scholarly journals Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Georg S. Reuber ◽  
Frederik J. Simons
Keyword(s):  
Acoustic Wave ◽  
Mass Density ◽  
Resolving Power ◽  
Surface Velocity ◽  
Seismic Displacement ◽  
Material Parameters ◽  
Gradient Based ◽  
Geophysical Imaging ◽  
The Cost ◽  
Inversion Techniques

AbstractWe discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynamics equations of Stokes for incompressible steady-state flow in the mantle. The observables are the gravitational potential, the seismic displacement, and the surface velocity, all measured at the surface. The inversion parameters of interest are the mass density, the acoustic wave speed, and the viscosity. These systems of partial differential equations and their adjoints were implemented in a single Python code using the finite-element library FeNICS. To investigate the shape of the cost functions, we present a grid search in the parameter space for three end-member geological settings: a falling block, a subduction zone, and a mantle plume. The performance of a gradient-based inversion for each single observable separately, and in combination, is presented. We furthermore investigate the performance of a shape-optimizing inverse method, when the material is known, and an inversion that inverts for the material parameters of an anomaly with known shape.

An Adaptive EFG-FE Computational Model for Thermal Elasto-Plastic Frictional Contact Problems

2008 ◽  
Vol 33-37 ◽  
pp. 821-826
Author(s):  
Zheng Zhang ◽  
Geng Liu ◽  
Tian Xiang Liu
Keyword(s):  
Frictional Heating ◽  
Contact Problems ◽  
Coupling Model ◽  
Adaptive Refinement ◽  
Frictional Heat ◽  
Plastic Behavior ◽  
Initial Stiffness ◽  
Gradient Based ◽  
Local Adaptive Refinement ◽  
The Cost

An adaptive meshless element-free Galerkin-finite element (EFG-FE) coupling model for thermal elasto-plastic contact problems is developed to investigate the influences of the steady-state frictional heating on the contact performance of two contacting bodies. The thermal elasto-plastic contact problems using the initial stiffness method is presented. The local adaptive refinement strategy and the strain energy gradient-based error estimation for EFG-FE coupling method are combined. The adaptive meshless model takes into account the temperature variation, micro plastic flow, and the coupled thermo-elasto-plastic behavior of the materials, considering the strain-hardening property of the materials and temperature-dependent yield strength. The adaptive model is verified through the contact analysis of a cylinder with an elasto-plastic plane. The thermal effects on the contact pressure, stresses distributions with certain frictional heat inputs are studied. The results show that the accuracy of the solutions from the adaptive refinement model is satisfactory but the cost of the CPU time is much less than that for the uniform refinement calculation.

scholarly journals On the Jump Conditions for Shock Waves in Condensed Materials

2021 ◽  
Author(s):  
R K Anand
Keyword(s):  
Stainless Steel ◽  
Mach Number ◽  
Shock Front ◽  
Particle Velocity ◽  
Mass Density ◽  
Jump Conditions ◽  
Condensed Material ◽  
Material Parameters ◽  
Stainless Steel 304 ◽  
Condensed Materials

Abstract In this article, we have proposed Rankine–Hugoniot (RH) boundary conditions at the normal shock-front which is passing through the condensed material. These RH conditions are quite general, and their convenient forms for the particle velocity, mass density, pressure and temperature have been presented in terms of the upstream Mach number, and the material parameters for the weak and the strong shocks, respectively. Finally, the effects on the mechanical quantities of the shock compressed materials e.g. titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc. have been discussed.

