Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Impacto de la circulación ecuatorial en la zona mínima de oxógeno presente en el norte del Ecosistema de la Corriente del Humboldt

El Norte del Ecosistema de la Corriente Humboldt (NECH) constituye una de las mayores zonas de afloramiento, localizada en el borde oriental del Pacifico Sur, la cual presenta características particulares, entre las que destacan una alta producción primaria y la presencia de una de las zonas mínimas de oxigeno (ZMO) más intensas en el océano abierto. La ZMO presente en esta zona es producto de la alta demanda de oxígeno durante la remineralización de la materia orgánica, el largo tiempo de residencia de sus aguas y su poca ventilación. En el presente estudio nos enfocamos en estudiar la influencia de cambios en la ventilación en la ZMO del NECH, tomando como las principales fuentes de aporte de oxígeno en esta zona a la Corriente Sub-superficial Ecuatorial (EUC) y las Contracorrientes Sub-superficiales del Sur (SSCCs) o también conocidas como los Jets de Tsuchiya. Utilizamos el modelo acoplado físico-biogeoquímico ROMS-PISCES, para observar la sensibilidad de la ZMO a diferentes condiciones de la circulación ecuatorial provenientes de dos modelos oceánicos de circulación general (SODA y MERCATOR). Los resultados muestran que el flujo de oxígeno a los 88ºW disminuye latitudinalmente de la EUC a los SSCCs; además, se observa que la ZMO desaparece de los 4ºN - 4ºS en la simulación que presenta una circulación más intensa (RPSoda) por lo que se puede concluir que una intensificación de la circulación ecuatorial afectaría principalmente a la zona ecuatorial y no frente a Perú, debido a que una mayor ventilación sería compensada con un mayor consumo de oxigeno durante la remineralización, producto de una alta productividad generada por un mayor flujo de nutrientes.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

On The Spot Damage Detection Methodology for Highway Bridges, July 2010

Vibration-based damage identification (VBDI) techniques have been developed in part to address the problems associated with an aging civil infrastructure. To assess the potential of VBDI as it applies to highway bridges in Iowa, three applications of VBDI techniques were considered in this study: numerical simulation, laboratory structures, and field structures. VBDI techniques were found to be highly capable of locating and quantifying damage in numerical simulations. These same techniques were found to be accurate in locating various types of damage in a laboratory setting with actual structures. Although there is the potential for these techniques to quantify damage in a laboratory setting, the ability of the methods to quantify low-level damage in the laboratory is not robust. When applying these techniques to an actual bridge, it was found that some traditional applications of VBDI methods are capable of describing the global behavior of the structure but are most likely not suited for the identification of typical damage scenarios found in civil infrastructure. Measurement noise, boundary conditions, complications due to substructures and multiple material types, and transducer sensitivity make it very difficult for present VBDI techniques to identify, much less quantify, highly localized damage (such as small cracks and minor changes in thickness). However, while investigating VBDI techniques in the field, it was found that if the frequency-domain response of the structure can be generated from operating traffic load, the structural response can be animated and used to develop a holistic view of the bridge’s response to various automobile loadings. By animating the response of a field bridge, concrete cracking (in the abutment and deck) was correlated with structural motion and problem frequencies (i.e., those that cause significant torsion or tension-compression at beam ends) were identified. Furthermore, a frequency-domain study of operational traffic was used to identify both common and extreme frequencies for a given structure and loading. Common traffic frequencies can be compared to problem frequencies so that cost-effective, preventative solutions (either structural or usage-based) can be developed for a wide range of IDOT bridges. Further work should (1) perfect the process of collecting high-quality operational frequency response data; (2) expand and simplify the process of correlating frequency response animations with damage; and (3) develop efficient, economical, preemptive solutions to common damage types.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Monte Carlo simulation of kilovolt electron transport in solids

A Monte Carlo procedure to simulate the penetration and energy loss of low¿energy electron beams through solids is presented. Elastic collisions are described by using the method of partial waves for the screened Coulomb field of the nucleus. The atomic charge density is approximated by an analytical expression with parameters determined from the Dirac¿Hartree¿Fock¿Slater self¿consistent density obtained under Wigner¿Seitz boundary conditions in order to account for solid¿state effects; exchange effects are also accounted for by an energy¿dependent local correction. Elastic differential cross sections are then easily computed by combining the WKB and Born approximations to evaluate the phase shifts. Inelastic collisions are treated on the basis of a generalized oscillator strength model which gives inelastic mean free paths and stopping powers in good agreement with experimental data. This scattering model is accurate in the energy range from a few hundred eV up to about 50 keV. The reliability of the simulation method is analyzed by comparing simulation results and experimental data from backscattering and transmission measurements.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex time-dependent behavior does not break the basic, single-roll structure.

