Sparsely Efficient Full Waveform Inversion Based On Optimized Initial Model

The rapid development of global economy has simulated the demand on oil and gas industries,which provides larger chances of development to the Geo-exploitation.There is an increasing demand on the technology of Geo-exploitation led by the increase of difficulties in exploiting.To meet the practical demands comes the Full Waveform Inversion(FWI).FWI could provide a high quality model and help to obtain a better image in the complicated geologic structures.FWI is the leading research of seismic exploration,which can utilize both the kinematics and the dynamics information of seismic wave.The aim of FWI is to iteratively update velocity model to estimate medium parameters accurately by minimizing the residual between observed data and calculated data.Comparing with some other traditional velocity modeling methods,the FWI is more capable to recover the construction underground since it can use more information including travel-time,amplitude and phase.FWI can provide migration higher precision velocity model,which is beneficial to the recognition of lithologic characteristic and stratum.This paper provides a joint method of initial model optimization to improve the stability and precision of the FWI.FWI is a nonlinear under-determined problem which leads to the non-uniqueness of solution,that is,different models may correspond to the same seismic records.And this may lead to a failure to convergence to the unique solution.Limited by the amount of data,The FWI has to use some local optimization algorithms for inversion and therefore,its objective function is easily trapped into local minimum.And what worse is that the real data lack of low-frequency data,making it more difficulty to restore the long wavelength part of the model.Considering the downsides above,in order to ensure the correct convergence of the FWI,we have to improve the precision of the initial model to avoid the cycle skipping caused by the large difference between the initial model and real model.This paper combines the modified Least squares filter with wave-field reconstruction and improves the precision of the initial model as well as the matching degree between seismic recordings by re-moulding the recordings and expanding the search space.This joint method reduces the dependence of inversion on the low frequency data and thus improves the stability and precision of FWI.This paper offers the Curvelet based non-monotone spectral projection gradient(NSPG)FWI,which improves the computational efficiency by increasing the convergence rate.FWI is consist of two part: forward modeling and inversion.The calculation of forwarding model in the FWI is proportional to the number of sources and receivers which means huge calculating quantity when many sources and receivers are used.In order to ensure the correctness of the inversion,avoiding the objective function to be trapped into local minimum caused by optimization algorithms,the FWI needs to iterate hundreds times and every iteration contains at least four times of forward modeling.Therefore,the calculated amount in the FWI is generally very large.This paper improves the computational efficiency by improving the convergence rate.different with monotone line search method,the non-monotone line search method only needs the objective function to be decreased in limited steps which reducing the computing time and improving the convergence rate.Besides,the Curvelet based non-monotone spectral projection gradient(NSPG)FWI can also improve the precision because of the sparsity.The wave-field is sparse in Curvelet domain and so is the update since the update is achieved by cross-correlating the residual wave-field and forward wave-field.Combining the sparsity,flexible steps as well as NSPG method,FWI can achieve better results with a high convergence rate.Compared with the land data set,the marine data set has a higher SNR since it contains less human activities and better coupling between receiver and medium.The higher SNR of marine data set makes it easy to record long offset information as well as full azimuth information,which makes it available to utilize diving wave and direct wave effectively.These waves' amplitude and travel-time have nothing to do with the reflectors,making them more suitable for building initial model and thus making Full waveform inversion more suitable for ocean data.Here we test the FWI with two-dimensional conventional streamer data set.Some preconditioning should be taken on marine data set before the FWI since it always contains obvious low-frequency noise.Combining the preconditioning,parameter selection and inversion strategy,the FWI performed on the marine data set achieves a good velocity model.And the results exhibited by the migration also implies the feasibility of the FWI.