二阶Born近似有限频率走时敏感核

有限频率层析成像考虑了非均匀介质中波的散射、衍射、波前愈合等物理性质,使得其对速度异常体的分辨能力远大于射线层析成像.推导和计算有限频率敏感核是进行有限频率层析成像的关键,当前推导有限频率敏感核多借助一阶Born近似,但这只适用于弱散射介质的情况.本文基于二阶Born近似并利用傅里叶变换推导了三维均匀介质情况下有限频率敏感核的解析表达式,并将其推广到非均匀介质中得到了三维非均匀介质中有限频率敏感核.研究表明:当介质中速度扰动小于2%时,基于二阶Born近似的有限频率敏感核与基于一阶Born近似的有限频率敏感核差别很小,可近似认为相同;当介质中速度扰动大于5%时,基于二阶Born近似的有限频率敏感核与基于一阶Born近似的有限频率敏感核有较大不同,表明此时已不能忽略二次散射.

Finite-frequency traveltime sensitivity kernel based on second-order Born approximation

Finite-frequency tomography has the better resolution to velocity anomalies than ray tomography because it considers scattering, diffraction and wave front healing when seismic waves propagate in an inhomogeneous medium. Derivation and calculation of the finite-frequency sensitive kernel is the key in finite-frequency tomography. This kernel can be derived by the first-order Born approximation, but only applicable to a weak scattering medium. Based on the second-order Born approximation and by using the Fourier transform, we deduce the analytical expression of the finite-frequency sensitive kernel in a three-dimensional homogeneous medium, and extend it to the inhomogeneous medium to obtain such a kernel in a 3D inhomogeneous medium. Research shows that when the medium velocity disturbance is less than 2%, the difference of kernels between based on the second Born approximation and based on first-order Born approximation is small, so both can be considered identical. When medium velocity disturbance is greater than 5%, such difference is relatively large, implying that secondary scattering cannot be ignored.