Surface Velocity Field Research Articles

3D Surface Velocity Field Inferred from SAR Interferometry: Cerro Prieto Step-Over, Mexico, Case Study

The Cerro Prieto basin, a tectonically active pull-apart basin, hosts significant geothermal resources currently being exploited in the Cerro Prieto Geothermal Field (CPGF). Consequently, natural tectonic processes and anthropogenic activities contribute to three-dimensional surface displacements in this pull-apart basin. Here, we obtained the Cerro Prieto Step-Over 3D surface velocity field (3DSVF) by accomplishing a weighted least square algorithm inversion from geometrically quasi-orthogonal airborne UAVSAR and RADARSAT-2, Sentinel 1A satellite Synthetic Aperture-Radar (SAR) imagery collected from 2012 to 2016. The 3DSVF results show a vertical rate of 150 mm/yr and 40 mm/yr for the horizontal rate, where for the first time, the north component displacement is achieved by using only the Interferometric SAR time series in the CPGF. Data integration and validation between the 3DSVF and ground-based measurements such as continuous GPS time series and precise leveling data were achieved. Correlating the findings with recent geothermal energy production revealed a subsidence rate slowdown that aligns with the CPGF’s annual vapor production.

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

2D and 3D Computational Modeling of Surface Flooding in Urbanized Floodplains: Modeling Performance for Various Building Layouts

AbstractUnderstanding the strengths and limitations of the modeling capacity of surface flooding in urbanized floodplains is of utmost importance as such events are becoming increasingly frequent and extreme. In this study, we assess two computational models against laboratory observations of surface urban flooding in a reduced‐scale physical model of idealized urban districts. Four urban layouts were considered, involving each three inlets and three outlets as well as a combination of three‐ and four‐branch crossroads together with open spaces. The first model (2D) solves the shallow‐water equations while the second one (3D) solves the Reynolds‐averaged Navier‐Stokes equations. Both models accurately predict the flow depths in the inlet branches. For the discharge partition between the outlets, deviations between the computations and laboratory observations remain close to the experimental uncertainties (maximum 2.5 percent‐points). The velocity fields computed in 3D generally match the measured surface velocity fields. In urban layouts involving mostly a network of streets, the depth‐averaged velocity fields computed by the 2D model agree remarkably well with those of the 3D model, with differences not exceeding 10%, despite the presence of helicoidal flow (revealed by the 3D computations). In configurations with large open areas, the 3D model captures generally well the trajectory and velocity distribution of main surface flow jet and recirculations; but the 2D model does not perform as well as it does in relatively channelized flow regions. Visual inspection of the jet trajectories computed by the 2D model in large open areas reveals that they substantially deviate from the observations.

Disagreements in Geodetically Inferred Strain Rates in the Western US With Stress Orientations and Geologic Moment Rates

AbstractI employ an elasticity‐based method to invert a geodetically derived surface velocity field in the western US using for present‐day surface strain rate fields with uncertainties. The method uses distributed body forces in a thin elastic sheet and allows for discontinuities in velocity across creeping faults using the solution for dislocations in a thin elastic plate. I compare the strain rate fields with previously published stress orientations and moment rates from geological slip rate data and previous geodetic studies. Geologic and geodetic moment rates are calculated using slip rate and off‐fault strain rates from the 2023 US National Seismic Hazard Model (NSHM) deformation models. I find that computed total geodetic moment rates are higher than NSHM summed moment rates on faults for all regions of the western US except the highest deforming rate regions including the Western Transverse Ranges and the northern and southern San Andreas Fault (SAF) system in California. Computed geodetic moment rates are comparable to the moment rates derived from the geodetically based NSHM deformation models in all regions. I find systematic differences in orientations of maximum horizontal shortening rate and maximum horizontal compressive stress in the Pacific Northwest region and along much of the SAF system. In the Pacific Northwest, the maximum horizontal stress orientations are rotated counterclockwise 40–90° relative to the maximum horizontal strain rate directions. Along the SAF system, the maximum horizontal stresses are rotated systematically 25–40° clockwise (closer to fault normal) relative to the strain rates.

