NG11A-0167 

Using a dynamical systems approach to characterize climate for physical interpretation and comparison of models to observations

* Newman, D E (ffden@uaf.edu), Physics Department/CNSM Univ. of Alaska Fairbanks, Reichardt Building, Fairbanks, AK 99775, United States Bhatt, U (bhatt@gi.alaska.edu), GI/Atmospheric Science Program CNSM Univ. of Alaska Fairbanks, 903 Koyukuk Dr., Fairbanks, AK 99775, United States Polyakov, I (igor@iarc.uaf.edu), IARC Univ. of Alaska Fairbanks, 903 Koyukuk Dr., Fairbanks, AK 99775, United States Sanchez, R (sanchezferlr@ornl.gov), Fusion Energy Division Oak Ridge National Lab, P.O. Box 2008, MS 6169, Oak Ridge, TN 37831-6169, United States Wackerbauer, R (ffraw1@uaf.edu), Physics Department/CNSM Univ. of Alaska Fairbanks, Reichardt Building, Fairbanks, AK 99775, United States

Complex geophysical systems such as the climate need many measures to properly characterize their state and dynamics. This is needed both to understand the physical processes in the system and to enable realistic comparison with models. Now that the IPCC fourth assessment is finished, the next step is to use this type of comparison to carefully scrutinize our models and evaluate the key processes that we need to improve for the next generation of climate models. To this end, we apply a variety of tools from a dynamical systems approach that are designed to probe the "temporal dynamics" inherent in a time series and the PDFs of these series. These methods provide additional information than what can be obtained from our standard set of climate evaluation methods. Hurst's R/S analysis is one such method that is able to detect differences in the ordering of the time series and make the correlations hidden within them apparent. We will present results that evaluate a suite of CCSM3 simulations and observations using R/S analysis and a range of other techniques to determine to what extent the model captures the long-term dynamics of the real climate systems. We will also look at the applicability of the standard diffusion model for parameterization in these models.

NG11A-0168 

Spatio-temporal gap filling in satellite datasets of Southern Ocean

* Kondrashov, D (dkondras@atmos.ucla.edu AF: AF: AF: AF:

Data sets in the geosciences are often full of gaps. This is usually the case for geological and paleoclimatological proxy data from the remote past, as well as for historical records from the more recent past. In modern times, data points may be missing because of the way the measurements are obtained. For example, remote sensing instrumentation can be hampered by clouds, aerosols, or heavy precipitation. The presence of gaps in data sets presents various problems, for example in spectral estimation, specifying boundary conditions in numerical models, and so on. While the microwave sensors installed on recently launched NASA satellites provided unprecedented quality of sea-surface temperature and sea-level wind observations in the region of the Southern Ocean, there are still gaps in data coverage in the heavy rain regions, as well as in the regions of strong winds. We demonstrate how Singular Spectrum Analysis (SSA) and multi-channel SSA can be applied to fill the missing data in the remotely sensed datasets of the Southern Ocean with an iteratively inferred smooth "signal" that represents coherent spatio-temporal structures, while the "noise" variance is discarded or reduced (Kondrashov and Ghil, 2006). Doing so can be quite valuable in a wide variety of other applications, ranging from reconstruction of paleoclimatic and instrumental climate data to oceanographic and space physics data.

NG11A-0169 

Detecting abrupt changes in tide-gauge records

* Becker, M (mbecker@univ-lr.fr), Centre Littoral de Geophysique, Universite de La Rochelle Pole Science, La Rochelle, 17042, France Karpytchev, M (mkarpytc@univ-lr.fr), Centre Littoral de Geophysique, Universite de La Rochelle Pole Science, La Rochelle, 17042, France Davy, M (manuel.davy@ec-lille.fr), Laboratoire d'Automatique Genie Informatique et Signal, Cite Scientifique, Villeneuve d'Ascq, 59650, Doekes, K (koos.doekes@rws.nl), Rijkswaterstaat, RIKZ/ZDI, P.O.Box 20907, EX The Hague, 2500, Netherlands

The tide gauge records contain a whole spectrum of different signatures, from the tidal sea level variations to vertical land motion provoked by global eustatic changes over periods of centuries. The spatial scales and the physical nature of these processes are also extremely variable : they range from local effects (e.g. groundwater pumping or seismic activity close to tide gauges) to global-scale land motion induced by the deglaciation. We develop a systematic statistical approach for detecting the abrupt changes in sea level records taking into account their complicated covariance structure. Examples of abrupt changes detection in several tidal records are presented. Their impact on estimation of the long term sea level rise is discussed.

