基于拟微分算子的横向各向同性介质黏声波方程

VTI viscoacoustic wave equation based on quasi-differential operator

由于地层的各向异性与黏滞性,地震波在传播过程中表现出方向上的各向异性和振幅值的吸收衰减特征.若简单地将地下介质视为各向同性,实际地质结构的地震波响应可能会被曲解,甚至忽略了有效信息.为了得到深部储层的高精度成像,本文将标准线性固体模型(SLS)扩展到各向异性介质中,并结合各向异性拟声波方程,推导出时间空间域的各向异性介质黏声波方程组,该方程中用伪微分算子来表述地震波的衰减特征.在逆时偏移的过程中,为了解决高频不稳定问题,文中通过引入规则化算子来构建稳定的逆时传播算子.模型的正演模拟表明该方程既能准确的描述各向异性介质下的标量波的传播规律,又能体现地层的吸收衰减效应.

The underground medium is far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. The existence of anisotropy and viscosity affect the effect of migration seriously. So, in this paper, based on the dissipation mechanism of standard linear solid model, we derive a viscoacoustic wave equation of VTI media in the time domain, which describes the attenuation characteristics of seismic wave by a Pseudo-differential operator in the equations. The results of numerical simulation show that the equation propagation can not only describe the propagation of scalar wave in anisotropic media accurately, but also reflect the effect of absorption and attenuation. Model shows directly that reverse-time migration imaging based on anisotropic viscoacoustic wave equation can produce clearly imaging and improve amplitude beneath high-attenuation zones.