NG23B-1130
Investigating Seismic Precursory Signatures in Earthquake-related Self-potential Signals by using Fisher Information Measure Analysis
The time fluctuations of self-potential data, recorded at the monitoring station Acapulco (Mexico) during 1994-1996 in the seismic area of Guerrero-Oaxaca, are analyzed by means of the Fisher Information Measure (FIM), a nonlinear powerful method to investigate complex dynamics in time series. The time evolution of the FIM shows a clear correlation with the largest earthquakes occurred in the monitored area during the observation period. Seismic precursory patterns in the FIM evolution are also revealed
NG23B-1131
Self-organization and geometric properties of polygonal fracture networks
Qualitatively, polygonal fracture patterns are highly recognizable, but are difficult to quantify and model due to the irregularity of individual fracture spacing and orientation within the patterns,. We documented ~50 polygonal fracture networks in the Tuolumne Intrusive Suite, Sierra Nevada Batholith, to investigate fracture network organization. Measurements (size, orientation, length) of fractures and fracture-bound polygons were taken in nearly isotropic granitic rocks, away from zones of fabric development. Each fracture network is constrained to an exfoliation sheet; the free surfaces of the exfoliation sheet form the bounding surfaces for the polygonal fracture network. Data indicate that the size of fracture-bound polygons logarithmically scales with exfoliation sheet thickness. The size frequency distribution (normalized) of the networks' polygons has a positively skewed distribution, indicating that polygons larger than the average are more abundant than polygons smaller than the average. Fracture-bound polygons are not isotropic; a shape preferred orientation exists for all networks that is independent of scale, layer thickness, and dip. Rather, the degree of anisotropy correlates with the degree of exfoliation sheet curvature. These fracture networks likely formed due to freeze-thaw cycles. Each fracture network exhibits a distinct pattern, but data indicate that quantitative similarities exist between networks. We propose that the observed patterns are a product of interactions between fractures, not extrinsic conditions, and that simple geometric rules govern the system. Thus, any proposed formation model does not necessarily need to reproduce the exact fracture pattern, but must adhere to the observed quantitative properties of the natural networks. Using these properties as controls (e.g., observed size distributions, degree of polygon anisotropy, etc.), we propose a self-organization fracture model based on the Plug and Werner (2001) ice-wedge polygon model to describe fracture network development.
NG23B-1132
Stochastically constrained, simplified controlled source electromagnetic modeling for Gulf of Mexico hydrocarbon exploration
Controlled source electromagnetic geophysical prospecting (CSEM) is gaining increased attention as a means of aiding marine petroleum exploration. The rather complex physics governing electromagnetic induction usually relegates rapid interpretation to the examination of hydrocarbon-indicative attributes within the measured signal, such as magnitude and phase versus offset (MVO and PVO respectively). A more detailed interpretation may be reached through inversion of the CSEM response. The usual expense of inversion is curtailed by replacing a general three-dimensional numerical forward model with a simplified model that approximates the electromagnetic character of a typical Gulf of Mexico reservoir. A first-order model simply assumes a uniform conductivity outside the region of interest, though more specialized models are under investigation. The model parameters are determined in a maximum likelihood sense, constrained by probability distributions determined from the statistical examination of typical Gulf of Mexico reservoirs. A detailed pdf is determined by kernel density estimation from a significant sample of reservoir parameters. The ability to assess hydrocarbon presence will be quantified by Monte Carlo simulation and examination of the Cramer-Rao lower bound (CRLB) of our estimator.
NG23B-1133
Fractal Modeling of Complex Geological Objects
Modeling of complex geological structure is based on geometrical simplifications to meet the computational efficacy. The arbitrary shape regular geometrical model approximates causative body, which often has irregular geometry. We have made an attempt to generate complex geological model of the causative body using Lp norm modified Voronoi tessellation. Application of the modified Voronoi tessellation scheme gives realistic irregular geometry of the causative body using a few parameters known as Voronoi centers. This method has three advantages over the conventional methods viz. (a) It makes application of inversion algorithm easier by virtue of changing the model geometry merely by shifting few Voronoi centers or in some cases just by changing the exponent 'p' of Lp norm. (b) It provides such a geometrical representation that does not encounter reentrant (undefined body) conditions during inversion and (c) With the help of affine companding it is possible to generate models of longer horizontal extent than vertical and vice versa, this particular feature is an advantage over the existing Voronoi tessellation. The usefulness of this method has been demonstrated through the computation of gravity response of fractal subsurface and modeling of field gravity data acquired over Jabera – Damoh area of Vindhyan basin, Central India.
NG23B-1134
Dependences of posterior pdf on observational constraint and model errors in nonlinear data assimilation.
