Physics

We investigate experimentally the short-range interactions occurring between two subaqueous barchans. The experiments were conducted in a water channel of transparent material where controlled grains were poured inside, and a camera placed on the top acquired images of the bedforms. We varied the grain types (diameter, density and roundness), pile masses, transverse distances, water flow rates and initial conditions. As a result, five different patterns were identified for both aligned and off-centered configurations and we propose interaction maps that depend basically on the ratio between the number of grains of each dune, Shields number and alignment of barchans. In addition, we show experimental indications that an ejected barchan has roughly the same mass of the impacting one in some cases, and that in wake-dominated processes the asymmetry of the downstream dune is large. The present results shed light on the size regulation of barchans found on Earth and other planets.

This paper focuses on state-of-the art of various approaches for the modelling of deformation behavior of soils when subjected to cyclic loading. The various approaches are broadly classified into implicit and explicit. Models within each category are discussed and some of their limitations are pointed out.

We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and explicit (numerical) solutions for the response obey this law for the case of a cylindrical, rectangular protuberance. Both the low-order (poor approximations of the response) as well as higher-order (supposedly better approximations) turn out to satisfy the conservation of flux relation, which means that the satisfaction of this relation is a necessary, but not sufficient, means for determining whether a solution to the scattering problem is valid.

In the workflow of Full-Waveform Inversion (FWI), we often tune the parameters of the inversion to help us avoid cycle skipping and obtain high resolution models. For example, typically start by using objective functions that avoid cycle skipping, like tomographic and image based or using only low frequency, and then later, we utilize the least squares misfit to admit high resolution information. We also may perform an isotropic (acoustic) inversion to first update the velocity model and then switch to multi-parameter anisotropic (elastic) inversions to fully recover the complex physics. Such hierarchical approaches are common in FWI, and they often depend on our manual intervention based on many factors, and of course, results depend on experience. However, with the large data size often involved in the inversion and the complexity of the process, making optimal choices is difficult even for an experienced practitioner. Thus, as an example, and within the framework of reinforcement learning, we utilize a deep-Q network (DQN) to learn an optimal policy to determine the proper timing to switch between different misfit functions. Specifically, we train the state-action value function (Q) to predict when to use the conventional L2-norm misfit function or the more advanced optimal-transport matching-filter (OTMF) misfit to mitigate the cycle-skipping and obtain high resolution, as well as improve convergence. We use a simple while demonstrative shifted-signal inversion examples to demonstrate the basic principles of the proposed method.

Most of the seismic inversion techniques currently proposed focus on robustness with respect to the background model choice or inaccurate physical modeling assumptions, but are not apt to large-scale 3D applications. On the other hand, methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously bogged down by local minima and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting model or inaccurate physics when compared to full waveform inversion. The method is based on a dual (Lagrangian) reformulation of the classical wavefield reconstruction inversion, whose robustness with respect to local minima is well documented in the literature. However, it is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation. The proposed reformulation allows the deployment of state-of-the-art time-domain finite-difference methods, and is computationally mature for industrial scale problems.

Focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid is discussed. For the uniform grid the model sensitivity matrices exhibit block Toeplitz Toeplitz block structure, by blocks for each depth layer of the subsurface. Then, through embedding in circulant matrices, all forward operations with the sensitivity matrix, or its transpose, are realized using the fast two dimensional Fourier transform. Simulations demonstrate that this fast inversion algorithm can be implemented on standard desktop computers with sufficient memory for storage of volumes up to size n≈1M . The linear systems of equations arising in the focusing inversion algorithm are solved using either Golub Kahan bidiagonalization or randomized singular value decomposition algorithms in which all matrix operations with the sensitivity matrix are implemented using the fast Fourier transform. These two algorithms are contrasted for efficiency for large-scale problems with respect to the sizes of the projected subspaces adopted for the solutions of the linear systems. The presented results confirm earlier studies that the randomized algorithms are to be preferred for the inversion of gravity data, and that it is sufficient to use projected spaces of size approximately m/8 , for data sets of size m . In contrast, the Golub Kahan bidiagonalization leads to more efficient implementations for the inversion of magnetic data sets, and it is again sufficient to use projected spaces of size approximately m/8 . Moreover, it is sufficient to use projected spaces of size m/20 when m is large, m≈50000 , to reconstruct volumes with n≈1M . Simulations support the presented conclusions and are verified on the inversion of a practical magnetic data set that is obtained over the Wuskwatim Lake region in Manitoba, Canada.

