Filtering by Subject: Applied Mathematics

Estimating the Occurrence of Slow Slip Events and Earthquakes with an Ensemble Kalman Filter

Hamed Ali Diab-Montero, Meng Li, Ylona van Dinther, et al.

Published: 2022-08-07
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics

Our ability to forecast earthquakes and slow slip events is hampered by limited information on the current state of stress on faults. Ensemble data assimilation methods permit estimating the state by combining physics-based models and observations, while considering their uncertainties. We employ an Ensemble Kalman Filter (EnKF) to estimate shear stresses, slip rates, and the state theta acting [...]

A High-order Accurate Summation-by-Parts Finite Difference Method for Fully-dynamic Earthquake Sequence Simulations within Sedimentary Basins

Tobias Harvey, Brittany Angela Erickson, Jeremy Edward Kozdon

Published: 2022-08-06
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics

We present a computationally efficient numerical method for earthquake sequences that incorporates wave propagation during rupture. A vertical strike-slip fault governed by rate-and-state friction is embedded in a heterogeneous elastic half-space discretized using a high-order accurate Summation-by-Parts finite difference method. We develop a two solver approach: Adaptive time-stepping is [...]

A computational framework for time dependent deformation in viscoelastic magmatic systems

Cody Rucker, Brittany Angela Erickson, Leif Karlstrom, et al.

Published: 2022-04-01
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Mathematics

Time-dependent ground deformation is a key observable in active magmatic systems, but is challenging to characterize. Here we present a numerical framework for modeling transient deformation and stress around a subsurface, spheroidal pressurized magma reservoir within a viscoelastic half-space with variable material coefficients, utilizing a high-order finite-element method and explicit [...]

Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk

Mariana C A Clare, Tim Leijnse, Robert McCall, et al.

Published: 2022-03-14
Subjects: Applied Mathematics, Earth Sciences, Hydrology, Risk Analysis, Statistical Methodology, Statistics and Probability

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficiency of low fidelity models. Here, we apply the [...]

Diapycnal Displacement, Diffusion, and Distortion of Tracers in the Ocean

Henri Francois Drake, Xiaozhou Ruan, Raffaele Ferrari

Published: 2022-01-07
Subjects: Applied Mathematics, Fluid Dynamics, Non-linear Dynamics, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Indirect microstructure measurements of in situ turbulence suggest that mixing is bottom enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. Tracer release experiments (TREs), in which inert tracers are purposefully [...]

Dynamics of Eddying Abyssal Mixing Layers over Sloping Rough Topography

Henri Francois Drake, Xiaozhou Ruan, Raffaele Ferrari, et al.

Published: 2022-01-07
Subjects: Applied Mathematics, Earth Sciences, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

The abyssal overturning circulation is thought to be primarily driven by small-scale turbulent mixing. Diagnosed water-mass transformations are dominated by rough topography “hotspots,” where the bottom enhancement of mixing causes the diffusive buoyancy flux to diverge, driving widespread downwelling in the interior—only to be overwhelmed by an even stronger upwelling in a thin bottom boundary [...]

A review of model-based scenario analysis of poverty for informing sustainability

QI LIU, Zhaoxia Guo, Lei Gao, et al.

Published: 2021-11-22
Subjects: Applied Mathematics, Dynamic Systems, Environmental Sciences, Natural Resources Management and Policy, Physical Sciences and Mathematics, Sustainability

Ending poverty in all its forms everywhere is the first goal being targeted by the United Nations 2030 Agenda for Sustainable Development. Poverty eradication is a long-term process that faces the challenges of many uncertainties and complex interactions with other Sustainable Development Goals (SDGs). In order to better understand poverty and contribute to addressing poverty in a sustainable [...]

Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

Mariana C A Clare, Stephan C Kramer, Colin J Cotter, et al.

Published: 2021-08-03
Subjects: Applied Mathematics, Fluid Dynamics, Geomorphology, Numerical Analysis and Computation, Partial Differential Equations, Programming Languages and Compilers

The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure related parameters in both the hydrodynamic and [...]

Modeling P waves in seismic noise correlations: Advancing fault monitoring using train traffic sources

Korbinian Sager, Victor C. Tsai, Yixiao Sheng, et al.

Published: 2021-06-19
Subjects: Applied Mathematics, Earth Sciences, Geophysics and Seismology, Physics

The theory of Green's function retrieval essentially requires homogeneously distributed noise sources. Even though these conditions are not fulfilled in nature, low-frequency (<1 Hz) surface waves generated by ocean-crust interactions have been used successfully to image the crust with unprecedented spatial resolution. In contrast to low-frequency surface waves, high-frequency (>1 Hz) body waves [...]

Detection of Interannual Ensemble Forecast Signals over the North Atlantic and Europe using Atmospheric Circulation Regimes

Swinda Klaasje Jantine Falkena, Jana de Wiljes, Antje Weisheimer, et al.

Published: 2021-05-27
Subjects: Applied Mathematics, Atmospheric Sciences, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

To study the forced variability of atmospheric circulation regimes, the use of model ensembles is often necessary for identifying statistically significant signals as the observed data constitute a small sample and are thus strongly affected by the noise associated with sampling uncertainty. However, the regime representation is itself affected by noise within the atmosphere, which can make it [...]

A damage model for the frictional shear failure of brittle materials in compression

Simon Philip Gill

Published: 2021-05-13
Subjects: Applied Mathematics, Computational Engineering, Earth Sciences, Engineering, Geology, Materials Science and Engineering, Physical Sciences and Mathematics

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces [...]

Utilizing Random Forest Machine Learning Models to Determine Water Table Flood Levels through Volunteered Geospatial Information

Raghav Sriram

Published: 2021-04-27
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Environmental Sciences, Physical Sciences and Mathematics

Many people use smartphone cameras to record their living environments through captured images, and share aspects of their daily lives on social networks, such as Facebook, Instagram, and Twitter. These platforms provide volunteered geographic information (VGI), which enables the public to know where and when events occur. At the same time, image-based VGI can also indicate environmental changes [...]

Dilatancy and compaction of a rate-and-state fault in a poroelastic medium: Linearized stability analysis

Elias Rafn Heimisson, John Rudnicki, Nadia Lapusta

Published: 2021-04-06
Subjects: Applied Mathematics, Geophysics and Seismology, Tectonics and Structure

Faults in the crust at seismogenic depths are embedded in a fluid-saturated, elastic, porous material. Slip on such faults may induce transient pore pressure changes through dilatancy or compaction of the gouge or host rock. However, the poroelastic nature of the crust and the full coupling of inelastic gouge processes and the host rock have been largely neglected in previous analyses. Here, we [...]

An idealized 1.5-layer isentropic model with convection and precipitation for satellite data assimilation research. Part II: model derivation

Onno Bokhove, Luca Cantarello, Steven Tobias

Published: 2021-01-22
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

In this part II paper we present the analytical derivation of the isentropic 1.5-layer shallow water model described and used in part I of this study. The mathematical derivation presented here is based on a combined asymptotic and slaved Hamiltonian analysis. The scaling assumptions throughout the paper are supported by real observations based on radiosonde data. Eventually, a fully consistent [...]

An idealized 1.5-layer isentropic model with convection and precipitationfor satellite data assimilation research. Part I: model dynamics

Luca Cantarello, Onno Bokhove, Steven Tobias

Published: 2021-01-22
Subjects: Applied Mathematics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

An isentropic 1.5-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic [...]


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