基于压缩感知技术的全波形反演

全波形反演技术虽然已经得到了成功应用，但其求解一个最小二乘非凸优化问题的计算量仍是一个很大的难题。通过随机降采样技术可以减少反演过程中炮数和频率数，从而可以极大程度地降低全波形反演的计算量；然而这种方法受到奈奎斯特采样定律例证的“维数灾难”的限制以及背离‘摩尔定律’现象。为此,研究了基于改进压缩感知的随机化降维技术,应用压缩感知理论减少随机采样;联合随机采样和稀疏促进技术,成功减少了地震数据的维数,同时保持了有效信息。通过该项技术的应用,牛顿类方法的计算量相当于全波场采样梯度类算法的计算量;将稀疏约束应用在反演过程中的模型更新上,不改变波形反演的目标函数,并且能够压制由欠采样产生的虚像噪声。北海模型数据测试结果证明了该方法的可行性和有效性。

Although full waveform inversion technique has been successfully applied,the amount of calculation of least-squares non-convex optimization problem is still a challenge.Random sampling technology reduces the number of shot and frequency,and save the full waveform inversion calculation greatly,but it brings curse of dimensionality and departure from Moore’s Law.In this paper with the successful improvement of full-waveform inversion,the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem size numerically.Two main culprits can be identified.First,there is the so-called curse of dimensionality exemplified by Nyquist’s sampling criterion,which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases.Secondly,there is the recent departure from Moore’s law that forces us to lower our expectations to compute ourselves out of this.In this paper,we address this situation by randomized dimensionality reduction,which we adapt from the field of compressive sensing.In this approach,we combine deliberate randomized subsampling with structure-exploiting transform-domain sparsity promotion.Our approach is successful because it reduces the size of seismic data volumes without loss of information.With this reduction,we compute Newton-like updates at the cost of roughly one gradient update for the fully-sampled wavefield.Sparsity constrain is employed in the model update in inversion without changing the target function of waveform inversion and suppressing the virtual image noise raised by sub-sampling.The North Sea model testing result proves the feasibility and validity of the method.