In this study, the relationship between data assimilation solutions and nonlinear model properties together with observational constraint is analyzed using a numerical technique based on the inverse problem theory formulated by Mosegaard and Tarantola. By this theory, the inverse problem and solution are defined via convolution and conjunction of probability density functions (pdfs) that represent stochastic information obtained from the model, observations and prior knowledge in a joint multidimensional space. This theory provides an explicit analysis of the nonlinear model function, together with information about uncertainties in the model, observations, and prior knowledge through construction of the joint probability density, from which marginal posterior solution functions can then be evaluated. The numerical analysis technique derived from the theory computes the component probability density functions in discretized form via a combination of function mapping on a discrete grid in the model and observation phase space, and sampling from known parametric distributions. This numerical diagnostic analysis technique was first demonstrated in Vukicevic and Posselt (2008) on examples of two well known simplified models of Atmospheric physics: Damped oscillations and Lorenz' 3-component model of dry cellular convection. In the current study the diagnostic analysis of the controls of posterior pdf in data assimilation is performed using a beta plane quasi- geostrophic numerical model. The control parameter space in the model consists of coefficients of two- dimensional Fourier decomposition of stream function fields within regions of unstable dynamical modes. The impact of assumed modeling errors and spatial and temporal distribution of observations on the posterior multi dimensional pdf is studied to evaluate conditions which render this pdf uni-modal. The validity of the Gaussian approximation is then evaluated.
NG23B-1135
The equatorial counterpart of the quasigeostrophic model
A uniformly valid balanced model that represents the quasigeostrophic model's counterpart in the equatorial region is derived. The standard derivation of the quasigeostrophic model fails in the equatorial region because of the assumption of a small Rossby number. Leith presented in 1980 a derivation of the quasigeostrophic model on a mid-latitude f--plane independent of Rossby number, using the geometric framework of nonlinear normal mode initialization. In this paper, Leith's derivation is repeated on an equatorial β--plane leading to an equatorial balanced model that thus represents the equatorial counterpart of the quasigeostrophic model. As such it also coincides with the quasigeostrophic model sufficiently far away from the equator. Its dispersion relation can be expressed in an explicit, analytic form and, compared to that of other balanced models of similar simplicity, approximates that of the shallow water equations strikingly well.
NG23B-1136
Empirical Mode Reduction and non-Gaussian Signatures of Planetary Low-Frequency Atmospheric Modes.
We demonstrate here a use of Empirical Mode Reduction (EMR) in identifying the relative contributions of resolved and unresolved atmospheric modes to "double-swirls" in mean phase-space tendencies for a global, quasi-geostrophic, three-level (QG3) atmospheric model. In EMR, multiple polynomial regression is used to estimate the nonlinear, deterministic propagator of the dynamics, as well as multi-level additive stochastic forcing, directly from the data set. In this approach, the residual stochastic forcing at a given level is subsequently modeled as a function of the extended state vector involving the variables of all preceding levels. The estimated mean-phase space tendencies of QG3 and EMR agree very well, further confirming the usefulness of our EMR approach. The explicit quadratic form of the EMR model's dynamical operator facilitates estimating the contributions of linear and nonlinear interactions to the resulting tendencies. Purely linear tendencies would be characterized by antisymmetry for reflections through the origin and constant speed along ellipsoids. The characteristic double-swirl pattern for tendencies are indicative of strong nonlinear and non-Gaussian behavior. The EMR approach also allows one to separate the relative contributions, from additive and multiplicative noise, to the full nonlinear tendencies. These contributions are, in turn, related to the attribution of different EOFs to "resolved" and "unresolved" modes. The EOF spectrum of the QG3 model is characterized by higher-order modes having shorter time scales, and somewhat smaller spatial scales, than the leading modes; there is, however, no pronounced time-scale separation. The four leading EOFs are clearly well resolved, since they have the most pronounced deviations from Gaussianity in terms of skewness and kurtosis, and they determine the most interesting dynamical aspects of the QG3 model's low-frequency variability: linear (intraseasonal oscillations) as well as nonlinear (multiple regimes). Our results show that the nonlinear double-swirl features of mean tendencies are mostly due to the resolved nonlinear interactions while the effect of unresolved modes is small. Our study highlights the fact that extra care is needed in assessing the effects of linear and nonlinear deterministic interactions, as well as of additive and multiplicative noise, on the non-Gaussian signatures of planetary low-frequency waves.
NG23B-1137
Indirect Interaction of Barchan Dunes by Inter-dune Sand Flow
The most impressive sand structure seen in desert is crescent sand dunes called barchan. Barchan dune has two horns and sand flow release from the tips of them. Seeing aerial photos of deserts, we recognize that barchan dunes tend to align in a characteristic pattern, that is, the horn of one barchan pointing to the center of leeward barchan. As a result, barchans form a convoy with a geese-flying like triangular pattern or align in an slanted line. The pattern has been observed also for barchans found on Mars, and thus there should be some universal mechanism underlying it. Also barchan dunes are highly mobile; human-made structures such as roads or pipelines in their way are sometimes buried in sand. It has been a long-standing problem how we can control this unstoppable march of barchan dunes. There are some interaction such as collision and inter-dune sand flow in marching barchan dunes. Here we investigated interaction dynamics of barchan dunes focusing on the effect of indirect interactions mediated by an inter-dune sand flow using computer simulations. We showed that a barchan is driven laterally by a sand stream to right below the point source of sand.Principal mechanism of this motion is a fast mixing of sand in a barchan that keeps the symmetric shape unchanged.We thereby propose a possibility of controlling the motion of a barchan using a sand stream. In addition,the very same mechanism produces an indirect interaction between barchans mediated by sand stream and can induce the self-organization of the geese-flying like pattern.
