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地震反射数据的全波形反演是非线性的,其原因是因为观测数据与合成地震数据之间的不对称性函数的形态是不规则的。非线性主要来源于描述地震速度的参数,完全非线性反演有另一种可选择的反演方法,就是相对于速度仍然是非线性的,但相对于波阻抗比却是线性的。消除非线性和线性部分之间的相互影响的传统方法是根据旅行时计算背景速度,根据波形计算波阻抗比。另一个更好的方法是通过利用单一最小二乘方范数波形失配标准同时得到地下的背景速度和波阻抗比。用一个稀疏网格将完全代表介质总特征的背景速度参数化,而用一个密集网格对波阻抗比进行参数化。对于每一个更新的速度模型来讲,波阻抗比是通过一个线性反演算法计算出来的。对于1D速度背景,用WKBJ和波恩近似法在f-k域进行反演非常有效。该方法均可对合成数据和野外数据进行很好地反演。
The full waveform inversion of seismic reflection data is nonlinear because the shape of the asymmetric function between the observed data and the synthetic seismic data is irregular. The nonlinearity comes mainly from parameters that describe the seismic velocity. There is another alternative inversion method for complete nonlinear inversion, which is still non-linear with respect to velocity but linear with respect to wave impedance. The traditional method of eliminating the interaction between nonlinear and linear parts is to calculate the wave impedance ratio from the waveform based on the calculated background speed while traveling. Another, better approach is to obtain both the ground background velocity and the wave impedance ratio by using a single least squares norm waveform mismatch criterion. A sparse grid is used to parameterize the background velocity that completely represents the overall characteristics of the medium, while a dense grid is used to parameterize the wave impedance ratio. For each newer velocity model, the wave impedance ratio is calculated using a linear inversion algorithm. For the 1D velocity background, it is effective to perform inversion in the f-k domain using WKBJ and Bonn approximation. This method can both well invert the composite data and the field data.