Review of Geodetic and Geologic Deformation Models for 2023 U.S. National Seismic Hazard Model

ABSTRACT We review five deformation models generated for the 2023 update to the U.S. National Seismic Hazard Model (NSHM), which provide input fault-slip rates that drive the rate of earthquake moment release. Four of the deformation models use the Global Positioning System-derived surface velocity field and geologic slip-rate data to derive slip-rate estimates (Evans, Pollitz, Shen-Bird, and Zeng), and one model uses geologic data (the “geologic model”). The correlation between the geologic model preferred slip rates and geodetically derived slip rates is high for the Pollitz, Zeng, and Shen-Bird models, and the median of all slip-rate models has correlation coefficient of 0.88. The median geodetic model slip rates are systematically lower than the preferred geologic model rates for faults with slip rates exceeding 10 mm/yr and systematically higher on faults with slip rates less than 0.1 mm/yr. Geodetically derived slip rates tend to the low end of the geologic model range along sections of the San Andreas fault and the Garlock fault, whereas they tend to be higher across north coast California faults. The total on-fault moment rates agree well across models with all rates within 18% of the median. Estimated off-fault strain rate orientations and styles vary considerably across models and off-fault moment rates vary more than on-fault moment rates. Path integrals across the western U.S. accounting for fault-slip rate and off-fault deformation are generally consistent with Pacific-North America plate motion with the median deformation rates recovering about 98% of the plate motion with about 20% of the total plate motion accommodated by off-fault strain rate. The geologic model, which has no off-fault deformation, accounts for about 82% of plate motion with fault slip. Finally, we make a recommendation for relative weighting of the models for the NSHM as well as several recommendations for future NSHM deformation model development.

SSIMS-Flow: Image velocimetry workbench for open-channel flow rate estimation

Image-based hydrological measurement techniques have surged in popularity over the last decade, with the most common type of data obtained being the open-channel surface velocity field and flow rate. The lack of a feature-rich image velocimetry software often forces practitioners to use multiple tools as part of a cumbersome workflow, which restricts the uptake of such methods and reduces the reproducibility of results. We present the free and open-source software SSIMS-Flow, which handles extraction of video frames, removal of geometric distortions, video stabilization, orthorectification, image enhancement, and velocity and flow rate estimation using the Farnebäck optical flow method improved with specific pooling techniques developed in this study. SSIMS-Flow performance is tested in two case studies and compared with known reference values and those obtained using industry-standard PIVlab software. In low seeding and tracerless conditions, SSIMS-Flow demonstrates higher velocity estimation accuracy, while delivering several times faster computational runtime.

Investigation of the Source of Iceland Basin Freshening: Virtual Particle Tracking with Satellite-Derived Geostrophic Surface Velocities

In the 2010s, a large freshening event similar to past Great Salinity Anomalies occurred in the Iceland Basin that has since propagated into the Irminger Sea. The source waters of this fresh anomaly were hypothesized to have come from an eastward diversion of the Labrador Current, a finding that has since been supported by recent modeling studies. In this study, we investigate the pathways of the freshwater anomaly using a purely observational approach: particle tracking using satellite altimetry-derived surface velocity fields. Particle trajectories originating in the Labrador Current and integrated forward in time entered the Iceland Basin during the freshening event at nearly twice the frequency observed prior to 2009, suggesting an increased presence of Labrador Current-origin water in the Iceland Basin and Rockall Trough during the freshening. We observe a distinct regime change in 2009, similar to the timing found in the previous modeling papers. These spatial shifts were accompanied by faster transit times along the pathways which led to along-stream convergence and more particles arriving to the eastern subpolar gyre. These findings support the hypothesis that a diversion of relatively fresh Labrador Current waters eastward from the Grand Banks can explain the unprecedented freshening in the Iceland Basin.

Particle dispersion and clustering in surface ocean turbulence with ageostrophic dynamics

Upper-ocean turbulent flows at horizontal length scales smaller than the deformation radius depart from geostrophic equilibrium and develop important vertical velocities, which are key to marine ecology and climatic processes. Due to their small size and fast temporal evolution, these fine scales are difficult to measure during oceanographic campaigns. Instruments such as Lagrangian drifters have provided another way to characterize these scales through the analysis of pair-dispersion evolution and have pointed out striking particle convergence events. By means of numerical simulations, we investigate such processes in a model of surface-ocean turbulence that includes ageostrophic motions. This model originates from a Rossby-number expansion of the primitive equations and reduces to the surface quasi-geostrophic model, a paradigm of submesoscale dynamics, in the limit of vanishing Rossby number. We focus on the effect of the ageostrophic dynamics on the pair-dispersion and clustering properties of Lagrangian tracer particles at the ocean surface. Our results indicate that while over long times the pair separation process is barely affected by the ageostrophic component of the velocity field, the latter is responsible for the formation of temporary particle aggregates, and the intensity of this phenomenon increases with the Rossby number. We further show that Lagrangian tracers preferentially accumulate in cyclonic frontal regions, which is in agreement with observations and other more realistic modeling studies. These findings appear interesting to improve the understanding of the turbulent transport by ocean fine scales and in light of upcoming, new high-resolution satellite data of surface velocity fields.

