Computational Rock Physics Using a Hamiltonian Particle Method for Effective Elastic Properties of Cracked Media

A particle based continuum model is presented for seismic wave propagation with an arbitrary refinement of spatial resolution. In the present study, we apply a Hamiltonian Particle Method (HPM) to the simulation of seismic ground motion. HPM has some advantages over the conventional continuum simulators in terms of; (i) the traction-free boundary conditions are automatically introduced, (ii) the data structure in HPM become simple, (iii) an arbitrary refinement of spatial resolution can be carried out easily. First, we simulated the seismic wave propagation in a homogeneous media using several numerical models. The models were partially refined in space, but the refinement level of each model was different. This numerical test was conducted to confirm whether the refinement of spatial resolution in HPM generates the artificial dispersion or not. The obtained results showed that the abrupt refinement of particles can be accepted in HPM. Next, we made the heterogeneous model with the low velocity zone modeled after the sedimentary basin structure to demonstrate the effectiveness of refinement technique in HPM. Our results showed that HPM can reproduce seismic ground motion on the free surface with the arbitrary spatial refinement. This means that the method can be an alternative to existing simulators of seismic ground motion.

Better understanding of failure mechanism of rocks benefits in many fields from rock engineering to earth sciences. Especially, it is essential to understand how fractures initiate and propagate under various loading conditions in order to clarify real rock fracture processes. For the interpretation of rock failure, many attempts have been made experimentally or using fracture mechanics theory. Although much of the knowledge available today is based on experimental observations and the theory successfully represented the propagation of predefined cracks, the failure mechanics are not fully understood by experimental results and it is difficult to describe the initiation and coalescence of cracks using the theory. Thus, in the recent years, numerical modeling, which may be less restrictive, has been applied to study crack behaviors, and we also approach to the rock failure based on numerical simulations. To represent rock failure, we use a Hamiltonian Particle method (HPM), one of particle methods. In the HPM, we do not need to use grids or meshes to discretize the rock model, and thus we could deal with the failure relatively easily. In spite of this advantage of the HPM, the applicability of the method to the failure phenomena have yet to be revealed fully. In the present study, we apply the HPM to rock failure under some different specimens and different loading conditions. As a result of our simulations, the HPM successfully reproduce failure pattern of brittle fracture observed rock fracture experiments and can observe micro cracks initiation and propagation. This suggests that the HPM is the useful tool to analyze rock failure.

A particle-based continuum model is presented for the simulation of seismic wave propagation. Accurate simulation of seismic ground motion for the model with arbitrary free surface of the ground is a key issue for not only scientific interest but also in practical fields to estimate seismic signals traveled through subsurface structure. In the present study, a Hamiltonian particle method (HPM) is proposed to seismological numerical modeling. HPM has some advantages comparing to traditional continuous and discontinuous methods in terms of; (i) the introduction of the traction-free boundary conditions is easier than that in finite difference methods (FDM), (ii) data structure in HPM is simpler than that in finite element methods (FEM) because of no need to consider the connectivity between nodes and elements when discretizing object of analysis, and (iii) no need to calibrate material parameters that is a cumbersome process in distinct element method (DEM) with a hexagonal arrangement. In this paper, we first calculate the seismic wave propagation in a homogeneous media and compare the results with that from FDM to demonstrate the performance of the method. Next, we simulate surface wave propagation in a model with arbitrary surface topology. These results indicate that HPM can calculate elastic and surface wave propagation with sufficient accuracy for models with a free surface of arbitrary shape.

Deep learning techniques elucidate and modify the shape factor to extend the effective medium theory beyond its original formulation

In this paper, from the point of view reducing the system calculation cost, a digital channelized receiver is proposed. The decimation factor of the proposed digital channelized receiver with low calculation cost is equal to the number of signal channels, which is acquired by changing the input signal of the embedded instantaneous frequency measurement receiver. Due to the increase of the system decimation factor, the data to be processed are decreased and the system processing speed is improved indirectly. In this paper, the architecture and working principle of the proposed digital channelized receiver with low calculation cost is firstly given; secondly, the overlapping channel division method used in the digital channelized receiver with low calculation cost is put forward. Meanwhile, the channel arbitration method of the unmodulated or modulated signal in the case of overlapping channel division is analyzed. Then, the frequency measurement principle of the embedded instantaneous frequency measurement receiver is deduced in detail. Through the use of the overlapping channel division method, the proposed digital channelized receiver with low calculation cost is able to avoid the existence of blind spots between channels and increases the interception probabilities of the input signals. And, the proposed digital channelized receiver can distinguish two signals coming simultaneously to the same channel by using the overlapping channel division method. In addition, the channel of the input signal truly residing can be simply determined by using the channel arbitration in the case of overlapping channel division and according to the output frequency of the embedded instantaneous frequency measurement receiver. Finally, the related simulation results verify the correctness and feasibility of the theories and method involved in this paper.

