Time Domain Envelope Full Waveform Inversion Based On Wavelet Transform

The need of high accuracy seismic exploration is getting higher and higher.The high precision inversion method of seismic exploration has become the hot spot of people's research.Full waveform inversion is a seismic imaging technique based on data fitting objective function.Full waveform inversion uses all the waveform information(amplitude,phase,etc.),so it can reconstruct the stratum with high resolution.However,in actual field data,the signal received by geophone usually lacks low frequency signals due to the use of the source type and the absorption of the stratum.The lack of low frequency signals will make the inversion of the full waveform highly nonlinear,which makes the inversion easily fall into the local minimum.The great calculation cost of full waveform and the lack of the low frequency information of the seismic record have hindered the application of the full waveform inversion in practice.The traditional full waveform inversion requires a number of forward and gradient calculations in each iteration,which is one of the most important problem for the full waveform inversion.In this paper,the forward,gradient calculation and optimization algorithms of full waveform inversion are studied in detail.In view of the lack of low frequency information,a wavelet packet full waveform inversion method for calculating the wavelet packet of seismic records is proposed to provide low frequency information for the inversion.In order to solve the problem of full waveform inversion,a fast time domain full waveform inversion based on OBFGS algorithm is proposed in this paper.Aiming at the problem of strong nonlinearity in full waveform inversion,the envelope full waveform inversion based on Hilbert transform is proposed by Xin Rui Luo and Chi Ben,which reduces the nonlinearity of full waveform inversion.However,when the asymmetric signal is enveloped,the Hilbert envelope has fake peaks that the original signal does not exist.In this paper,a full waveform inversion based on wavelet packet is proposed.Wavelet packet analysis is a branch of multiresolution analysis.It can decompose the signal at both the low frequency node and the high frequency node.By contrast the Hilbert waveform envelope and the wavelet packet envelope,it can be seen that the envelope of low-frequency signal node of wavelet packet decomposition has better shape and the low frequency wavelet packet network does not have fake peak,so wavelet packet envelope can recover the low frequency of the seismic records more accurately.In the early stage of inversion,and the full waveform inversion is carried out by the seismic record of the wavelet packet.In the middle and late inversion of the inversion,the original seismic record is used for inversion and the final result is obtained.It can effectively reduce the nonlinearity of the inversion and make the algorithm more stable.In order to improve the computational efficiency of the full waveform inversion,the OBFGS algorithm is introduced in this study.OBFGS method is first introduced in the field of machine learning,it is an intelligent optimization algorithm that does not rely on line search principle(such as Wolfe principle).The OBFGS algorithm improves the method of calculating the step size in each iteration.In the traditional full waveform inversion is usually required by certain step for step to obtain the principle,if the current step does not meet the requirements of standards,according to a certain principle the step is shortened and forward modeling and the gradient would be calculated again.This line search principle is one of the main reasons for the huge amount of the full waveform inversion calculation.The OBFGS algorithm does not depend on the step size convergence criterion to set the initial step size OBFGS algorithm requires only reasonable,it can adaptively adjust the step in the whole process of inversion,avoid in one iteration by repeatedly calculating the forward and gradient to test the appropriate step size,so as to improve computational efficiency.To verify the validity of the method,Marmousi model and the three layer on the wedge model are tested.Experimental results show that the full waveform inversion wavelet packet network can provide accurate information for the inversion based on low frequency.It has good stability and high precision.The full waveform inversion based on OBFGS algorithm is also tested on Marmousi model and a three layers wedge model.The inversion result proofs that it is a fast inversion method with high precision.