Experimental and numerical estimation of velocity and concentration distributions in partially vegetated open channels

Transport phenomena are crucial components of the biological and chemical processes that govern fluvial environments. The presence of vegetation along rivers plays a significant role in affecting the flow velocity, which becomes unevenly distributed, and consequently is an important factor that can affect longitudinal and transversal dispersion and mixing of pollutants. Therefore, in this study, to provide a better understanding and further insights of the velocity field and the pollutant dispersion in open channels partially covered by sparse vegetation and dense vegetation, an experimental campaign is presented to compare them with the no-vegetation scenario. Novel datasets are produced by applying the Particle Image Velocity (PIV) and the Planar Concentration Analysis (PCA) technologies, which were used to measure simultaneously the surface velocity field and pollutant concentration map within the open channel tested. Results obtained have been used to calibrate and validate a numerical model designed to simulate velocity fields (via Discrete Boltzmann Model D2Q16) and pollutant concentration maps (via the Lattice Boltzmann model D2Q9). Results have shown that as the density of vegetation increases, the flow velocity in the vegetation zone decreases while the velocity in the no-vegetation zone increases. So, the velocity gradient in the transition zone increases accordingly. Besides, the water surface difference between inlet and outlet is higher as the density increases. Finally, the simulated results have been compared with corresponding experimental data and good agreements have been achieved, which indicates that the model developed can accurately predict features that were observed and measured within the experimental facility.

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

This study presents a comprehensive continuum approach to modeling granular surface flows using the Incompressible Non-Newtonian Smoothed Particle Hydrodynamics (INNSPH) method. The model integrates an incompressible SPH method, where pressure is computed by solving a pressure-Poisson equation with a non-Newtonian rheology. Projection-based SPH has a strong and rigorous theoretical basis can lead to stable and accurate simulations. This paper aims to develop a projection-based SPH method for modeling complex granular flows. INNSPH method combines incompressible SPH and μ(I) rheology models to simulate non-Newtonian viscoplastic fluid behavior in granular flows. Surface deposition, and velocity and pressure fields are estimated using a rheology model. Validation is performed by comparing simulation results, including surface profiles and run-out distances with experimental data, showing good agreement. INNSPH method is then employed to model a 2D column collapse and a dam-break scenario on horizontal and inclined planes for sands and glass beads. The method captures three distinct final deposition morphologies; truncated cone, conic, and Mexican hat shapes in collapsing columns. INNSPH computational efficiency enables simulations of large-scale granular flows, and its open-source nature facilitates collaboration and further modifications by researchers. The method provides a good understanding of granular flow dynamics in various industrial applications including powder technology.

Estimating ice discharge of the Antarctic Peninsula using different ice-thickness datasets

Abstract The Antarctic Peninsula Ice Sheet (APIS) has become a significant contributor to sea-level rise over recent decades. Accurately estimating the ice discharge from the outlet glaciers of the APIS is crucial to quantify the mass balance of the Antarctic Peninsula. We here compute the ice discharge from the outlet glaciers of the APIS north of 70 ${^\circ }$ S for the five most widely used ice-thickness reconstructions, using a common surface velocity field and a common set of flux gates, so the differences in ice discharge can be solely attributed to the differences in ice thickness at the flux gates. The total volumetric ice discharge for 2015–2017 ranges within 45–141 km3 a−1, depending on the ice-thickness model, with a mean of 87 ± 44 km3 a−1. The substantial differences between the ice-discharge results, and a multi-model normalized root-mean-squared deviation of 0.91 for the whole data set, reveal large differences and inconsistencies between the ice-thickness models, giving an indication of the large uncertainty in the current ice-discharge estimates for the APIS. This manifests a fundamental problem of the region: the scarcity of appropriate ice-thickness measurements and the difficulty of the current models to reconstruct the ice-thickness distribution in this complex region.

