Search NASA⌕ Search

SEARCH · Search NASA

Results for “subsurface flow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Predicting Thermal Performance of an Enhanced Geothermal System From Tracer Tests in a Data Assimilation Framework

Abstract Predicting the thermal performance of an enhanced geothermal system (EGS) requires a comprehensive characterization of the underlying fracture flow patterns from practically available data such as tracer data. However, due to the inherent complexities of subsurface fractures and the generally insufficient geological/geophysical data, interpreting tracer data for fracture flow characterization and thermal prediction remains a challenging task. The present study aims to tackle the challenge by leveraging a data assimilation method to maximize the utilization of information inherently contained in tracer data, and meanwhile maintain the flexibility to handle various uncertainties. A tracer data interpretation framework was proposed with the following three components integrated: (a) We use principal component analysis (PCA) to reduce the dimensionality of model parameter space. (b) We use ES‐MDA (ensemble smoother with multiple data assimilation) to invert for fracture aperture/flow fields and obtain posterior model ensembles for uncertainty quantification. Various data types are assimilated jointly to improve the predictive ability of the posterior ensemble. (c) The inverted fracture aperture fields are then incorporated into reservoir models to predict thermal performance. We developed a field‐scale EGS model to verify the ability of the framework to characterize highly heterogeneous fracture aperture/flow fields and predicting thermal performance. We also applied the framework to a mesoscale field experiment to demonstrate its potential application in real‐world geothermal reservoirs. The results indicate that the proposed framework can effectively retrieve fracture flow information from tracer data for thermal prediction and uncertainty quantification, and thus provide informative guidance for EGS optimization and risk management.

15 GEOTHERMAL ENERGY↗

Strong temporal variability in methane fluxes from natural gas well pad soils

We measured methane and carbon dioxide fluxes at natural gas well pad soils and undisturbed soils in the Rocky Mountain and Gulf Coast regions of the United States, including producing and gas storage wells. We collected both short-term (15 min) and multi-day (between 3 and 8), continuous measurements at 47 well pads and two undisturbed locations. Methane fluxes varied by more than an order of magnitude over periods as short as 30 min (e.g., 19–593 mg m -2 h -1 in one instance), and diurnal and seasonal variability was also significant (e.g., spring-to-fall change from 509 to 14174 mg m -2 h -1 ). We hypothesize that short-term flux variability was caused by pulsed flow of methane during its migration through the subsurface. Barometric pressure and well conditions likely impacted fluxes, but we found only weak evidence for this. Bacterial methanotrophy appeared to impact methane flux magnitude and variability. We injected methane into the subsurface at one well, and we found that, while fluxes of methane and carbon dioxide, and combustible soil gas concentrations, increased in response to the injection, the response was not uniform, and fluxes exhibited high hourly-scale variability, in spite of a constant injection rate. Methane fluxes tended to be higher at well pad soils compared to background soils (often much higher), and fluxes tended to be higher at well pad locations closer to the well head.

03 NATURAL GAS↗

Operational and geological controls of coupled poroelastic stressing and pore-pressure accumulation along faults: Induced earthquakes in Pohang, South Korea

Coupled poroelastic stressing and pore-pressure accumulation along pre-existing faults in deep basement contribute to recent occurrence of seismic events at subsurface energy exploration sites. Our coupled fluid-flow and geomechanical model describes the physical processes inducing seismicity corresponding to the sequential stimulation operations in Pohang, South Korea. Simulation results show that prolonged accumulation of poroelastic energy and pore pressure along a fault can nucleate seismic events larger than M w 3 even after terminating well operations. In particular the possibility of large seismic events can be increased by multiple-well operations with alternate injection and extraction that can enhance the degree of pore-pressure diffusion and subsequent stress transfer through a rigid and low-permeability rock to the fault. This study demonstrates that the proper mechanistic model and optimal well operations need to be accounted for to mitigate unexpected seismic hazards in the presence of the site-specific uncertainty such as hidden/undetected faults and stress regime.

58 GEOSCIENCES↗

Model data for Flood Frequency Analysis using Stochastic Storm Transposition and an Integrated Surface-Subsurface Hydrological Model

This archived provides scripts and input files used for the implementation of a novel approach to conduct process-based Flood Frequency Analysis using a Stochastic Storm Transposition (SST) and an Integrated Surface-Subsurface Hydrological Model (ISSHM). As a proof-of-concept, this study uses the ISSHM, Advanced Terrestrial Simulator (Amanzi-ATS) model, and the SST model, RainyDay, to conduct flood frequency analysis by simulating the flood response to 5,000 annual synthetic storm events in a ~2000 km2 Southeast Texas watershed.The Watershed Workflow package is implemented in Python3. The Jupyter notebooks can be executed through multiple open-source tools, for example, Anaconda Jupyter Lab, VS Studio Code, etc. Other data files include TXT, CSV, DAT, SBATCH, SHP, TIF, NetCDF, and HDF5 files, which can be read through Python scripts. The input files for the ATS model and RainyDay model have .XML and .SST extensions, respectively, and can be edited in any commonly used text editors.This archive contains:* Scripts and data files essential for generating the ATS model input. It uses the Watershed Workflow package to produce both mesh and ATS input files. * Jupyter notebooks designated for the ATS model evaluation, covering both long-term simulations and 40 rainfall-runoff events.* Input files required to simulate SST storm events using RainyDay.