NG11A-0170 

Identifying Weak Signals in Tide Gauge Records

* Karpytchev, M (mikhail.karpytchev@univ-lr.fr), Centre Littoral De Geophysique,Pole Sciences, Universite de la Rochelle Avenue Michel Crepeau, LA ROCHELLE, 17042, France Becker, M (mbecker@univ-lr.fr), Centre Littoral De Geophysique,Pole Sciences, Universite de la Rochelle Avenue Michel Crepeau, LA ROCHELLE, 17042, France Davy, M (manuel.davy@ec-lille.fr), Laboratoire d'Automatique Genie Informatique et Signal, Cite Scientifique, Villeneuve d'Ascq, 59650, France

The monthly tide gauge (TG) records are often dominated by a nonlinear sea level trend (Jevrejeva et al, 2006) and seasonal/annual variations. In order to identify the weak signals in the TG records, we propose a method based on statistical techniques of the detection theory . A special focus is made on modelling the temporal and spatial correlations in the TG sea level data. An efficiency of the proposed method is tested through intensive numerical tests. Examples of succeful identification of sea level variations provoked by (1) urbanisation effects and (2) seismic activity are presented discussed.

NG11A-0171 

Three-dimensional controlled-source electromagnetic modeling and inversion for hydrocarbon reservoir mapping: The bathymetry problem

* Commer, M (MCommer@lbl.gov), Lawrence Berkeley National Lab Earth Sciences Division, 1 Cyclotron Rd. MS 90-1116, Berkeley, CA 94720, United States Newman, G A (GANewman@lbl.gov), Lawrence Berkeley National Lab Earth Sciences Division, 1 Cyclotron Rd. MS 90-1116, Berkeley, CA 94720, United States

The effects of bathymetry on controlled-source electromagnetic (CSEM) methods for geophysical exploration are investigated. Such effects cannot be neglected when aiming for reliable and accurate modeling and inversion results, owing to the high seawater conductivity, 3.3 S/m on average, and thus potentially high contrasts in the electrical properties between water and seabed. In the presented study, we make use of the possibilities of the finite-difference method to allow three-dimensional (3D) inversions with a high degree of model discretizations in order to simulate complex seafloor surfaces. At the same time, we separate the computational mesh for the forward operator from the model discretization mesh, through usage of a proper averaging scheme for the electrical conductivity, limiting the computational requirements. Reliability of the method is demonstrated through modeling and inversion studies for a marine survey scenario.

NG11A-0172 

Complexity Of Earthquakes: Learning From Simple Models And Exploring Statistical Surrogate Techniques

* Elbanna, A E (aettaf@caltech.edu), California Institute of Technology, 1200 E. California Blvd MC 104-44, Pasadena, CA 91125, Heaton, T (heaton_t@caltech.edu), California Institute of Technology, 1200 E. California Blvd MC 104-44, Pasadena, CA 91125,

It has long been recognized that earthquakes exhibit similarity at many length scales which suggests fractal characteristics of earthquake ruptures. One of the well known manifestations of earthquake complexity is the fractal nature of the Gutenberg-Richter law. Moreover, there is growing evidence that earthquakes ruptures are very complex processes; as the resolution of source inversions has increased, so has the temporal and spatial complexity of the rupture. What are the key physical parameters that control this complexity? Many methods have been tailored in an attempt to uncover the details of the complex rupture processes but due to different numerical and computational limitations scientists could not go beyond a few orders of magnitude on both of the spatial and temporal scales. Statistical methods provide an alternative way to overcome the difficulties associated with numerical models of spontaneous dynamic ruptures. Here, we present an outline for an innovative approach that aims at reproducing the different earthquake complex scaling laws using methods of statistical mechanics with the ultimate goal of finding the scaling behavior of the strength of the Earth's crust. The emphasis of this presentation is on exploring the conditions that might lead to complexity in earthquakes using simple mechanical models similar to the Burridge-Knopoff spring-block-slider models and how to describe the evolution of the system in this case. Although there are limitations in the usage of spring-block- sliders to interpret real earthquakes, these models have the advantage that they are computationally efficient and produce some earthquake statistics. This allows us to explore the nature of complexity that is produced by different types of models of dynamic friction. We show that chaotic behavior occurs for friction models with velocity or slip hyperbolic weakening rather than traditional slip weakening models. We would also show that the evolution of the spring block slider system could be predicted using a new statistical method based on Markov Modeling. The method hinges on the observation that slip pulses - which represent the prevailing rupture mode in our models- are so localized in space in a manner suggestive that the slip at any point is correlated to the pre- existing stress only over a small interaction zone surrounding that point. Using the Markovian technique we could track the variation of this interaction zone width statistically.The slip time and consequently the slip at any point is approximated as a weighted average for the pre-existing stress over the interaction zone of that point. We believe that this method could be a surrogate for solving the full equilibrium equations and could produce rough earthquake statistics.