Precipitation and dissolution are prime processes in carbonate rocks and being able to monitor them is of major importance for aquifer and reservoir exploitation or environmental studies. Electrical conductivity is a physical property sensitive both to transport phenomena of porous media and to dissolution and precipitation processes. However, its quantitative use depends on the effectiveness of the petrophysical relationship to relate the electrical conductivity to hydrological properties of interest. In this work, we develop a new physically-based model to estimate the electrical conductivity by upscaling a microstructural description of water-saturated fractal porous media. This model is successfully compared to published data from both unconsolidated and consolidated samples, or during precipitation and dissolution numerical experiments. For the latter, we show that the permeability can be linked to the predicted electrical conductivity.

Advances in the field of seismic interferometry have provided a basic theoretical interpretation to the full spectrum of the microtremor horizontal-to-vertical spectral ratio [H/V(f)]. The interpretation has been applied to ambient seismic noise data recorded both at the surface and at depth. The new algorithm, based on the diffuse wavefield assumption, has been used in inversion schemes to estimate seismic wave velocity profiles that are useful input information for engineering and exploration seismology both for earthquake hazard estimation and to characterize surficial sediments. However, until now, the developed algorithms are only suitable for on land environments with no offshore consideration. Here, the microtremor H/V(z, f) modeling is extended for applications to marine sedimentary environments for a 1D layered medium. The layer propagator matrix formulation is used for the computation of the required Green's functions. Therefore, in the presence of a water layer on top, the propagator matrix for the uppermost layer is defined to account for the properties of the water column. As an application example we analyze eight simple canonical layered earth models. Frequencies ranging from 0.2 to 50 Hz are considered as they cover a broad wavelength interval and aid in practice to investigate subsurface structures in the depth range from a few meters to a few hundreds of meters. Results show a marginal variation of 8 percent at most for the fundamental frequency when a water layer is present. The water layer leads to variations in H/V peak amplitude of up to 50 percent atop the solid layers.

We present a minimal one-dimensional model for the transition from crack-like to pulse-like propagation of frictional rupture. In its non-dimensional form, the model depends on only two free parameters: the non-dimensional pre-stress and an elasticity ratio that accounts for the finite height of the system. The model contains stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. Results demonstrate that the existence of pulse-like ruptures requires only elastic relaxation and redistribution of initial pre-stress. The novelty of our findings is that pulse-like propagation along frictional interfaces is a generic elastic feature, whose existence is not sensitive to particular rate- or slip-dependencies of dynamic friction.

The purpose of this study is to propose a modified micromorphic continuum model for granular materials based on a micromechanics approach. In this model, Cauchy stress and the couple stress are symmetric conjugated with the symmetric strain and the symmetric curvature respectively, and the relative stress measures are asymmetric conjugated with the asymmetric relative strain measures. This modified micromorphic model considers a continuum material point as a granular volume element whose deformation behavior is influenced by the translation and the rotation of particles. And this study proposes that the microscopic actual motion is decomposed into a macroscopic motion and a fluctuation between the macro-micro motion. Based on this decomposition, the micromorphic constitutive relationships are derived for granular materials. In the constitutive relationships, the macroscopic constitutive relationships are first-order because of the introduce of the independent rotation of particle instead of the second-order micro-deformation gradient. Furthermore, the complex constitutive moduli in the micromorphic model are obtained in the expressions of the microstructural information such as the contact stiffness and the internal length.