocity, which is a differential form of the initial input velocity model, manifestly controls the CFL conditions of the associated Riemannian-finite difference operator. Numerical and synthetic examples indicated that this approach is more stable and efficient in extrapolating a smooth Riemannian wavefield while maintaining Claerbout’s principle for locating subsurface reflectors also choosing an appropriate sampling rate for the new vertical axis is related inversely by the maximum frequency of the impulse wavelet and directly with minimum velocity value in the given model. The LSRTM wavefield extrapolation usually uses the two-dimensional constant density acoustic wave equation, by considering the change of velocity field distribution, and converts it to the corresponding pseudodepth domain, so as to solve the oversampling problem in the true depth domain. For each point in the Cartesian coordinate system, there is a corresponding point in the pseudo depth domain. Therefore, we can interpolate and remodel the reconstructed finite difference modelled wavefield in the new coordinate system through the Cartesian-to-pseudodepth mapping function. Regardless of the applied finite difference algorithm and boundary conditions, wavefield extrapolation in pseudodepth domain can ensure high accuracy and efficiency. Through the test of synthetic and actual data, compared with the traditional LSRTM results, pseudodepth domain LSRTM shows great potentiality in amplitude preserving imaging. On the other hand, pseudodepth domain LSRTM has great advantages in computational efficiency and ensures computational accuracy.

Description: Masters

Description: 基于笛卡尔的最小二乘逆时偏移（LSRTM）旨在通过计算和求解Hessian矩阵获得相对高分辨率和保幅的成像。此外，共轭梯度算法被证明是一种有效的迭代方法，这使得传统的LSRTM在实际数据处理应用中是可行的。LSRTM的每个迭代过程包括两个主要部分；第一部分是波场的正演模拟，第二部分是波场的反向传播。然而，这两部分的计算需要花费大量时间，并且在计算过程中会出现过采样效应。本论文对伪深度域LSRTM方法进行了研究，给出了该方法波场外推的信息，获取了保幅的图像，并且该方法有较低的内存和时间成本。 地震勘探面临的地下介质通常包括低速体、高陡构造和孔隙裂隙单元。在模拟这些介质中的地震波场时，为了保证有限差分法的模拟精度和计算稳定性，需要非常小的网格间距，这导致了传统的笛卡尔坐标系有限差分正演模拟方法的过采样问题。为了克服这一问题，将伪深度域算法应用于LSRTM，以提高其计算效率。伪深度域波场稳定是因为引入了映射函数和速度，还有垂直轴算子，并将有限差分解从时间域转换为频率域。稳定性和收敛性分析表明，除了映射速度之外，黎曼轴的空间导数还应该通过傅里叶伪谱方法来近似，该方法使用一种特殊的类高斯脉冲函数来生成有限差分算子内复数震源项的向量矩阵，它是初始输入速度模型的微分形式，控制相关黎曼有限差分算子的CFL条件。合成数据的例子表明，这种方法在推导平滑的黎曼波场时更加稳定和高效，同时保持了Claerbout地下反射体的定位原则，也为新纵轴选择了合适的采样率，该采样率与脉冲小波的最大频率成反比，与给定模型中的最小速度值直接相关。 LSRTM波场外推法采用二维常密度声波方程，通过考虑速度场分布的变化，将其转换为相应的伪深度域，从而解决真深度域的过采样问题。对于笛卡尔坐标系中的每个点，伪深度域中都有一个对应点。因此，我们可以通过笛卡尔到伪深度映射函数，在新坐标系下对重建的有限差分模拟波场进行插值和重塑。无论采用何种有限差分算法和边界条件，伪深度域的波场外推都能保证较高的精度和效率。通过对合成数据和实际数据的测试，与传统的LSRTM结果相比，伪深度域LSRTM在保幅成像方面显示出巨大的潜力。另一方面，伪深度域LSRTM在计算效率和计算精度方面也有很大优势。