NG11A-0173 

Evaluating Long-Range Correlations in Seismic Catalogs

* Jimenez, A (ajimene@uwo.ca), University of Western Ontario, Department of Earth Sciences Biological & Geological Sciences, London, ON N6A 5B7, Canada Tiampo, K F (ktiampo@seis.es.uwo.ca), University of Western Ontario, Department of Earth Sciences Biological & Geological Sciences, London, ON N6A 5B7, Canada Posadas, A M (aposadas@ual.es), University of Almeria, Ctra. Sacramento s/n, Almeria, 04120, Spain

Self-similarity and scaling phenomena are commonly found in seismicity. The identification of long-range dependence (LRD) in seismic catalogs, if it exists, would help us to understand how those time series are generated, and what physical mechanisms produce them. Despite its importance, though, LRD analysis is hindered by the difficulty of objectively identifying dependence and estimating its parameters unambiguously. LRD is defined for Hurst exponents greater than 1/2, and it assumes Gaussian statistics. The calculation of both the Hurst coefficient by means of R/S statistics or wavelet methods, and the scaling exponent evaluated through the Shannon entropy S(t) of the diffusion generated by the fluctuations of a time series (diffusion entropy analysis), provide a solution to determine whether the original time series is actually a Gaussian noise which represents LRD. Here we use those techniques in earthquakes catalogs from around the world.

NG11A-0174 

On Physical Nature of the 70-km Seismic Boundary Caused by Tidal and Fluid Effects.

* Elena, S (sasorova_lena@mail.ru), P.P. Shirshov Institute of Oceanology,RAS, Nakhimovsky prosp.,36, Moscow, 117997, Russian Federation Boris, L (lewinbw@mail.ru), Institute of Marine Geology and Geophysics, FEB of RAS, Nauka, 1b, Yuzhno-Sakhalinsk, 692022, Russian Federation Michail, R (rodkin@wdcb.ru), Geophysical Center, RAS, Molodezhnaja str, 3, Moscow, 117994, Russian Federation

Statistic analysis of the EQ catalogs (ISC, NEIC, 1960-2006; Harward Catalog, 1976-2005) showed that the seismic boundary at the 70-km depth marked out often as a real boundary, which divides all events into two separate classes: non-deep seismic events (about 85% of all events) which respond to external perturbation effects, and the deep-focus events non-responded to an outer influence. The results of two series of statistical analyses were presented. All events were subdivided into two groups: shallow events (H<=Htr) and deep events (H>Htr), where Htr is threshold value of the EQ source depth. The statistical verification of hypothesis about within-year variability existence for the events of various energy levels [Sasorova, Zhuravlev, 2006] was carried out in the first series. It was disproved the null hypothesis about uniform EQ distributions in the course of year for shallow events. But it was confirmed the null hypothesis for deep EQ. The statistical verification of hypothesis about existence non-random component in time distribution of the EQ's between the northern and southern part of the Pacific [Sasorova et al, 2006] was carried out in the second series. It was found (according the distribution-free test) that nonrandom component does not exist for deep EQs. But it is clearly manifested in time distribution of the shallow events. In both cases it was found that the Htr boundary between the shallow and the deep events was arranged at the depth between 60 and 80 km (we let to vary Htr value from 15 to 300 km). Thus the EQ with sources located above this boundary are affected by external factors, which may trigger the process of EQ generation, while the external factors don't influence on the EQ sources located below this boundary. The drastic change of EQ source parameter values via hypocenter depth was also observed near the 70-km depth boundary [Rodkin, 2004]. Revealed parameter change is connecting with difference in the deep fluid behavior. The equation of state for water was analyzed. It was shown that water stays on a free state only at the depth less than 70 km (this depth value is correspond to the pressure equal to 2 GPa). Tidal forces generate in the Earth crust the areas with damage accumulation (shear and tension cracks). An ascending motion of the water fluid upward the fractures under the influence of the deep rock pressure and Sun-Moon tidal forces lead to interaction water fluid with damaged rock and to adsorption decreasing of the rock strength (Rebinder effect). In this case the fracture force threshold decreases in tens times. A water-saturated rock is medium with non-linear response to periodic effects. The weak effects of tidal forces were accumulated in such water-containing medium. In rocks where free state water is absent, tidal effects cannot be accumulated and non-linear mechanism of deformation storage is not realized.