Present-Day Crustal Deformation of the Northwestern Tibetan Plateau Based on InSAR Measurements

In this study, The ENVISAT advanced synthetic aperture radar observations from 2003 to 2010 of a descending track covering an area of 100 km × 300 km were used to map the surface velocity field in northwestern Tibet. The derived line-of-sight (LOS) velocity map revealed that interseismic deformation was mainly located on the Altyn Tagh Fault (ATF) and other four immature subsidiary faults (i.e., Tashikule Fault, Muzitage-jingyuhe Fault, Heishibeihu Fault, and Woniuhu Fault). A 2D elastic screw dislocation model was used to interpret the interferometric synthetic aperture radar (InSAR) velocity profiles, which revealed the following results. (a) The oblique movement is partitioned between left-lateral slip at a rate of 6.3 ± 1.4 mm/y on the ATF and 5.9 ± 2.8 mm/y on the subsidiary faults. The low slip rate of the ATF indicates that the ATF does not drive the northeastward extrusion of material, with most of the extrusion occurring in the eastern interior of the plateau and the four subsidiary faults localizing the oblique convergence partitioned in the west. This can reasonably explain why catastrophic earthquakes and rapid slip do not occur all over along the ATF. (b) Based on the four subsidiary faults accommodating the oblique movement and the traces amalgamation with the EKLF (delineated Bayan Har plate boundary to the northeast), we concluded guardedly that the four subsidiary faults are the evoluting plate boundary of the Bayan Har block to the northwest. (c) The Tanan top-up structure had an uplift rate of ~0.6 mm/y at the south of the Tarim Basin.

Computational fluid dynamics analysis of a micro-scale chamber for measuring organic chemical emission parameters

Computational fluid dynamics simulations are used to model the velocity field and the transport of a passive scalar within a micro-scale chamber used to measure diffusional transport through various building materials. Comparisons of solutions obtained using a steady, laminar flow assumption with velocity measurements obtained from hot-wire anemometry show that the numerical method generally underpredicts the near surface velocity field. The results improve for higher flow rates and for carpeted test materials, modeled as a porous resistive layer. Calculations involving scalar transport within the upper chamber of the sampling device are performed for different flow rates and Schmidt numbers. The results are used to develop a model for the convective mass transfer coefficient, correlated as a function of the Reynolds and Schmidt numbers as well as the porosity of the carpet. This model is integrated into a steady-state mass transport model for predicting the diffusion of gaseous formaldehyde through various test materials. Predictions of diffusion and partition coefficients for vinyl flooring, gypsum wall board, and carpet are within the ranges of literature data. The results indicate that a perfectly mixed upper part of the sampling device is an adequate assumption.

The Study of Velocity Field in Front Opening Unified Pod by CAE

The front opening unified pod (FOUP) is a packing box for contamination control for semiconductor wafer transport. As the wafer fabrication process developes towards nanoor atom level, the semiconductor wafer storage device should advance from the particle prevention function into the airborne molecular contamination (AMC) removal function. Therefore, it is necessary to design/redesign a function for removing AMC or moisture inside the FOUP. This study used the design of leading diffuser tubes in the FOUP and pores in the surfaces of diffuser tubes to generate gas diffusion. This is to achieve a uniform distribution of the wafer surface velocity field and a uniform dehumidification function of the wafer surface. Based on the analysis results, when circular diffuser tubes are introduced in the FOUP and the intake air flow was set at 0.2-0.3 m3/hr, the interlayer wafer surface in the FOUP could achieve uniform distribution of velocity field. As a result, the humidity difference among various zones of wafer surface could be reduced, and the yield and quality of the wafer cutting process could be controlled.

Fractures in glaciers—Crack tips and their stress fields by observation and modeling

AbstractHigh‐resolution optical camera systems are opening new opportunities to study fractures in ice. Here, we present data obtained from the Modular Aerial Camera System camera system operated onboard of Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research (AWI) polar aircraft in northeast Greenland in 2022. In addition, we are using optical and radar satellite imagery. The study area is the 79°N Glacier (Nioghalvfjerdsbræ, 79NG), an outlet glacier of the Northeast Greenland Ice Stream. We found that crack tips are exhibiting additional isolated cracks ahead of the main crack. Subsequent crack propagation is starting from those isolated cracks, leading to an advance of the crack, with bridges between crack faces. The bridges provide information of the episodic crack propagation. Fractures have typically a length scale of kilometers and the distance of crack faces is in the order of meters to tenths of meters. Fracture modes will be inferred from stress fields computed by an inverse modeling approach using the Ice Sheet and Sea Level System Model. To this end, a surface velocity field derived from satellite remote sensing is used for the optimal control method that constrains model parameters, for example, basal friction coefficient or rheology.

