This thesis develops five novel methods for seismic imaging and inversion to improve both their computational efficiency and accuracy. Three of them improve the accuracy of the fi nal inverted images by novel preconditioning strategies, and the other two are machine learning (ML) methods applied to seismic data.
(1) Conventional viscoacoustic least-squares reverse time migration, also denoted as Q-LSRTM, su ffers from slow-convergence and low-resolution problems due to the attenuative property of the adjoint Q propagators. To mitigate these problems, I propose a viscoacoustic deblurring fi lter (DF) as a preconditioner for Q-LSRTM. Moreover, to avoid the usage of the attenuative adjoint Q propagator, I propose the application of a hybrid deblurring filter to acoustic reverse time migration (RTM) images to correct for attenuation distortions. Numerical tests demonstrate that both deblurring filter strategies can produce images with higher resolution than Q-LSRTM and much cheaper in computation.
(2) The deblurring fi lter is less eff ective when the migration image contains strong migration artifacts. To mitigate this problem, I develop a novel support vector machine-based (SVM) fi ltering method which employs the features of coherency, amplitude, and dipping angle from selected dip-angle angle-domain common-image gathers (ADCIGs) to automatically distinguish signals from artifacts. Our numerical results show that SVM fi ltering can efficiently remove the aliasing artifacts and improves the image quality.
(3) The accurate imaging of subsurface requires the correct estimates of the velocity model. Here, I present the strategy of multiscale reflection phase inversion (MRPI) with a deblurring filter for inverting the low-wavenumber components of the velocity model. This method employs amplitude replacement, trace integration and o ffset-selection of traces to mitigate the cycle-skipping problem. It also uses deblurring fi lters as an inexpensive alternative to LSRTM to compute the perturbation image. Numerical results show that MRPI + DF can efficiently recover the low-wavenumber velocity model and is less prone to getting stuck in local minima compared to conventional reflection inversion method.
(4) Non-linear inversion gets stuck in a local minimum because the data are very complex (i.e, wiggly in time), which means that the objective function is characterized by many local minima. To avoid this problem, I present a wave-equation inversion method that inverts for the subsurface velocity model from data skeletonized by a machine learning method. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained autoencoder. The input data to the autoencoder are the seismic traces, while the implicit function theorem is used to determine the formula for the Frechet derivative used in the gradient calculation. Empirical results suggest that the cycle-skipping problem is largely mitigated by replacing the waveform di fferences with the latent-space parameters. We denote this method as Newtonian machine learning because it unites, for the first time, the parameter inversion of the governing equations of Newtonian physics with the dimensional reduction properties of a neural network.