AN APPROACH TO INVERSE FILTERING OF NEAR‐SURFACE LAYER EFFECTS FROM SEISMIC RECORDS

Geophysics ◽  
1961 ◽  
Vol 26 (6) ◽  
pp. 754-760 ◽  
Author(s):  
Pierre L. Goupillaud
Keyword(s):  
Surface Layer ◽  
Seismic Reflection ◽  
Normal Incidence ◽  
Resolving Power ◽  
Surface Velocity ◽  
Inverse Filtering ◽  
Near Surface ◽  
Seismic Records ◽  
Stratification Variable ◽  
Velocity Information

This paper suggests a scheme for compensating the effects that the near‐surface stratification, variable from spread to spread, produces on both the character and the timing of the seismic traces. For this purpose, accurate near‐surface velocity information is mandatory. This scheme should greatly reduce the correlation difficulties so frequently encountered in many areas. It may also be used to enhance the resolving power of the seismic reflection technique. The approach presented here is based on the rather restrictive assumptions of normal incidence, parallel equispaced plant reflectors, and noiseless conditions.

Fluid and Structure Interaction in Cochlea’s Similar Geometry

2010 ◽  
Author(s):  
Mahmoud Hamadiche
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Wave ◽  
Transverse Wave ◽  
Basilar Membrane ◽  
Striking Similarity ◽  
Partial Differential ◽  
Material Parameters ◽  
Non Linear

A non linear mathematical model addressing the passive mechanism of the cochlea is proposed in this work. In this respect, the interaction between the basilar membrane seen as an elastic solid and fluids in both scala vestibuli and tympani is developed. Via the fluid/solid interface, a full fluid/solid interaction is taking into account. Furthermore a significant improvement of the existing models has been made in both fluid flow modelling and solid modelling. In the present paper, the flow is three dimensional and the solid is non homogeneous two dimensional membrane where the material parameters depend only on the axial distance. The problem formulation leads to a system of non linear partial differential equations. Solution of the linearized system of partial differential equations of the proposed approach is presented. The numerical results obvious a lower and upper limits of the cochlea resonance frequency versus the material parameters of the basilar membrane. It is shown that a monochromatic acoustic wave energises only a portion of the basilar membrane and the location of the excited portion depends on the frequency of the incident acoustic wave. Those results explain the ability of the cochlea in deciphering the frequency of sound with high resolution in striking similarity with the known experimental results. The mathematical model shows that the excited strip of the basilar membrane by a monochromatic acoustic wave is very small when a transverse wave exists in the basilar membrane. Thus, a transverse wave improves highly the resolution of the cochlea in deciphering the high frequency of the incident acoustic wave.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

scholarly journals Extended lens reconstructions with grale: exploiting time-domain, substructural, and weak lensing information

2020 ◽  
Vol 494 (3) ◽  
pp. 3253-3274
Author(s):  
Jori Liesenborgs ◽  
Liliya L R Williams ◽  
Jenny Wagner ◽  
Sven De Rijcke
Keyword(s):  
Mass Density ◽  
Gravitational Lens ◽  
Weak Lensing ◽  
Small Scale ◽  
Source Position ◽  
Cluster Galaxy ◽  
Weak Inversion ◽  
Sufficient Detail ◽  
Inversion Techniques

ABSTRACT The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to ‘overfocusing’ the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small-scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.

Intelligent gradient-based search of incompletely defined design spaces

1997 ◽  
Vol 11 (3) ◽  
pp. 199-210 ◽  
Author(s):  
Mark Schwabacher ◽  
Andrew Gelsey
Keyword(s):  
Numerical Optimization ◽  
Computation Method ◽  
Rule Based ◽  
Transport Aircraft ◽  
Supersonic Transport ◽  
Engineering Designs ◽  
Gradient Computation ◽  
Gradient Based ◽  
Complex Engineering ◽  
The Cost

AbstractGradient-based numerical optimization of complex engineering designs offers the promise of rapidly producing better designs. However, such methods generally assume that the objective function and constraint functions are continuous, smooth, and defined everywhere. Unfortunately, realistic simulators tend to violate these assumptions. We present a rule-based technique for intelligently computing gradients in the presence of such pathologies in the simulators, and show how this gradient computation method can be used as part of a gradient-based numerical optimization system. We tested the resulting system in the domain of conceptual design of supersonic transport aircraft, and found that using rule-based gradients can decrease the cost of design space search by one or more orders of magnitude.

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