An automatic ANN-based procedure for detecting optimal image sequences supporting LS-PIV applications for rivers monitoring

River flow monitoring has recently experienced rapid development due to advancements in optical methods, which are non-intrusive and enhance safety conditions for operators. Surface velocity fields are obtained recording and analyzing displacements of floating tracer materials, artificially introduced or already present on the water surface. River discharge can be assessed coupling the surface velocity fields with geometric data of a cross section. The accuracy of optical techniques is strongly affected by different environmental and hydraulic factors, and software parameterization, with tracer features that often play a prominent role. An adequate density and spatial distribution of tracer is required to ensure a complete characterization of surface velocity fields. In practical applications such conditions might occur only for a limited portion of the entire acquired images sequence. This work proposes an automatic procedure for identifying and extracting the best portion of a recorded video in terms of seeding characteristics and demonstrates how LS-PIV software performances can be enhanced through this approach. The procedure is implemented through a data-driven empirical approach based on an Artificial Neural Network, trained using data collected during an extensive measurement campaign across different rivers in Sicily (Italy). Performances are evaluated in terms of error in reproducing surface velocity profiles along specific transects, where benchmark profiles derived using an Acoustic Doppler Current Profiler are available. The procedure, also tested via numerical simulations on synthetic image sequences, outperformed an approach based on an existing metric for seeding characterization and represents a simple and useful tool for LS-PIV based applications.

Influence of the Weak Surface Film on Formation and Propagation of Wind Waves in a Channel

Processes of the wind waves formation remain poorly understood, despite the numerous studies. One of the main reasons, in our opinion, is that simplified theoretical analysis does not take into account the weak film of natural contaminants. In the present work waves generation in two channels is experimentally studied and compared for ethanol, water and water with addition of soluble surfactant SDS (sodium dodecyl sulphate) in various concentrations. The employed concentrations hardly affect the surface tension coefficient, but lead to significant modification of the subsurface flow structure. In ethanol the surface film is not formed, so it can be considered as reference case. In water and water with added surfactant the film gets broken and the surface becomes clean at certain critical wind speed, which grows for increasing surfactant concentration. For the surface to remain clean, the contaminant adsorption to the surface must be compensated by its removal by the tangential stress. Three experimental techniques are used to study the influence of cool skin on formation of the wind waves. The surface relief is measured with modified color schlieren technique and the liquid velocity fields are determined with Particle Image Velocimetry (PIV). The surface temperature fields, which allow identification of the regions of the cool skin rupture, are obtained with IR thermography. IR thermography is also used to study the surface velocity field (IR PIV). The film is shown to have significant influence on both the waves amplitude and the structure of subsurface flow.

4D-Var data assimilation and observation impact on surface transport of HF-Radar derived surface currents in the North-Western Mediterranean Sea

We investigated the effect of the assimilation of surface velocities from two HF-Radars (HFRs) and satellite sea surface temperature (SST) into an ocean circulation model, implemented on the North-Western Mediterranean Sea, using the ROMS 4D-Var Data Assimilation (DA) System. A three months period from September to November 2020 is analysed. A model free run is used as reference simulation to quantify the impact of the data assimilation procedure on the surface circulation. The DA framework consists of a sequence of 3-day windows during which the observations are assimilated into the model, followed by forecast simulations, starting from the last time step of the analysis run. The comparison of simulated velocities and SST against the assimilated observations shows that both forecast and analysis runs improve the solution as compared to the freerun, with error reduction up to the 47% and doubling of correlation values. If SST is not assimilated, the simulated sea surface temperature slightly degrades as a result of the DA procedure. Furthermore, we used surface velocities from Lagrangian drifters to test the model against independent observations. The results show that both the forecast and the analysis simulate surface circulation better than the free run within the areas covered by HFR observations, with error reduction ranging from 10% to 50%, and increase in correlation from 5% to more than doubled. Nevertheless, farther afield, outside the area covered by HFRs, improvements and degradations of the solution due to the DA procedure balance each other. The impact of assimilated observation on the alongshore transport of the upper 50 m is analysed along three transects adjacent to the two HFR areas and along a section in between. The transport increment is significant where the surface velocities are assimilated whereas it is negligible elsewhere. The effect of SST is to modify the velocity distribution along the transects, while keeping the transport increment unchanged. Modifications to the initial conditions have the most significant effect on the alongshore transport, whereas the corrections to boundary conditions and atmospheric forcing have different importance according to the analysed transects. The assimilation of surface velocities and SST affects more the ageostrophic component of the surface velocity field, rather than the geostrophic one.

