We develop and apply a full waveform inversion method that incorporates seismic data on a wide range of spatio-temporal scales, thereby constraining the details of both crustal and upper-mantle structure. This is intended to further our understanding of crust-mantle interactions that shape the nature of plate tectonics, and to be a step towards improved tomographic models of strongly scale-dependent earth properties, such as attenuation and anisotropy. The inversion for detailed regional earth structure consistently embedded within a large-scale model requires locally refined numerical meshes that allow us to (1) model regional wave propagation at high frequencies, and (2) capture the inferred fine-scale heterogeneities. The smallest local grid spacing sets the upper bound of the largest possible time step used to iteratively advance the seismic wave field. This limitation leads to extreme computational costs in the presence of fine-scale structure, and it inhibits the construction of full waveform tomographic models that describe earth structure on multiple scales. To reduce computational requirements to a feasible level, we design a multigrid approach based on the decomposition of a multiscale earth model with widely varying grid spacings into a family of single-scale models where the grid spacing is approximately uniform. Each of the single-scale models contains a tractable number of grid points, which ensures computational efficiency. The multi-to-single-scale decomposition is the foundation of iterative, gradient-based optimization schemes that simultaneously and consistently invert data on all scales for one multi-scale model. We demonstrate the applicability of our method in a full waveform inversion for Eurasia, with a special focus on Anatolia where coverage is particularly dense. Continental-scale structure is constrained by complete seismic waveforms in the 30-200 s period range. In addition to the well-known structural elements of the Eurasian mantle, our model reveals a variety of subtle features, such as the Armorican Massif, the Rhine Graben and the Massif Central. Anatolia is covered by waveforms with 8-200 s period, meaning that the details of both crustal and mantle structure are resolved consistently. The final model contains numerous previously undiscovered structures, including the extension-related updoming of lower-crustal material beneath the Menderes Massif in western Anatolia. Furthermore, the final model for the Anatolian region confirms estimates of crustal depth from receiver function analysis, and it accurately explains cross-correlations of ambient seismic noise at 10 s period that have not been used in the tomographic inversion. This provides strong independent evidence that detailed 3-D structure is well resolved.

/pdf/multiscale-full-waveform-inversion-4o83w8lo92.pdf

Multiscale full waveform inversion

High-resolution image and waveform inversion of smallscale targets requires the handling of high-frequency seismic wavefields. However, conventional finite-difference (FD) methods have strong numerical dispersions in the presence of high-frequency components. To reduce these numerical dispersions, we optimized the constant coefficients of the FD operator by maximizing the wavenumber coverage within a given error limitation. We set up three general criteria to enhance the convergence of the algorithm and reduce the optimization effort. We selected the error limitation to be 0.0001, this being the smallest in the literature, which led to perfect agreement between theoretical analyses and numerical experiments. The accuracy of our optimized FD methods can even reach that of much higher order unoptimized FD methods, which means great savings of computational efforts and memory demand. These advantages become even more apparent with 3D modeling, especially for saving memory demand.

/pdf/optimized-finite-difference-operator-for-broadband-seismic-2kpm9wlhyk.pdf

Optimized finite-difference operator for broadband seismic wave modeling

Directly imaging steeply dipping fault zones is difficult for conventional migration, including reverse-time migration (RTM). We developed a new least-squares RTM (LSRTM) method to directly image steeply dipping fault zones. The method uses a wavefield-separation imaging condition and updated source wavefields during each iteration. Our new imaging method produces horizontal-looking images that show mostly steeply dipping fault zones. Conventional least-squares RTM does not update source wavefields and cannot directly image vertical fault zones. We numerically determined that it is crucial to update source wavefields to image steeply dipping fault zones. Using synthetic seismic data, we proved that our new LSRTM method can directly image steeply dipping fault zones with dipping angles up to 90°. Compared with conventional LSRTM, our LSRTM method was less sensitive to the smoothness and the velocity error of the initial migration velocity model.

Least-squares reverse-time migration with a wavefield-separation imaging condition and updated source wavefields

In this paper we propose a self-adaptive trust region algorithm.The trust region radius is updated at a varable rate according to the ratio between the actual reduction and the predicted reduction of the objective function,rather than by simply enlarging or reducing the original trust region radius at a constant rate.We show that this new algorithm preserves the strong convergence property of traditional trust region methods.Numerical results are also presented.

A self—adaptive trust region algorithm

The computational accuracy and efficiency of finite element method and spectral element method (SEM) are investigated thoroughly in time-domain elastic wavefield modeling. The diagonal mass matrices of the FEM and SEM free from matrix inversion are compared comprehensively by making full use of the mass-lumped technique and quadrature rules. We investigate the FEM and SEM based, respectively, on quadrilateral with the polynomials of degrees one and two, and on triangular grids with the polynomials of degrees one and three. Generally, the numerical solutions based on quadrilateral grids have a higher precision than those computed on triangular grids when the same order of polynomials is used. The FEM has a comparable accuracy to the SEM with the same number of interpolant points. In view of the triangular and quadrilateral SEMs, the former suffers from larger computational costs and relatively lower accuracy compared with the latter. Furthermore, the convergence study proves that the triangular SEM produces consistently larger errors than the quadrilateral SEM for any order and element sizes. However, the triangular SEM can adapt to arbitrary complex geometries effectively. In terms of efficiency, the FEM has an efficiency comparable with the SEM on condition that the order of interpolation polynomials is identical. In addition, a perfectly matched layer (PML) boundary condition in variational form is deduced. By introducing four intermediate variables in frequency domain, the PML avoids convolution calculation and obtains an exact solution through inverse Fourier transform in time domain. The numerical examples verify the validity and effectiveness of the PML.

A comparative study of finite element and spectral element methods in seismic wavefield modeling

We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces.

http://iopscience.iop.org/article/10.1088/1742-2132/11/5/055009/pdf

A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling

Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system. We define the Lie operators associated with kinetic and potential energy, and construct a new kind of second order symplectic scheme, which is extremely suitable for high efficient and long-term seismic wave simulations. Three sets of optimal coefficients are obtained based on the principle of minimum truncation error. We investigate the stability conditions for elastic wave simulation in homogeneous media. These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments. One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability. The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.

A new kind of optimal second-order symplectic scheme for seismic wave simulations

Numerical simulation research on two-phase flow boiling heat transfer in helically coiled tube

An adaptive subspace trust-region method for frequency-domain seismic full waveform inversion

Experimental investigation on the validity of the local thermal equilibrium assumption in ablative-material response models

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