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在声波近似中,地层仅用密度和体变模量来描述。假设有平滑的密度变化,反射波就可用单一的函数——休波速度来描述。如果一个与实际介质足够接近的参考模型已知,由观测数据估算介质速度的问题就可以被线性化。在ω-к域内,利用最小平方公式,均匀参考介质的线性反演问题就可通过非递归算法来解决,这种算法与叠前偏移相比要经济一些。利用合成数据和实际资料所作数值验算证明了这种方法的可行性及其数值稳定性,其数值结果与未经叠加资料的偏移得到的结果能很好地吻合,尽管仅当该问题的物理意义(包括弹性声波效应、三维传播及准确的震源估计)得到切合实际的考虑时,才可能获得高质量的结果。
In sonic approximation, the formation is only described by density and bulk modulus. Assuming a smooth density change, the reflected wave can be described by a single function, the breakaway speed. If a reference model close enough to the actual medium is known, the problem of estimating the velocity of the medium from the observed data can be linearized. In the ω-к domain, using the least squares formula, the problem of linear inversion of a uniform reference medium can be solved by a non-recursive algorithm, which is more economical than prestack migration. The numerical results of synthetic data and real data prove the feasibility and numerical stability of this method. The numerical results are in good agreement with the results obtained without the offset of the superposed data. However, Meaning (including elastic acoustic effects, three-dimensional propagation and accurate source estimates) is realistic enough to yield high-quality results.