基于横纵波速度比值迭代的纵横波联合反演方法

在利用弹性阻抗EI反演纵、横波速度和密度时,若无速度信息,通常设定横纵波速度比k为常数,从而与真实的k值存在误差,将导致反演结果不准确。进一步研究发现,当缺乏大入射角信息时单独基于EI反演纵、横波速度和密度,反演结果易受噪声影响而很不稳定。为此,利用参数分辨矩阵分析了k值对反演结果的影响,发现纵波速度和密度几乎不受k值误差的影响,横波速度对k值的变化十分敏感。基于此提出了非线性k值迭代方法,通过逐次迭代求取准确的k值,相应得到准确的横波速度,进而基于Aki-Richards转换横波反射系数近似方程推导了转换横波弹性阻抗(SEI)方程,提出了基于k值迭代的纵横波联合反演方法。利用层状模型和Marmous 2的部分模型测试了上述方法,结果表明该方法能使k值较快地收敛到真实值,可更加稳定地反演纵、横波速度和密度。

Joint inversion of PP- and PS- waves based on the iteration of ratio of S-wave velocity and P-wave velocity

If we do not have velocity information when extracting P-wave velocity, S-wave velocity, and density from EI (elastic impedance), k (ratio of S-wave velocity and P-wave velocity) is set to a constant, which is always different from real k. This assumption leads to errors in the inversion results. It is found that inversion of P-wave velocity, S-wave velocity, and density based on EI is unstable due to noise (lack of information of big incident angles). We analyze influences of k on inversion results by the parameter resolution matrix, and have found that P-wave velocity and density are hardly affected by k, and that S-wave velocity is very sensitive to k. Based on this point, we design a nonlinear k value iteration method to obtain first accurate k value, and then accurate S-wave velocity. Then we derive P-SV wave elastic impedance accurate (SEI) formula based on Aki-Richards P-SV wave reflection coefficient approximation formula. Finally we propose a joint iteration of k value to extract P-wave velocity, S-wave velocity, and density from EI and SEI. The proposed join inversion is tested on a four-layer model and Marmousi 2 model. The tests results show that k value can rapidly converge to its real value and inversed P-wave velocity, S-wave velocity and density are more accurate and stable.