Gabor框架下的各向异性介质扰动高斯波包模拟与成像方法

Scattering Gaussian wave packet modeling and imaging method in anisotropic media based on Gabor function

地球介质广泛存在波动各向异性,为研究地球内部结构、组分提供了新的信息.现今,考虑介质的各向异性在地震波传播、成像以及反演中的作用越来越重要.高斯波包/束类正反演方法因其具有高效、简便等特点,近年来在地震背景速度建模和成像方面取得了较大进展.因此,在拟声学近似下,本文发展了基于Gabor框架的各向异性介质扰动高斯波包模拟与成像方法.与传统的网格化参数扰动方式不同,本文用空间分布的局部化Gabor基函数特征表达地下介质的参数扰动,建立了模型域Gabor函数与数据域高斯波包的映射关系.该方法继承了各向同性高斯波包的优势和特点,例如(1)基于Gabor框架的扰动高斯波包模拟具有计算效率高、内存占用量小的特点;(2)可以处理多波至,能应用于复杂构造(盐丘、气云边界)和中深层构造的成像;(3)利用Gabor函数可以稀疏表达地下的构造,适合目标导向的灵活成像;而且,(4)相较于各向同性高斯波包成像方法,考虑介质的各向异性后,本文的模拟结果更加准确,成像剖面同向轴能量更加聚焦.通过数值实验对本文方法进行测试,实验结果证实了该方法的有效性、高效性和灵活性.

Wave anisotropy exists widely in the earth′s medium,which provides new information for the study of the earth′s internal structures and components.Nowadays,the anisotropy of media plays a more and more important role in seismic wave propagation,imaging and inversion.Gaussian wave packet/beam forward and inversion methods have made great progress in seismic background velocity modeling and imaging in recent years because of their high efficiency and simplicity.Therefore,under the pseudo acoustic approximation,this paper develops a scattering Gaussian wave packet modeling and imaging method for anisotropic media based on Gabor framework.Different from the traditional grid parameter perturbation method,the characteristics of spatially distributed localized Gabor basis functions are used to express the parameter perturbation of underground media.Then the mapping relationship between Gabor function in model domain and Gaussian wave packet in data domain is established.This method not only inherits the advantages and characteristics of isotropic Gaussian wave packet,such as(1)the scattering Gaussian wave packet modeling based on Gabor framework has the characteristics of high computational efficiency and small memory occupation;(2)it can deal with multi wave arrivals and can be applied to the imaging of complex structures(salt dome,gas cloud boundary)and middle or deep structures;(3)Gabor function can be used to sparsely express the underground structures,which is suitable for target oriented flexible imaging;in addition,(4)compared with the isotropic Gaussian wave packet imaging method,considering the anisotropy of the medium,the results in this paper are more accurate and the energy of the events of the imaging section is more focused.The proposed method is tested by numerical experiments.The experimental results confirm the effectiveness,efficiency and flexibility of the method.