Three-dimensional numerical modelling of static and transient Coulomb stress changes on intra-continental dip-slip faults

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Three-dimensional finite-element modeling of Coulomb stress changes on normal and thrust faults caused by pore fluid pressure changes and postseismic viscoelastic relaxation

The analysis of Coulomb stress changes has become an important tool for seismic hazard evaluation because such stress changes may trigger or delay subsequent earthquakes. Processes that can cause significant Coulomb stress changes include coseismic slip and transient postseismic processes such as poroelastic effects and viscoelastic relaxation. However, the combined influence of poroelastic effects and viscoelastic relaxation on co- and postseismic Coulomb stress changes has not been systematically studied so far. Here, we use three-dimensional finite-element models with arrays of normal and thrust faults to investigate how pore fluid pressure changes and viscoelastic relaxation overlap during the postseismic phase. In different experiments, we vary the permeability of the upper crust and the viscosity of the lower crust or lithospheric mantle while keeping the other parameters constant. In addition, we perform experiments in which we combine a high (low) permeability of the upper crust with a low (high) viscosity of the lower crust. Our results show that the coseismic (i.e., static) Coulomb stress changes are altered by the signal from poroelastic effects and viscoelastic relaxation during the first month after the earthquake. For sufficiently low viscosities, the Coulomb stress change patterns show a combined signal from poroelastic and viscoelastic effects already during the first postseismic year. For sufficiently low permeabilities, Coulomb stress changes induced by poroelastic effects overlap with the signals from viscoelastic relaxation and interseismic stress accumulation for decades. Our results imply that poroelastic and viscoelastic effects have a strong impact on postseismic Coulomb stress changes and should therefore be considered together when analyzing Coulomb stress transfer between faults

Dependence of late glacial sea-level predictions on 3D Earth structure

Glacial isostatic adjustment is dominated by Earth rheology resulting in a variability of relative sea-level (RSL) predictions of more than 100 meters during the last glacial cycle. Seismic tomography models reveal significant lateral variations in seismic wavespeed, most likely corresponding to variations in temperature and hence viscosity. Therefore, the replacement of 1D Earth structures by a 3D Earth structure is an essential part of recent research to reveal the impact of lateral viscosity contrasts and to achieve a more consistent view on solid-Earth dynamics. Here, we apply the VIscoelastic Lithosphere and MAntle model VILMA to predict RSL during the last deglaciation. We create an ensemble of geodynamically constrained 3D Earth structures which is based on seismic tomography models while considering a range of conversion factors to transfer seismic velocity variations into viscosity variations. For a number of globally distributed sites, we discuss the resulting variability in RSL predictions, compare this with regionally optimized 1D Earth structures, and validate the model results with relative sea-level data (sea-level indicators). This study is part of the German Climate Modeling initiative PalMod aiming the modeling of the last glacial cycle under consideration of a coupled Earth system model, i.e. including feedbacks between ice-sheets and the solid Earth

Validating GIA models based on an ensemble of 3D Earth structures with present-day GPS uplift rates

Glacial-isostatic adjustment (GIA) models simulate the viscoelastic response of the solid earth due to loading. During the last glacial maximum, large areas in the northern and southern hemisphere were covered by km-thick ice sheets. Although most of the ice has been melted already 8,000 year ago, the time-delayed response of the viscoelastic earth is still a significant contribution to present-day uplift rates. The implementation of GIA models in global climate models is an essential part of the current research. Hereby, the choice of an appropriate earth structure in the GIA model plays an important role and has to be constrained by observational data. Here, we apply present-day uplift data to constrain a set of GIA models that differ in 3D earth structure. To this end, these different GIA models are validated against GPS uplift rates provided by Schumacher et al. (2019). The GPS stations are globally distributed and not necessarily clustered in regions with strong GIA signal. For validation, regions with the largest gradient present in the GIA signal are most crucial. Thus, we use a weighting scheme, where those GPS stations get a higher weight that are less correlated to all other stations. Additionally, uncertainties in the GPS rates appear due to the length of the GPS time series and due to station specifics such as the used GPS receiver, and are provided together with the rates as standard deviations. Thence, the weighting used for the validation is the sum of the correlation derived weights and the uncertainty derived weights. With this weighting in place, different GIA models can be validated against present day uplift rates by means of root mean square errors or mean absolute error

Data assimilation for a visco-elastic Earth deformation model

We present a data assimilation algorithm for the time-domain spectral-finite element code VILMA. We consider a 1D earth structure and a prescribed glaciation history ICE5G for the external mass load forcing. We use the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the model in order to obtain better estimates of the viscosity structure of mantle and lithosphere. For this purpose, we apply a particle filter in which an ensemble of models is propagated in time, starting shortly before the last glacial maximum. At epochs when observations are available, each particle's performance is estimated and they are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. In a proof of concept we show that with this method it is possible to reconstruct a synthetic viscosity distribution from which synthetic data were constructed. In a second step, paleo sea level data are used to infer an optimised 1D viscosity distribution

