Nonlinear Processes in Geophysics

Journal: Nonlinear Processes in Geophysics

Abbreviation

Nonlinear Process. Geophys.

Publisher

Copernicus

ISSN

1023-5809
1607-7946

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Publications 1 - 10 of 15

A viscoelastic Rivlin-Ericksen material model applicable to glacier ice
Riesen, Patrick; Hutter, Kolumban; Funk, Martin (2010)
Nonlinear Processes in Geophysics
We present a viscoelastic constitutive relation which describes transient creep of a modified second grade fluid enhanced with elastic properties of a solid. The material law describes a Rivlin-Ericksen material and is a generalization of existing material laws applied to study the viscoelastic properties of ice. The intention is to provide a formulation tailored to reproduce the viscoelastic behaviour of ice ranging from the instantaneous elastic response, to recoverable deformation, to viscous, stationary flow at the characteristic minimum creep rate associated with the deformation of polycrystalline ice. We numerically solve the problem of a slab of material shearing down a uniformly inclined plate. The equations are made dimensionless in a form in which elastic effects and/or the influence of higher order terms (i.e., strain accelerations) can be compared with viscous creep at the minimum creep rate by means of two dimensionless parameters. We discuss the resulting material behaviour and the features exhibited at different parameter combinations. Also, a viable range of the non-dimensional parameters is estimated in the scale analysis.
An extended approach for spatiotemporal gapfilling: dealing with large and systematic gaps in geoscientific datasets
von Buttlar, Jannis; Zscheischler, Jakob; Mahecha, Miguel D. (2014)
Nonlinear Processes in Geophysics
Spatiotemporal observations in Earth System sciences are often affected by numerous and/or systematically distributed gaps. This data fragmentation is inherited from instrument failures, sparse measurement protocols, or unfavourable conditions (e.g. clouds or vegetation thickness in case of remote-sensing data). Missing values are problematic as they may cause analytic biases and often inhibit advanced statistical analyses. Hence, gapfilling is an undesired but necessary task in Earth System sciences. State-of-the-art gapfilling algorithms based on Singular Spectrum Analysis (SSA) exploit the information contained in periodic temporal patterns to fill gaps in the observations. Here we propose an extension of this method in order to additionally consider the spatial processes and patterns underlying most geoscientific datasets. The latter has been made possible by including a recently developed 2-D-SSA approach. Using both artificial and real-world test data, we show that simultaneously exploiting spatial and temporal patterns improves the gapfilling substantially. We outperform conventional approaches particularly for large and systematically recurring gaps. The new method is reasonably fast and can be applied with a minimum of a priori assumptions regarding the structure of the data and the distribution of gaps. The algorithm is available as a ready-to-use open source software package.
Static behaviour of induced seismicity
Mignan, Arnaud (2016)
Nonlinear Processes in Geophysics
The standard paradigm to describe seismicity induced by fluid injection is to apply non-linear diffusion dynamics in a poroelastic medium. I show that the spatio-temporal behaviour and rate evolution of induced seismicity can, instead, be expressed by geometric operations on a static stress field produced by volume change at depth. I obtain laws similar in form to the ones derived from poroelasticity while requiring a lower description length. Although fluid flow is known to occur in the ground, it is not pertinent to the geometrical description of the spatio-temporal patterns of induced seismicity. The proposed model is equivalent to the static stress model for tectonic foreshocks generated by the Non-Critical Precursory Accelerating Seismicity Theory. This study hence verifies the explanatory power of this theory outside of its original scope and provides an alternative physical approach to poroelasticity for the modelling of induced seismicity. The applicability of the proposed geometrical approach is illustrated for the case of the 2006, Basel enhanced geothermal system stimulation experiment. Applicability to more problematic cases where the stress field may be spatially heterogeneous is also discussed.
Path-integrated Lagrangian measures from the velocity gradient tensor
Pérez-Muñuzuri, Vicente; Huhn, Florian (2013)
Nonlinear Processes in Geophysics
Spatial maps of the finite-time Lyapunov exponent (FTLE) have been used extensively to study LCS in two-dimensional dynamical systems, in particular with application to transport in unsteady fluid flows. We use the time-periodic double-gyre model to compare spatial fields of FTLE and the path-integrated Eulerian Okubo–Weiss parameter (OW). Both fields correlate strongly, and by solving the dynamics of the deformation gradient tensor, a theoretical relationship between both magnitudes has been obtained. While for long integration times more and more FTLE ridges appear that do not seem to coincide with the stable manifold, ridges in the field of path-integrated OW represent fewer additional structures.
Size distribution and structure of Barchan dune fields
Durán Vinent, Orencio; Schwämmle, Veit; Lind, Pedro G.; et al. (2011)
Nonlinear Processes in Geophysics
Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction.
Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation
Bocher, Marie; Fournier, Alexandre; Coltice, Nicolas (2018)
Nonlinear Processes in Geophysics
Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016). Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF) to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.
A tri-stage cluster identification model for accurate analysis of seismic catalogs
Nanda, Satyasai Jagannath; Tiampo, Kristy F.; Panda, Ganapati; et al. (2013)
Nonlinear Processes in Geophysics
