High Resolution Multiscale Full Waveform Inversion And Migration Based On Deep Learning And Wavefield Reconstruction

In the field of geophysics,as computer processing power has improved,researchers have demanded higher precision in detecting underground structures.There are various methods used to image subsurface structures,among which reverse-time migration(RTM)based on the two-way wave equation is widely favored for its high imaging accuracy.However,RTM is limited by high computational cost,which makes it impractical for large-scale industrial applications.Calculating only the one-way wavefield can effectively save computational cost,but due to the limited angle of wavefield propagation,the one-way wave equation-based migration cannot achieve high-precision imaging for structures with large dip angles,and it suffers from low signal-to-noise ratio,amplitude distortion,and inaccurate phase.By analyzing the advantages and disadvantages of these two migration methods,we have developed a convolutional neural network(CNN)application mode(i.e.,improving one migration method by learning from another migration method)and used the CNN to combine the advantages of these two migration methods.As a result,one-way wave migration can maintain high computational efficiency while possessing high resolution,high signal-to-noise ratio,and accurate imaging of large dip structures.The CNN model is designed based on the classic U-net,with the one-way wave migration image based on the generalized screen propagator(GSP)as the input and the time-domain two-way wave RTM image as the label.The trained CNN model can enhance the GSP-based migration results and enable it to depict geological structures with large dip angles.Applying the trained CNN model to GSP-based migration images can eliminate errors and artifacts caused by large lateral velocity perturbations and improve resolution.Our approach makes GSP-based migration results approach RTM results.Compared to RTM,the combination of CNN model and GSP-based migration can produce high-quality images while saving a significant amount of computational cost.High-resolution migration imaging heavily relies on a precise velocity model,which is commonly obtained through full waveform inversion(FWI).To avoid cycle skipping,FWI typically requires low-frequency data with a high signal-to-noise ratio to compute a low-wavenumber model.To reduce the limitations of observational data quality on FWI,we have established a frequency-domain wavefield reconstruction method based on the first type of Rayleigh-Sommerfeld integral and utilized the advantages of multiple reconstructed wavefields(MRW)to improve the robustness of FWI in processing noisy data.MRW is the superposition of different reconstructed wavefields,and due to the superposition operation,the reflected waves are enhanced in MRW.Reflected waves play a very important role in the inversion of velocity models in deep regions.The wavefields that propagate deep into the model and cannot be received by detectors on the model surface are useless for FWI;therefore,the cross-correlation between the false residual wavefield caused by noise and the useless wavefield is detrimental to FWI.By cross-correlating with the residual wavefield,the enhanced reflection waves in MRW can effectively suppress this harmful cross-correlation for the gradient of FWI.We use MRW to optimize the gradient of FWI,making FWI more robust against noise.MRW is also effective in preventing overfitting of FWI to noisy data.We have provided a noise-resistant method for 1-BFGS-based FWI.Finally,we apply the reconstructed wavefield to RTM,improving the resolution of the RTM image.In the time domain,a multi-scale inversion strategy can be implemented by data filtering and FWI gradient filtering.Compared to data filtering,gradient filtering can make time-domain FWI a natural multi-scale inversion method.At present,gradientbased FWI methods are either not mature enough or too expensive.We propose a timeshift method to low-pass filter the gradient.Assigning different weights to the crosscorrelations of wavefields with different time shifts and summing them up can facilitate the extraction of low-wavenumber gradients.Updating the velocity model with the lowwavenumber gradient can yield a large-scale velocity model,providing an inexpensive and reliable multiscale strategy.We validate the practicality of time-shift FWI using actual offshore seismic data,and the experimental results show that our method can effectively handle practical data and improve the resolution of migration.