NG11A-0175 

Non-linear dynamic of singular long-period volcanic tremors observed at Mt. Asama

* Takeo, M (takeo@eri.u-tokyo.ac.jp), Earthquake Research Institute, Univ. Tokyo, 1-1-1, Yayoi, Bunkyo, Tokyo, 113-0032, Japan

On September 1, 2004, a middle-scale eruption occurred at Mt.Asama. Before the eruption, we observed three long-period tremors with singular waveforms, which occurred at 4:25, 11:30, and 20:30 on June 24, 2004. The common characteristic of these tremors is that the tip of the waveform is sharp. This sharp-pointed waveform may suggest a non-linear dynamics of the source process. In addition, these singular tremors occurred at intervals of 7 to 9 hours on the same day, suggesting that the source process of these tremors is in common. In this paper, the dynamical structure and characteristics of these tremors are investigated by employing some reliable and robust techniques in the estimation of geometrical and dynamical parameters. Embedding by the method of time delays has become the standard procedure in non-linear dynamical system analysis of a single time series. The first step for the nonlinear analysis of a single time series is to reconstruct a topologically equivalent attractor to the original in a relatively low-dimensional delay-coordinate space. We employed some reliable and robust techniques in the estimation of optimum delay time and minimum embedding dimension. To select the long-period component, we employ a FIR low-pass filter with a cut-off frequency of 0.4Hz. For the tremor occurred at 4:25, the optimum time lag of 0.24 sec and the minimum embedding dimension of 8 were obtained by employing these methods. We succeed in reconstructing an attractor of the tremors using these dimension and time lag. Then, we calculated a correlation integral curve of the reconstructed attractor, founding a scaling region over one decade with the correlation dimension of 2.04 plus minus 0.17. The correlation dimension converges a certain value as increasing the embedding dimension. This suggests that the time series is not random data and the correlation dimension is estimated correctly. The optimum time lag and the minimum embedding dimension for the tremor at 11:30 were 2.0 sec and 6, respectively. We find a certain degree of scaling region, and estimated that the correlation dimension is 2.84 plus minus 0.32. The optimum time lag of 0.36 sec and the minimum embedding dimension of 8 were obtained for the tremor at 20:30. In this case, a correlation integral curve of the reconstructed attractor represents a scaling region over one decade with the correlation dimension of 1.80 plus minus 0.20. The surrogate data analysis is a kind of statistical hypothesis testing. If testing parameters obtained from 39 sets of surrogate data shift clearly from that of the original data, the null-hypothesis is rejected with a significance level of 0.05. This surrogate data analyses for these three tremors indicate that the null-hypotheses are rejected with the strong rejection level, suggesting there exists a deterministic non-linear dynamics in the tremor excitation, which can be modeled with the system dimension ranging between 3 to 7.

NG11A-0176 

PSO : an efficient algorithm to solve geophysical inverse problems. The 1D-DC case

García-Gonzalo, M (jlfm@uniovi.es), . University of Oviedo, C/ Calvo Sotelo S/N, Oviedo, 33007, Spain * Kuzma, H A (hkuzma@berkeley.edu), University of California, Berkeley, P.O. Box 987, Truckee, CA 96160, United States Fernández-Alvarez, J (:pauli@uniovi.es), . University of Oviedo, C/ Calvo Sotelo S/N, Oviedo, 33007, Spain Fernández-Martínez, J (jlfm@uniovi.es), . University of Oviedo, C/ Calvo Sotelo S/N, Oviedo, 33007, Spain AU: , Menéndez-Pérez, C (jlfm@uniovi.es), . University of Oviedo, C/ Calvo Sotelo S/N, Oviedo, 33007, Spain

Most of the geophysical inverse problems are ill-posed. In the VES (Vertical Electrical Sounding) case this fact is known as the equivalence or suppression problem: the shape of the objective function is that of the bottom of a narrow, elongated valley with almost null gradients and many localized "sinkholes". Flat outer areas with ridges also prevent access from local minima to the bottom of the valley. These features become insurmountable difficulties for local optimization methods, since they are not able to discriminate among the multiple models consistent with the end criteria, driving to unpredictable results. Global optimization methods are a good alternative in such situations due to their probabilistic nature. PSO algorithm is an evolutionary technique inspired in social behavior in nature. By means of a fruitful mechanical analogy we analyze its convergence properties, giving some criteria to choose the PSO parameters. This approach allows a family of PSO variants to be proposed, some of them with better properties to cope with the VES difficulties. Finally, performance of PSO variants against Simulated Annealing and Genetic Algorithms is done for a salt water intrusion in a coastal aquifer in South Spain.

