弦截迭代法在求取P-S转换波转换点位置和旅行时中的应用——以单一水平界面VTI介质为例

Application of secant iterative method for calculating P-S wave converted-point position and travel time:case study of VTI medium with single horizontal reflector

(1.中国地震局地壳应力研究所,北京100085;2.北京大学地球与空间科学学院,北京100871;3.中国地震局地质研究所,北京100029)

Cai Xiaogang,The Institute of Crustal Dynamic,China Earthquake Administration,Beijing 100085,China

求取转换点位置是进行转换波资料处理的重要环节,目前主要有严格的解析方法、基于泰勒级数展开的近似解析方法和基于射线理论的迭代方法3种。以单层水平界面VTI介质为例,给出了弦截迭代方法计算转换点位置和旅行时的步骤和公式;通过各向同性介质、VTI介质模型计算,对3种方法的计算精度进行了对比,讨论了各向异性参数对转换点位置和走时的影响,通过强各向异性介质模型探讨了弦截迭代法应用的局限性。研究结果表明,弦截迭代法由于没有使用任何近似,因此在事先给定的计算精度范围内是准确的,但在长偏移距和强各向异性介质同时存在的情形下,反射的SV波会出现“三叉区”现象,从而导致该方法失效。

As an important step in P-S seismic data processing,the calculation of converted-point position can be obtained by three methods,including strict analytical method,approximate method based on Taylor series expanding and iterative method based on ray tracing.Taking VTI medium with single horizontal interface as example,the steps and formula for calculating converted-point position by secant iterative method were given.Based on isotropic and VTI medium,we compared the computation accuracy of three methods and discussed the influence of anisotropic parameters on calculating converted-point position and travel time.Furthermore limitations of secant iterative method were discussed on strong anisotropic medium.The results is accurate and satisfied with the given computation accuracy since the secant iterative method has no approximation However,when long offset and strong anisotropy are both existing,the cusps phenomenon for reflected SV wave will appear and the method is failed.

10.3969/j.issn.1000-1441.2012.01.011