In this paper we propose a tri-stage cluster identification model that is a combination of a simple single iteration distance algorithm and an iterative K-means algorithm. In this study of earthquake seismicity, the model considers event location, time and magnitude information from earthquake catalog data to efficiently classify events as either background or mainshock and aftershock sequences. Tests on a synthetic seismicity catalog demonstrate the efficiency of the proposed model in terms of accuracy percentage (94.81% for background and 89.46% for aftershocks). The close agreement between lambda and cumulative plots for the ideal synthetic catalog and that generated by the proposed model also supports the accuracy of the proposed technique. There is flexibility in the model design to allow for proper selection of location and magnitude ranges, depending upon the nature of the mainshocks present in the catalog. The effectiveness of the proposed model also is evaluated by the classification of events in three historic catalogs: California, Japan and Indonesia. As expected, for both synthetic and historic catalog analysis it is observed that the density of events classified as background is almost uniform throughout the region, whereas the density of aftershock events are higher near the mainshocks.
Structural and statistical properties of the collocation technique for error characterization
Zwieback, Simon; Scipal, Klaus; Dorigo, Wouter; et al. (2012)
Nonlinear Processes in Geophysics
The validation of geophysical data sets (e.g. derived from models, exploration techniques or remote sensing) presents a formidable challenge as all products are inherently different and subject to errors. The collocation technique permits the retrieval of the error variances of different data sources without the need to specify one data set as a reference. In addition calibration constants can be determined to account for biases and different dynamic ranges. The method is frequently applied to the study and comparison of remote sensing, in-situ and modelled data, particularly in hydrology and oceanography. Previous studies have almost exclusively focussed on the validation of three data sources; in this paper it is shown how the technique generalizes to an arbitrary number of data sets. It turns out that only parts of the covariance structure can be resolved by the collocation technique, thus emphasizing the necessity of expert knowledge for the correct validation of geophysical products. Furthermore the bias and error variance of the estimators are derived with particular emphasis on the assumptions necessary for establishing those characteristics. Important properties of the method, such as the structural deficiencies, dependence of the accuracy on the number of measurements and the impact of violated assumptions, are illustrated by application to simulated data.
Subvisible cirrus clouds - a dynamical system approach
Spreitzer, Elisa J.; Marschalik, Manuel P.; Spichtinger, Peter (2017)
Nonlinear Processes in Geophysics
Ice clouds, so-called cirrus clouds, occur very frequently in the tropopause region. A special class are subvisible cirrus clouds with an optical depth lower than 0.03, associated with very low ice crystal number concentrations. The dominant pathway for the formation of these clouds is not known well. It is often assumed that heterogeneous nucleation on solid aerosol particles is the preferred mechanism although homogeneous freezing of aqueous solution droplets might be possible, since these clouds occur in the low-temperature regime T < 235 K. For investigating subvisible cirrus clouds as formed by homogeneous freezing we develop a reduced cloud model from first principles, which is close enough to complex models but is also simple enough for mathematical analysis. The model consists of a three-dimensional set of ordinary differential equations, and includes the relevant processes as ice nucleation, diffusional growth and sedimentation. We study the formation and evolution of subvisible cirrus clouds in the low-temperature regime as driven by slow vertical updraughts (0 < w ≤ 0. 05 m s−1). The model is integrated numerically and also investigated by means of theory of dynamical systems. We found two qualitatively different states for the long-term behaviour of subvisible cirrus clouds. The first state is a stable focus; i.e. the solution of the differential equations performs damped oscillations and asymptotically reaches a constant value as an equilibrium state. The second state is a limit cycle in phase space; i.e. the solution asymptotically approaches a one-dimensional attractor with purely oscillatory behaviour. The transition between the states is characterised by a Hopf bifurcation and is determined by two parameters – vertical updraught velocity and temperature. In both cases, the properties of the simulated clouds agree reasonably well with simulations from a more detailed model, with former analytical studies, and with observations of subvisible cirrus, respectively. The reduced model can also provide qualitative interpretations of simulations with a complex and more detailed model at states close to bifurcation qualitatively. The results indicate that homogeneous nucleation is a possible formation pathway for subvisible cirrus clouds. The results motivate a minimal model for subvisible cirrus clouds (SVCs), which might be used in future work for the development of parameterisations for coarse large-scale models, representing structures of clouds.
Earthquake forecasting based on data assimilation: sequential Monte Carlo methods for renewal point processes
Werner, Maximilian Jonas; Ide, Kayo; Sornette, Didier (2011)
Nonlinear Processes in Geophysics
Data assimilation is routinely employed in meteorology, engineering and computer sciences to optimally combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts, than achieved by ignoring data uncertainties. Earthquake forecasting, too, suffers from measurement errors and partial model information and may thus gain significantly from data assimilation. We present perhaps the first fully implementable data assimilation method for earthquake forecasts generated by a point-process model of seismicity. We test the method on a synthetic and pedagogical example of a renewal process observed in noise, which is relevant for the seismic gap hypothesis, models of characteristic earthquakes and recurrence statistics of large quakes inferred from paleoseismic data records. To address the non-Gaussian statistics of earthquakes, we use sequential Monte Carlo methods, a set of flexible simulation-based methods for recursively estimating arbitrary posterior distributions. We perform extensive numerical simulations to demonstrate the feasibility and benefits of forecasting earthquakes based on data assimilation.

Publications 1 - 10 of 15

Journal: Nonlinear Processes in Geophysics

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