NG11A-0177 

Physically correct kernel learning for geophysics

* Kuzma, H A (hkuzma@berkeley.edu), University of California, Berkeley, P.O. Box 987, Truckee, CA 96160, Martinez, J F (jlfm@uniovi.es), Universidad de Oviedo, C/ Calvvo Sotelo SIN, Oviedo, 33007, Spain Rector, J W (jwrector@lbl.gov), University of California, Berkeley, P.O. Box 987, Truckee, CA 96160,

In this poster, we use the term Kernel Learning to encompass a class of computer learning algorithms in which the output of the algorithm is a linear combination of an input compared to a set of known inputsi. The comparison is done using a kernel function. Kriging, which is often used for spatial interpolation, is the most well-known kernel learning method in the earth sciences. Support Vector Machines (SVMs) and radial basis functions are also kernel algorithms. If the kernel is chosen to be a symmetric positive semi-definite function, then it can be interpreted as a transformation of the inputs into a feature space. The assumption of linearity in the model implies linearity between inputs and outputs once the inputs have been transformed into feature space. In many geophysical situations, the relationship between an earth model and data measured at specific locations can be expressed as the inner product of the model with a Green's function (which might possibly depend on the model parameters). If it is possible to use this knowledge to construct a feature space, then it should be possible to construct a kernel which transforms inputs into the same, or a closely related feature space. In this poster, we train SVMs to approximate forward and inverse relationships between earth models and synthetic geophysical data and study their performance as a function of the ability of a kernel to generate a physically appropriate feature space.

NG11A-0178 

Multivariate Dependence Estimation in Geophysics

* Ganguly, A R (gangulyar@ornl.gov), Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, United States Khan, S), AIR Worldwide Corporation, 131 Dartmouth Street, Boston, MA 02116, United States Bandyopadhyay, S), Institute for Systems Research, 3119 A.V. Williams Building University of Maryland, College Park, MD 20742, United States

Multivariate correlation is a useful tool for statistical analysis and prediction, and for developing or validating physically-based models. To illustrate, linear correlation is a basic tool for exploratory data analysis, and for predictive analysis, while linear auto- and cross-correlation functions, or their Fourier transforms corresponding to spectral or cross-spectral methods, are building blocks for time series analysis and prediction. Spatial auto- and cross-correlation functions and corresponding spectral methods are often the first steps in spatial statistics. However, one major gap in the literature is the limited applicability of rigorous approaches to quantify multivariate dependence structures beyond mere linear associations. While information theoretic measures based on mutual information capture the complete dependence in principle, useful recipes for estimating the mutual information from data are still emerging, and in most cases, remain untested on short and noisy, real-world data. A second major gap is the quantification of the associations within and among anomalies and extreme values, even though new approaches, for example based on copula estimation, have been proposed. Third, measures for multivariate dependence in space and time are still in their infancy. Here the state-of-the-art for multivariate dependence estimation in geophysical problems is described, with particular emphasis on new challenges, emerging methods, and real-world applications.

NG11A-0179 

Magnetoacoustic Phenomena in Saturated Porous Media

* Perepechko, Y (perep@online.sinor.ru), IGM SB RAS, 3, ave acad. Koptyuga, Novosibirsk, 630090, Russian Federation

This work deals with dynamic interaction between electromagnetic and hydrodynamic types of motions in a porous medium, saturated with electrolyte. The system of equations is a coupling of equations of the two-velocity continuous filtration theory and Maxwell equations in quasi-stationary approximation. The method of separation by the physical processes is used for numerical solution, and the hyperbolic system is approximated by the explicit expanded Godunov scheme, and the parabolic system is approximated by the inexplicit Crank-Nicolson scheme. Generation of the magnetic field was modeled in the process of 2D electrolyte filtration in a porous medium, which is considered to be conducing because of a double electric layer. An entrainment in the external magnetic field over the electrolyte flow into a porous medium is observed, and the location of magnetic field maximum relative to the inlet boundary is determined by the ratio of kinematic viscosity to magnetic viscosity. A rise of this ratio provides more intensive drag of a filtered liquid and increasing magnetic field, reached in a porous medium. Downward the flow the field decreases because of magnetic field diffusion. The problem with simultaneous excitation of acoustic and electromagnetic perturbations at the boundary of saturated porous medium was also considered, and this allows us to obtain additional knowledge about accompanying effects and phenomena, what is the main scientific and practical goal of geophysics and oil survey. This research was supported by the Russian Foundation for Basic Research grant 06-05-65110, by the President's grants NSh-1573.2003.5, and by the Russian Ministry Science and Education grant RNP.2.1.1.702.

Author(s) (2007), Title, Eos Trans. AGU, 88(52), Fall Meet. Suppl., Abstract #####-##.