Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

We formulate the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that both the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we show that the adjoint wave propagator preserves the dispersion and compensates the amplitude, while the time-reversed adjoint wave propagator behaves identically as the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit Q parameterization, which avoids the implicit Q in the conventional viscoacoustic/viscoelastic full waveform inversion ( Q-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. We find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel. After validating the Fréchet kernels using the finite-difference method, we conduct a numerical example to demonstrate the capability of the kernels to characterize both velocity and attenuation anomalies. The kernels of different misfit measurements are presented to investigate their different sensitivities. Our results suggest that rather than the traveltime, the amplitude and the waveform kernels are more suitable to capture attenuation anomalies. These kernels lay the foundation for the multiparameter inversion with the fractional formulation, and the decoupled nature of them promotes our understanding of the significance of different physical processes in the Q-FWI.

Introduction of the Hessian in joint migration inversion and improved recovery of structural information using an image-based regularization

Joint migration inversion (JMI) is a method based on the one-way wave equations that aims at fitting seismic reflection data to estimate an image and a background velocity. The depth-migrated image describes the high spatial-frequency content of the subsurface and, in principle, is true amplitude. The background velocity model accounts mainly for the large spatial-scale kinematic effects of the wave propagation. Looking for a deeper understanding of the method, we briefly review the continuous equations that compose the forward modeling engine of JMI for acoustic media and angle-independent scattering. Then, we use these equations together with the first-order adjoint-state method to arrive at a new formulation of the model gradients. To estimate the image, we combine the second-order adjoint-state method with the truncated-Newton method to obtain the image updates. For the model (velocity) estimation, in comparison to the image update, we reduce the computational cost by simply adopting a diagonal preconditioner for the corresponding gradient in combination with an image-based regularizing function. Based on this formulation, we build our implementation of the JMI algorithm. The proposed image-based regularization of the model estimate allows us to carry over structural information from the estimated image to the jointly estimated background model. As demonstrated by our numerical experiments, this procedure can help to improve the resolution of the estimated model and make it more consistent with the image.

Global adjoint tomography—model GLAD-M25

SUMMARY Building on global adjoint tomography model GLAD-M15, we present transversely isotropic global model GLAD-M25, which is the result of 10 quasi-Newton tomographic iterations with an earthquake database consisting of 1480 events in the magnitude range 5.5 ≤ Mw ≤ 7.2, an almost sixfold increase over the first-generation model. We calculated fully 3-D synthetic seismograms with a shortest period of 17 s based on a GPU-accelerated spectral-element wave propagation solver which accommodates effects due to 3-D anelastic crust and mantle structure, topography and bathymetry, the ocean load, ellipticity, rotation and self-gravitation. We used an adjoint-state method to calculate Fréchet derivatives in 3-D anelastic Earth models facilitated by a parsimonious storage algorithm. The simulations were performed on the Cray XK7 ‘Titan’ and the IBM Power 9 ‘Summit’ at the Oak Ridge Leadership Computing Facility. We quantitatively evaluated GLAD-M25 by assessing misfit reductions and traveltime anomaly histograms in 12 measurement categories. We performed similar assessments for a held-out data set consisting of 360 earthquakes, with results comparable to the actual inversion. We highlight the new model for a variety of plumes and subduction zones.