反射地震数据的逐层波形反演

本文针对层状介质并结合梯度法波形反演，提出逐层波形反演的方法. 首先给出介质扰动响应的概念，并在此基础上分析了梯度法波形反演方法. 波形反演实质上是将实测地震记录和预测地震记录的波形残差信息转化为实际地质模型和预测地质模型的模型残差信息. 波形反演的优点是利用大量振幅相位信息得到高分辨率的反演结果， 其缺点是运行耗时大；当初始模型和实际模型相差较大时，迭代算法容易陷入局部极小点，这是因为目标函数和初始模型同实际模型间的差异是非线性的关系. 逐层波形反演方法是使自上而下每一层的目标函数最小，这样总的目标函数也是最小的. 利用二分法速度扫描确定每一层速度不仅提高了运算速度也避免了迭代算法陷入局部极小点的问题. 结合介质扰动响应和目标函数值变化可以更为准确迅速地确定每一层速度和该层界面位置.

Layer by layer waveform inversion of seismic reflection data

A layer-by-layer waveform inversion method is developed to derive the velocities of multi-layered model. Firstly, one new concept-medium perturbation-response is introduced and the gradient method for waveform inversion is analysed. Essentially, waveform inversion is to extract residual structural information between the real earth and predicted model from the waveform residuals between the observed and the synthetic seismograms. The strength of waveform inversion is the high resolution of the inversion result by using a large quantity of waveform information. A weakness of waveform inversion is time-consuming. In addition, waveform information will tend to get stuck in local minima if the starting model is too far from the actual model. The reason for this failure is that the misfit function can be highly nonlinear with respect to velocity models. The layer-by-layer method is to minimize the misfit function for every layer from top to bottom. In this case the total misfit function will be minimum too. For each layer, we use dichotomy method to scan the velocity. This method can improve the speed of computation and avoid getting stuck in local minima for iterative algorithm. Velocity and reflection interfaces can be estimated quickly and accurately based on the medium perturbation- response and the change of the misfit function.