基于逆散射理论的介质参数与其地震响应的尺度对应关系研究

在反演过程中进行频带控制是多尺度反演的重要策略，但数据频率成分与要反演的参数之间的尺度对应关系尚不清晰。本文利用Kormendi论文中的测井曲线模型，基于逆散射理论将地下介质参数的扰动分解为0-0-9-11 Hz、9-11-18-22 Hz、18-22-36-44 Hz和36-44-80-90 Hz共4个尺度，并利用反射率正演模拟方法生成4个尺度扰动成分的地震响应。通过对比地下介质参数不同尺度的扰动及其地震响应的频带成分，发现二者在4个扰动尺度上均具有一致性，由此得出介质参数与其地震响应具有定量尺度对应关系的结论。据此从介质扰动的尺度概念引申出反射系数的尺度概念，从逆散射理论角度探讨实验结果的理论依据，并对其在指导反演分频参数选取及薄互层解释等方面的应用展望进行讨论。 

Research on the Scale Corresponding Relationship between the Medium Parameter and its Seismic Response Based on Inverse Scattering Theory

It is an important strategy to control the frequency range of seismic data in multi-scale inversion. And it is the premise for the frequency control to make the relationship between the frequency component of data and the parameter scale to be inverted clear. In this paper, Using log curve model given by Kormendi's paper, based on inverse scattering theory, disturbance of media parameter is divided into 0-0-9-11 Hz, 9-11-18-22 Hz, 18-22-36-44 Hz and 36-44-80-90 Hz etc four different scales and the Reflectivity forward modeling method is used to generate the seismic response corresponding to the different scale component of the underground medium parameter. And it is found that the medium disturbance and its seismic response have consistency on all the four scales. According to this conclusion, the scale concept of reflection coefficient is extended from the scale concept of medium parameter disturbance, and the theoretical basis of the research results is discussed from the viewpoint of inverse scattering theory, and the application prospect of the concept in guiding the selection of the frequency-division inversion strategy and the interpretation of thin inter-bed is discussed.