NG23B-1138
Nonequilibrium Mechanism of Geomaterials
Certain materials display surprisingly large dynamical nonlinearities, including conditioning and memory effects, appearing at wave strains smaller and parts per million. Geomaterials are prototypes for these apparently unrelated solids that include granular materials, sintered and damaged metals, some ceramics, and even high explosives. Rocks are hysteretic and can be strongly nonlinear; their relation between stress and strain depends on the rate of the measurement. These materials relax over very long durations after an initial impulse or wave disturbance, a nonequilibrium phenomenon termed "slow dynamics". The microphysics underlying slow dynamics remains unknown. Previous experiments by us established the existence of two strain regimes separated by a strain threshold. Below this surprisingly small threshold strain (lower than 1 part per million), the material is non linear and quasi-equilibrium thermodynamics applies; above this threshold the behavior becomes nonequilibrium, as well as nonlinear. Whereas the material behavior in the first (reversible) nonlinear regime is well-described by Landau theory, the second regime the intrinsic nonlinearities are hard to disentangle from the ongoing nonequilibrium relaxation process. In order to understand better the coupling between nonlinear and nonequilibrium effects we investigated the full dynamical range of phenomena considered: high frequency/low strain to almost static/high strain. We carried out two experimental procedures on a number of rocks samples: resonance bar methods, where we measure amplitude as a function of drive amplitude and frequency and quasi-static stress/strain measurements. In the quasi-static domain Barea sandstone has demonstrated for the first time that rate is important and that nonequilibrium effects can affect results. In order to disentangle conditioning and nonequilibrium effects from nonlinear effects in the domain of high frequency and low strain we run long term resonance bar experiments under extremely stable environmental conditions. We will present preliminary results obtained in this regime. Understanding these rates should help understand the physics of these kinds of rocks. Theoretical framework for implementing microstructure-motivated models is under development.
NG23B-1139
In Situ, Nonlinear Soil Response Applying an Active Source
Soil sites have a profound effect on ground motion during earthquakes due to their low wave speeds, layered structure, and nonlinear constitutive behavior. Measurements of nonlinear soil response under natural conditions are critical to understanding soil behavior during earthquakes. Currently, quantitative measurements of nonlinear soil response are derived from laboratory experiments on small samples. In this paper, we extend laboratory methods for measuring nonlinear soil response to field-scale. We observe the in situ, nonlinear response of a natural soil formation using measurements obtained immediately adjacent to a large vibrator truck. The source generates a steady-state wavefield in the soil formation at a range of discrete source frequencies and source amplitudes. Accelerometers within the source provide an estimate of the source output to the soil, and an array of 4 accelerometers adjacent to the source record the wavefield at 1.5 m spacing. We develop a homodyne analysis to extract the steady-state amplitude at each discrete source frequency and amplitude without contamination from source harmonics. Steady-state amplitude ratios are computed between the receivers and the source, and between adjacent receiver pairs within the array. Both sets of amplitude ratios show dramatic decreases in peak frequency as the source amplitude is increased. These peak frequency shifts are qualitatively similar to the nonlinear soil response observed for laboratory samples under resonance conditions. Amplitude ratios between adjacent receiver pairs suggest the nonlinear soil response persists across the receiver array and is not limited to the source-soil contact region. The magnitudes of the observed peak shifts appear to depend on their frequency, a proxy for depth, which is consistent with the confining pressure dependence of soil nonlinearity observed in laboratory experiments. Future work will include measurements of steady-state phase velocities across the array to better understand the nature of nonlinear wave propagation within natural soil formations (wavelengths, polarization, etc.). Forward modeling to match these field-scale observations of nonlinear soil response may lead to nonlinear site characterization tools and ultimately better predictions of local, nonlinear site response.
NG23B-1140
Nucleation and Growth of Damage in Rock Masses and on Sliding Surfaces
We are investigating the failure of rock masses resulting from the complex physics of microscopic dynamical processes in rocks, as manifested in the nucleation and growth of defects, microcracks, damage, and macroscopic fracture. These processes are a result of the complex emergent dynamics of self-organizing geological materials which we analyze using the methods of statistical physics and large scale simulations employing both molecular dynamics and Monte Carlo methods. A particular example is the nucleation and growth of damage on sliding surfaces associated with frictional failure. Fully interacting fields of defects and damage are generally not included in most current models for material deformation. Instead, defect density and damage fields are assumed to be non-interacting or dilute, implying a strictly mean field approach. We use statistical physics methods to understand the dynamics of interacting defect and damage fields, made possible by the construction and use of statistical field theories, to greatly improve our predictive capability for the macroscopic failure of materials. The important quantities to compute are the nucleation rate, or its inverse, lifetime to failure. We also discuss applications of this research to rock deformation across a range of spatial and temporal scales.