Source-independent Full-waveform Inversion In The Frequency Domain

One of the most important problems in the practical application of the full waveform inversion is the need for a more accurate seismic source wavelet.In this paper,based on the full waveform inversion in frequency domain,a new objective function?denoted as SOD?is constructed based on the similarity of the data.The objective function avoids the selection of a reference trace,and does not need more than one reference trace for sum.We derive the corresponding gradient formula,and complete the model test.Compared with a standard trace normalization?STN?,the average trace normalization?ATN?and the conventional L₂ norm objective function with known source signature?KSS?inversion methods.The results show that the SOD method is more efficient than the STN method because it does not need to use the reference trace and has a greater tolerance to the energy difference between the data.At the same time,using the SOD method of the frequency domain wave field data is more abundant than the ATN method using the amplitude data,so it has a higher inversion precision.It can be seen from the test of noise data that the noise immunity of the SOD method is only second to the KSS method,which shows the high stability of the random noise.In the initial model test,the dependence of the SOD method on the initial model is much lower than that of the KSS and STN methods.The huge computational complexity is one of the major challenges in the application of full waveform inversion?FWI?technology.Finite difference contrast source inversion?FDCSI?method based on frequency domain wave equation can be applied to inhomogeneous background media.This method only needs to carry out a multi shot forward simulation at the beginning of each frequency,and the background model remains unchanged in the iteration process,thus significantly reducing the computational complexity of sparse matrix decomposition.Like the conventional full waveform inversion,the FDCSI method requires a very accurate source wavelet in the inversion process.In order to avoid the wavelet extraction,this paper introduces the wavelet iterative estimation inversion strategy based on the FDCSI method.It can be seen from the trial result of Overthrust model that the inversion strategy of wavelet iterative estimation can obtain the same inversion effect with true wavelet.The test of synthetic data with different SNR shows that the method is not sensitive to random noise.Meanwhile,the results show that the method has low dependence on the initial model from the gradient initial model trial calculation.The most computationally expensive part of FWI is a forward modeling engine that numerically simulates wavefields.In this paper,an efficient iterative solver is proposed for wavefield continuation and applied to frequency-domain acoustic full-waveform inversion with constant density.We reformulate the forward propogation of the source wavefield and the back propogation of the residual wavefield as unconstrained optimization problems.We also derive calculating formula for gradient and step-length.Theoretically analysis indicate that the computational efficiency of the new method is significantly higher than that of the conventional FWI.Numerical examples prove that our method can obtain high-precision wavefields with several iterations and improve convergence rate compared with original GMRES method.With high-efficiency source encoding technology,the calculation time of the new method is only about 1/8 of that of the conventional FWI,which is consistent with the theoretical analysis?The number of wavefield iteration is 8,and the number of unknown parameters is about 70 thousands?.And when the number of wavefield iteration is 6,the inversion results of the new method is basically the same as that of the conventional FWI.