Revisiting the S-index for soil physical quality and its use in Brazil

The S-index was introduced in 2004 in a publication by A.R. Dexter. S was proposed as an indicator of soil physical quality. A critical value delimiting soils with rich and poor physical quality was proposed. At present, Brazil is world leader in citations of Dexter's publication. In this publication the S-theory is mathematically revisited and extended. It is shown that S is mathematically correlated to bulk density and total porosity. As an absolute indicator, the value of S alone has proven to be incapable of predicting soil physical quality. The critical value does not always hold under boundary conditions described in the literature. This is to be expected because S is a static parameter, therefore implicitly unable to describe dynamic processes. As a relative indicator of soil physical quality, the S-index has no additional value over bulk density or total porosity. Therefore, in the opinion of the author, the fact that bulk density or total porosity are much more easily determined than the water retention curve for obtaining S disqualifies S as an advantageous indicator of relative soil physical quality. Among the several equations available for the fitting of water retention curves, the Groenevelt-Grant equation is preferable for use with S since one of its parameters and S are linearly correlated. Since efforts in soil physics research have the purpose of describing dynamic processes, it is the author's opinion that these efforts should shift towards mechanistic soil physics as opposed to the search for empirical correlations like S which, at present, represents far more than its reasonable share of soil physics in Brazil.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among up and down configurations, and barriers that are always up but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

BEYOND THE “LEAST LIMITING WATER RANGE”: RETHINKING SOIL PHYSICS RESEARCH IN BRAZIL

As opposed to objective definitions in soil physics, the subjective term “soil physical quality” is increasingly found in publications in the soil physics area. A supposed indicator of soil physical quality that has been the focus of attention, especially in the Brazilian literature, is the Least Limiting Water Range (RLL), translated in Portuguese as "Intervalo Hídrico Ótimo" or IHO. In this paper the four limiting water contents that define RLLare discussed in the light of objectively determinable soil physical properties, pointing to inconsistencies in the RLLdefinition and calculation. It also discusses the interpretation of RLL as an indicator of crop productivity or soil physical quality, showing its inability to consider common phenological and pedological boundary conditions. It is shown that so-called “critical densities” found by the RLL through a commonly applied calculation method are questionable. Considering the availability of robust models for agronomy, ecology, hydrology, meteorology and other related areas, the attractiveness of RLL as an indicator to Brazilian soil physicists is not related to its (never proven) effectiveness, but rather to the simplicity with which it is dealt. Determining the respective limiting contents in a simplified manner, relegating the study or concern on the actual functioning of the system to a lower priority, goes against scientific construction and systemic understanding. This study suggests a realignment of the research in soil physics in Brazil with scientific precepts, towards mechanistic soil physics, to replace the currently predominant search for empirical correlations below the state of the art of soil physics.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Genome-wide analysis of Sphingomonas wittichii RW1 behaviour during inoculation and growth in contaminated sand.

The efficacy of inoculation of single pure bacterial cultures into complex microbiomes, for example, in order to achieve increased pollutant degradation rates in contaminated material (that is, bioaugmentation), has been frustrated by insufficient knowledge on the behaviour of the inoculated bacteria under the specific abiotic and biotic boundary conditions. Here we present a comprehensive analysis of genome-wide gene expression of the bacterium Sphingomonas wittichii RW1 in contaminated non-sterile sand, compared with regular suspended batch growth in liquid culture. RW1 is a well-known bacterium capable of mineralizing dibenzodioxins and dibenzofurans. We tested the reactions of the cells both during the immediate transition phase from liquid culture to sand with or without dibenzofuran, as well as during growth and stationary phase in sand. Cells during transition show stationary phase characteristics, evidence for stress and for nutrient scavenging, and adjust their primary metabolism if they were not precultured on the same contaminant as found in the soil. Cells growing and surviving in sand degrade dibenzofuran but display a very different transcriptome signature as in liquid or in liquid culture exposed to chemicals inducing drought stress, and we obtain evidence for numerous 'soil-specific' expressed genes. Studies focusing on inoculation efficacy should test behaviour under conditions as closely as possible mimicking the intended microbiome conditions.

Quantitative comparison between simulations of seismic wave propagation in heterogeneous poro-elastic media and equivalent visco-elastic solids for marine-type environments

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes an important seismic attenuation mechanism in porous rocks. As a consequence, centimetre-scale perturbations of the rock physical properties should be taken into account for seismic modelling whenever detailed and accurate responses of specific target structures are desired, which is, however, computationally prohibitive. A convenient way to circumvent this problem is to use an upscaling procedure to replace each of the heterogeneous porous media composing the geological model by corresponding equivalent visco-elastic solids and to solve the visco-elastic equations of motion for the inferred equivalent model. While the overall qualitative validity of this procedure is well established, there are as of yet no quantitative analyses regarding the equivalence of the seismograms resulting from the original poro-elastic and the corresponding upscaled visco-elastic models. To address this issue, we compare poro-elastic and visco-elastic solutions for a range of marine-type models of increasing complexity. We found that despite the identical dispersion and attenuation behaviour of the heterogeneous poro-elastic and the equivalent visco-elastic media, the seismograms may differ substantially due to diverging boundary conditions, where there exist additional options for the poro-elastic case. In particular, we observe that at the fluid/porous-solid interface, the poro- and visco-elastic seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an important result which has potentially far-reaching implications for wave-equation-based algorithms in exploration geophysics involving fluid/porous-solid interfaces, such as, for example, wavefield decomposition.