Pressure increase at the magma-hydrothermal interface at Krafla caldera, North-Iceland, 2018–2020: Magmatic processes or hydrothermal changes?

Following volcano deflation since 1989, the deformation pattern in Krafla caldera, North Iceland, changed in 2018. Geodetic measurements reveal a difference in surface velocity fields for 2015–2018 and 2018–2020 periods, reflecting a change in the deformation pattern. The difference velocity field broadly fits deformation caused by a spherical pressure source within a uniform elastic half-space, with a volume change of 2.6–3.8 × 105 m3/yr and centre depth of 2.1–2.5 km, which is close to the brittle-ductile boundary in the area, at a depth of 1.8 to 2.2 km. Potential processes causing the deformation change are evaluated: magmatic processes such as magma inflow or accumulation of volcanic gas, changes in the geothermal area because of change in geothermal production, or a combination of these. In particular, we evaluate if the change in deformation may relate to about 0.1 MPa/yr pressure increase in the geothermal system as measurements in monitoring well KG-10 indicate, eventually due to changes in the geothermal exploitation strategy at the Krafla power plant. Modelling shows that inferred volume change may be due to a spherical source with 1.4 km radius with 0.1 MPa/yr pressure change if the surrounding crust has a Young's modulus E of about 7 GPa. However, the average regional Young's modulus for the upper crust in Iceland has been estimated to be 30 GPa. We use the Finite Element Method (FEM) to assess the influence on the displacement due to the presence of a local crustal volume 5 × 5 × 4 km (horizontal dimensions × depth), which envelops the source (within the Krafla caldera), with E = 7 GPa in the central area and 30 GPa in the far field, in a three-dimensional model. Such a model can reproduce significant features of the observed deformation. There are no changes in seismicity in 2018. In late 2019, the earthquake rate increases following a slight decrease over few months. The seismic moment release is relatively steady until the end of 2019, when the rate increases and is relatively constant in 2020. Gravity measurements in late 2019, when compared to limited measurements in 2018, are inconclusive regarding the nature of the deformation, but useful for further monitoring. No noticeable changes have been observed in the chemical composition of fumarole discharge in the Krafla field that relate to new intrusions.

Robust global mantle flow trajectories and their validation via dynamic topography histories

SUMMARYThe ability to construct time-trajectories of mantle flow is crucial to move from studies of instantaneous to time-dependent earth models and to exploit geological constraints for mantle convection modelling. However mantle convection is chaotic and subject to the butterfly effect: the trajectories of two identical mantle convection models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated. Because one may use seismic inferences about the mantle state as a starting or terminal condition to project mantle flow forward or backward in time, and because the seismic inference is invariably subject to uncertainties, this seemingly would rule out any construction of robust mantle flow trajectories. Here we build upon earlier work which showed that assimilation of the horizontal component of the surface velocity field from a known reference model allows one to overcome the butterfly effect and to construct robust mantle flow trajectories, regardless of the choice of the initial state perturbation. To this end, we use high resolution 3-D spherical mantle convection models in four end-member configurations: an isoviscous purely internally heated model, an isoviscous purely bottom heated model, a model with a radial increase in viscosity along with pure internal heating as well as a model that combines the effects of radial viscosity increase, internal and bottom heating. In order to capture the impact of seismic filtering, we perturb the initial temperature fields of these end-member models through either radial or horizontal smoothing of the temperature field or the application of the tomographic filter of seismic model S20RTS. We assess the quality of the constructed model trajectories via a number of statistical measures as well as comparisons of their dynamic topography histories. The latter is an essential step since mantle flow cannot be directly observed but has to be inferred via its surface manifestations. Importantly, linking mantle flow to surface observations yields patterns representable on a latitude–longitude grid similar to meteorological observables such as precipitation. This invites the application of meteorological quality metrics, such as the power ratio and Taylor diagram, to assess the quality of mantle flow trajectories. We introduce these metrics for the first time in the context of mantle convection and demonstrate their viability based on the compact manner in which they summarize model performance.