MMC-LES modelling of droplet nucleation and growth in turbulent jets

Disentangled convolution for optimizing receptive field

A crack tensor and its relation to wave velocity anisotropy in jointed rock masses

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation such as that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation. In this experiment, a large number of hydrographs are generated with the modular modeling framework FUSE (Framework for Understanding Structural Errors), using eight numerical techniques across a variety of forcing data sets. All constructed models are conceptual and lumped. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational cost and numerical error associated with each hydrograph were recorded. Numerical error is assessed via root mean square error and normalized root mean square error. It was found that the root mean square error usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both a small numerical error and a low computational cost. A small literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be suboptimal. We conclude that relatively large numerical errors may be common in current models, highlighting the need for robust numerical techniques, in particular in the face of increasing precipitation extremes.

Crack damage results in a decrease of elastic wave velocities and in the development of anisotropy. Using non-interactive crack effective medium theory as a fundamental tool, we calculate dry and wet elastic properties of cracked rocks in terms of a crack density tensor, average crack aspect ratio and mean crack fabric orientation from the solid grains and fluid elastic properties. Using this same tool, we show that both the anisotropy and shear-wave splitting of elastic waves can be derived. Two simple crack distributions are considered for which the predicted anisotropy depends strongly on the saturation, reaching up to 60% in the dry case. Comparison with experimental data on two granites, a basalt and a marble, shows that the range of validity of the non-interactive effective medium theory model extends to a total crack density of approximately 0.5, considering symmetries up to orthorhombic. In the isotropic case, Kachanov’s (1994) non-interactive effective medium model was used in order to invert elastic wave velocities and infer both crack density and aspect ratio evolutions. Inversions are stable and give coherent results in terms of crack density and aperture evolution. Crack density variations can be interpreted in terms of crack growth and/or changes of the crack surface contact areas as cracks are being closed or opened respectively. More importantly, the recovered evolution of aspect ratio shows an exponentially decreasing aspect ratio (and therefore aperture) with pressure, which has broader geophysical implications, in particular on fluid flow. The recovered evolution of aspect ratio is also consistent with current mechanical theories of crack closure. In the anisotropic cases—both transverse isotropic and orthorhombic symmetries were considered—anisotropy and saturation patterns were well reproduced by the modelling, and mean crack fabric orientations we recovered are consistent with in situ geophysical imaging.

Construction of analytical solutions and numerical methods comparison of the ideal continuous settling model

The size of the measurement matrix in compressive sensing (CS) is proportional to calculation cost. To reduce the calculation cost, we utilize genetic algorithm (GA) to decrease the size of the measurement mother matrix, and propose an ultra-quick pulsar positioning and velocimetry method based on GA-optimized quantum CS (GQCS). There are two properties of the quantum measurement matrix. One is that the performance of the quantum measurement sub-matrices is different. The other one is that the combination of the quantum measurement sub-matrices affects the performance of the positioning and velocimetry method. Considering the randomness of the quantum measurement matrix, we select the quantum measurement sub-matrices from the quantum measurement mother matrix through GA. The quantum measurement matrix is divided into multiple sub-matrices. One gene in the chromosome determines whether the corresponding sub-matrix is retained or abandoned. The object of the fitness function is the estimated estimation errors of the quantum-based CS pulsar positioning and velocimetry (QCS). Through iteration, GA provides the sub-optimal combination of the quantum measurement sub-matrices, forming a small-sized and high-performance quantum measurement matrix. Simulation results indicate that the GQCS has a lower calculation cost and higher accuracy compared with the QCS.

Development of a 0D digital twin for assessment of the impact of vascular graft on ex-vivo porcine aortas.

We propose an effective-medium theory (EMT) for the surface charged dielectric nanoparticles (CDNPs) in the long wavelength limit, in which a homogenous CDNP is demonstrated to be equivalent to a conventional absorbing neutral particle of the same size but with different constitutive parameters (effective permittivity εe and effective permeability μe). It is found that while the surface charge induces negligible change of magnetic permeability in particle, it gives rise to a significant change of electric permittivity. The change in permittivity depends on the charge, the particle size, and the working frequency but is independent of the constituent material. In infrared frequencies, both the real and imaginary parts of the particle permittivity may be changed considerably by surface charging. At higher frequency, the surface charge can lead to a remarkable decrease in the real part of the permittivity while keeping its imaginary part nearly unchanged. Therefore, based on EMT we can tailor the optical properties of CDNPs by optimizing their parameters, allowing for many exotic phenomena, such as vanishing scattering efficiency, great enhancement of light absorption efficiency, and surface charge induced surface plasmon resonance.

Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints