Parallel Adaptive Mesh Coarsening for Seismic Tomography

International audienceSeismic tomography enables to model the internal structure of the Earth. In order to improve the precision of existing models, a huge amount of acquired seismic data must be analyzed. The analysis of such massive data require a considerable computing power which can only be delivered by parallel computational equipments. Yet, parallel computation is not sufficient for the task: we also need algorithms to automatically concentrate the computations on the most relevant data parts. The objective of the paper is to present such an algorithm. From an initial regular mesh in which cells carry data with varying relevance, we present a method to aggregate elementary cells so as to homogenize the relevance of data. The result is an irregular mesh which has the ad- vantage over the initial mesh of having orders of magnitude less cells while preserving the geophysical meaning of data. We present both a sequential and a parallel algorithm to solve this problem under the hypotheses and constraints inherited from the geophysical context

Parallel Seismic Ray Tracing

Seismic ray tracing is a common method for understanding and modeling seismic wave propagation. The wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby providing a mechanism to control ray density on the wavefront. In this thesis we present the design and implementation of a parallel wavefront construction algorithm (pWFC) for seismic ray tracing. The proposed parallel algo- rithm is developed using the stapl library for parallel C++ code.We present the idea of modeling ray tubes with an additional ray in the center to facilitate parallelism. The parallel wavefront construction algorithm is applied to wide range of models such as simple synthetic models that enable us to study various aspects of the method while others are intended to be representative of basic geological features such as salt domes. We also present a theoretical model to understand the performance of the pWFC algorithm. We evaluate the performance of the proposed parallel wavefront construction algorithm on an IBM Power 5 cluster. We study the effect of using different mesh types, varying the position of source and their number etc. The method is shown to provide good scalable performance for different models. Load balancing is also shown to be the major factor hindering the performance of the algorithm. We provide two load balancing algorithms to solve the load imbalance problem. These algorithms will be developed as an extension of the current work

3-D electrical resistivity tomography using adaptive wavelet parameter grids

We present a novel adaptive model parametrization strategy for the 3-D electrical resistivity tomography problem and demonstrate its capabilities with a series of numerical examples. In contrast to traditional parametrization schemes, which are based on fixed disjoint blocks, we discretize the subsurface in terms of Haar wavelets and adaptively adjust the parametrization as the iterative inversion proceeds. This results in a favourable balance of cell sizes and parameter reliability, that is, in regions where the data constrain the subsurface properties well, our parametrization strategy leads to a fine grid, whereas poorly resolved areas are represented only by a few large blocks. This is documented with eigenvalue analyses and by computing model resolution matrices. During the initial iteration steps, only a few model parameters are involved, which reduces the risk that the regularization dominates the inversion. The algorithm also automatically accounts for non-linear effects caused by pronounced conductivity contrasts. Inside conductive features a finer grid is generated than inside more resistive structures. The automated parameter adaptation is computationally efficient, because the coarsening and refinement subroutines have a nearly linear numerical complexity with respect to the number of model parameters. Because our approach is not tightly coupled to electrical resistivity tomography, it should be straightforward to adapt it to other data type

Three-dimensional time-lapse velocity tomography of an underground longwall panel

Three-dimensional velocity tomograms were generated to image the stress redistribution around an underground coal longwall panel to produce a better understanding of the mechanisms that lead to ground failure, especially rockbursts. Mining-induced microseismic events provided passive sources for the three-dimensional velocity tomography. Surface-mounted geophones monitored microseismic activity for 18 days. Eighteen tomograms were generated and high-velocity regions correlated with high abutment stresses predicted by numerical modeling. Additionally, the high-velocity regions were observed to redistribute as the longwall face retreated, indicating that velocity tomography may be an appropriate technology for monitoring stress redistribution in underground mines

Multi-scale dynamics and rheology of mantle flow with plates

Fundamental issues in our understanding of plate and mantle dynamics remain unresolved, including the rheology and state of stress of plates and slabs; the coupling between plates, slabs and mantle; and the flow around slabs. To address these questions, models of global mantle flow with plates are computed using adaptive finite elements, and compared to a variety of observational constraints. The dynamically consistent instantaneous models include a composite rheology with yielding, and incorporate details of the thermal buoyancy field. Around plate boundaries, the local resolution is 1 km, which allows us to study highly detailed features in a globally consistent framework. Models that best fit plateness criteria and plate motion data have strong slabs with high stresses. We find a strong dependence of global plate motions, trench rollback, net rotation, plateness, and strain rate on the stress exponent in the nonlinear viscosity; the yield stress is found to be important only if it is smaller than the ambient convective stress. Due to strong coupling between plates, slabs, and the surrounding mantle, the presence of lower mantle anomalies affect plate motions. The flow in and around slabs, microplate motion, and trench rollback are intimately linked to the amount of yielding in the subducting slab hinge, slab morphology, and the presence of high viscosity structures in the lower mantle beneath the slab

An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle

Mantle convection is the fundamental physical process within earth's interior responsible for the thermal and geological evolution of the planet, including plate tectonics. The mantle is modeled as a viscous, incompressible, non-Newtonian fluid. The wide range of spatial scales, extreme variability and anisotropy in material properties, and severely nonlinear rheology have made global mantle convection modeling with realistic parameters prohibitive. Here we present a new implicit solver that exhibits optimal algorithmic performance and is capable of extreme scaling for hard PDE problems, such as mantle convection. To maximize accuracy and minimize runtime, the solver incorporates a number of advances, including aggressive multi-octree adaptivity, mixed continuous-discontinuous discretization, arbitrarily-high-order accuracy, hybrid spectral/geometric/algebraic multigrid, and novel Schur-complement preconditioning. These features present enormous challenges for extreme scalability. We demonstrate that---contrary to conventional wisdom---algorithmically optimal implicit solvers can be designed that scale out to 1.5 million cores for severely nonlinear, ill-conditioned, heterogeneous, and anisotropic PDEs

Parallel Seismic Ray Tracing

Seismic ray tracing is a common method for understanding and modeling seismic wave propagation. The wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby providing a mechanism to control ray density on the wavefront. In this thesis we present the design and implementation of a parallel wavefront construction algorithm (pWFC) for seismic ray tracing. The proposed parallel algo- rithm is developed using the stapl library for parallel C++ code.We present the idea of modeling ray tubes with an additional ray in the center to facilitate parallelism. The parallel wavefront construction algorithm is applied to wide range of models such as simple synthetic models that enable us to study various aspects of the method while others are intended to be representative of basic geological features such as salt domes. We also present a theoretical model to understand the performance of the pWFC algorithm. We evaluate the performance of the proposed parallel wavefront construction algorithm on an IBM Power 5 cluster. We study the effect of using different mesh types, varying the position of source and their number etc. The method is shown to provide good scalable performance for different models. Load balancing is also shown to be the major factor hindering the performance of the algorithm. We provide two load balancing algorithms to solve the load imbalance problem. These algorithms will be developed as an extension of the current work

Gamra: Simple meshing for complex earthquakes

The static offsets caused by earthquakes are well described by elastostatic models with a discontinuity in the displacement along the fault. A traditional approach to model this discontinuity is to align the numerical mesh with the fault and solve the equations using finite elements. However, this distorted mesh can be difficult to generate and update. We present a new numerical method, inspired by the Immersed Interface Method (Leveque and Li, 1994), for solving the elastostatic equations with embedded discontinuities. This method has been carefully designed so that it can be used on parallel machines on an adapted finite difference grid. We have implemented this method in Gamra, a new code for earth modeling. We demonstrate the correctness of the method with analytic tests, and we demonstrate its practical performance by solving a realistic earthquake model to extremely high precision