An approach for constraining mantle viscosities through assimilation of palaeo sea level data into a glacial isostatic adjustment model

Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high

Gravitationally Consistent Mean Barystatic Sea Level Rise From Leakage‐Corrected Monthly GRACE Data

Gravitationally consistent solutions of the Sea Level Equation from leakage‐corrected monthly‐mean GFZ RL06 Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) Stokes coefficients reveal that barystatic sea level averaged over the whole global ocean was rising by 1.72 mm a−1 during the period April 2002 until August 2016. This rate refers to a truely global ocean averaging domain that includes all polar and semienclosed seas. The result corresponds to 2.02 mm a−1 mean barystatic sea level rise in the open ocean with a 1,000 km coastal buffer zone as obtained from a direct spatial integration of monthly GRACE data. The bias of +0.3 mm a−1 is caused by below‐average barystatic sea level rise in close proximity to coastal mass losses induced by the smaller gravitational attraction of the remaining continental ice and water masses. Alternative spherical harmonics solutions from CSR, JPL, and TU Graz reveal open‐ocean rates between 1.94 and 2.08 mm a−1, thereby demonstrating that systematic differences among the processing centers are much reduced in the latest release. We introduce in this paper a new method to approximate spatial leakage from the differences of two differently filtered global gravity fields. A globally constant and time‐invariant scale factor required to obtain full leakage from those filter differences is found to be 3.9 for GFZ RL06 when filtered with DDK3, and lies between 3.9 and 4.4 for other processing centers. Spatial leakage is estimated for every month in terms of global grids, thereby providing also valuable information of intrabasin leakage that is potentially relevant for hydrologic and hydrometeorological applications

An approach for constraining mantle viscosities through assimilation of palaeo sea level data into a glacial isostatic adjustment model

Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high

A statistical method to validate reconstructions of late-glacial relative sea level – Application to shallow water shells rated as low-grade sea-level indicators

In this study, we propose a statistical method to validate sea-level reconstructions using geological records known as sea-level indicators (SLIs). SLIs are often the only available data to retrace late-glacial relative sea level (RSL). Determining the RSL from SLI height is not straight forward, the elevation at which an SLI was found usually does not represent the past RSL. In contrast, it has to be related to past RSL by investigating sample’s type, habitat and deposition conditions. For instance, water distribution at which a specific specimen is found today can be related to the indicator's depositional height range. Furthermore, the precision of dating varies between geological samples, and, in case of radiocarbon dating, the age has to be calibrated using a non-linear calibration curve. To avoid an a-priori assumption like normal-distributed uncertainties, we define likelihood functions which take into account the indicative meaning’s available error information and calibration statistics represented by joint probabilities. For this conceptional study, we restrict ourselves to one type of indicators, shallow-water shells, which are usually considered as low-grade samples giving only a lower limit of former sea level, as the depth range in which they live spreads over several tens of meters, and does not follow a normal distribution. The presented method is aimed to serve as a strategy for glacial isostatic adjustment reconstructions, in this case for the German Paleo-Climate Modelling Initiative PalMod (https://www.palmod.de/en) and by extending it to other SLI types

Glacial inception through rapid ice area increase driven by albedo and vegetation feedbacks

We present transient simulations of the last glacial inception using the Earth system model CLIMBER-X with dynamic vegetation, interactive ice sheets, and visco-elastic solid Earth responses. The simulations are initialized at the middle of the Eemian interglacial (125 kiloyears before present, ka) and run until 100gka, driven by prescribed changes in Earth's orbital parameters and greenhouse gas concentrations from ice core data. CLIMBER-X simulates a rapid increase in Northern Hemisphere ice sheet area through MIS5d, with ice sheets expanding over northern North America and Scandinavia, in broad agreement with proxy reconstructions. While most of the increase in ice sheet area occurs over a relatively short period between 119 and 117gka, the larger part of the increase in ice volume occurs afterwards with an almost constant ice sheet extent. We show that the vegetation feedback plays a fundamental role in controlling the ice sheet expansion during the last glacial inception. In particular, with prescribed present-day vegetation the model simulates a global sea level drop of only g20gm, compared with the g35gm decrease in sea level with dynamic vegetation response. The ice sheet and carbon cycle feedbacks play only a minor role during the ice sheet expansion phase prior to g115gka but are important in limiting the deglaciation during the following phase characterized by increasing summer insolation. The model results are sensitive to climate model biases and to the parameterization of snow albedo, while they show only a weak dependence on changes in the ice sheet model resolution and the acceleration factor used to speed up the climate component. Overall, our simulations confirm and refine previous results showing that climate-vegetation-cryosphere feedbacks play a fundamental role in the transition from interglacial to glacial states characterizing Quaternary glacial cycles