54 ENVIRONMENTAL SCIENCES↗

Experimental forecasts of El Nino

A deterministic numerical model of the coupled evolution of the tropical ocean and atmosphere was used to forecast all El Nino/Southern Oscillation (ENSO) events from 1970 to 1986. More particularly, the model, originally developed for studying large-scale ocean-atmosphere interactions in the tropics, successfully predicted the characteristics of the spatial and temporal structure of ENSO observed in the study interval. The model indicated that rainfall moving eastward over the Pacific slackens the surface winds that would otherwise cool the eastern Pacific by drawing up cooler subsurface waters. The oceanic thermocline increases, a poleward flow of westerly flowing warn waters deplets the equatorial warm water reservoir, and sea surface temperatures decline. These ENSO conditions are statistically tractable with the model several months in advance, provided upper ocean layer thermal data are available.

Cane, M. A.↗

Time-Distance Helioseismology

Time-distance helioseismology is a method of ambient noise imaging using the solar oscillations. The basic realization that led to time-distance helioseismology was that the temporal cross correlation of the signals at two 'surface' (or photospheric) locations should show a feature at the time lag corresponding to the subsurface travel time between the locations. The temporal cross correlation, as a function of the location separation, is the Fourier transform of the spatio-temporal power spectrum of the solar oscillations, a commonly used function in helioseismology. It is therefore likely the characteristic ridge structure of the correlation function had been seen before without appreciation of its significance. Travel times are measured from the cross correlations. The times are sensitive to a number of important subsurface solar phenomena. These include sound speed variations, flows, and magnetic fields. There has been much interesting progress in the 17 years since the first paper on this subject (Duvall et al., Nature, 1993, 362, 430-432). This progress will be reviewed in this paper.

Duvall, Thomas L., Jr.↗

Emplacement of Volcanic Domes on Venus and Europa

Placing firmer constraints on the emplacement timescales of visible volcanic features is essential to obtaining a better understanding of the resurfacing history of Venus. Fig. 1 shows a Magellan radar image and topography for a putative venusian lava dome. 175 such domes have been identified, having diameters that range from 19 - 94 km, and estimated thicknesses as great as 4 km [1-2]. These domes are thought to be volcanic in origin [3], having formed by the flow of a viscous fluid (i.e., lava) onto the surface. Among the unanswered questions surrounding the formation of Venus steep-sided domes are their emplacement duration, composition, and the rheology of the lava. Rheologically speaking, maintenance of extremely thick, 1-4 km flows necessitates higher viscosity lavas, while the domes' smooth upper surfaces imply the presence of lower viscosity lavas [2-3]. Further, numerous quantitative issues, such as the nature and duration of lava supply, how long the conduit remained open and capable of supplying lava, the volumetric flow rate, and the role of rigid crust in influencing flow and final morphology all have implications for subsurface magma ascent and local surface stress conditions. The surface of Jupiter's icy moon Europa exhibits many putative cryovolcanic constructs [5-7], and previous workers have suggested that domical positive relief features imaged by the Galileo spacecraft may be volcanic in origin [5,7-8] (Fig. 2). Though often smaller than Venus domes, if emplaced as a viscous fluid, formation mechanisms for europan domes may be similar to those of venusian domes [7]. Models for the emplacement of venusian lava domes (e.g. [9-10]) have been previously applied to the formation of putative cryolava domes on Europa [7].

timescales↗

Cryogenic Fluid In-Situ Liquefaction for Landers: Prototype Demonstration

As the advancement of In-Situ Resource Utilization concepts and systems continue to develop, applicable technology development and maturation continues in parallel. While there are many different ways to use the resources found on other bodies, one of the most prevalent suggested applications is the manufacturing of propellants. One of the key technologies for the eventual use of these propellant production based ISRU systems is the liquefaction and storage of the produced propellants. The most mentioned propellant combinations include oxygen-hydrogen and oxygen-methane. The liquefaction of oxygen in these systems will be different than oxygen liquefaction systems on Earth, which mainly revolves around the distillation of air. These systems have been developed conceptually and many of the components have been previously tested or are in development. However, the need to demonstrate the system level operations still exists. The demonstration of a prototypical oxygen liquefaction system using tube-on-tank broad area cooling was completed to better understanding system level operations during liquefaction activities. Demonstration testing included system performance determination, constant liquefaction demonstrations, and transient liquefaction demonstrations. The demonstrations showed the operational capabilities of the tube-on-tank system with an integrated cryocooler. Additional testing explored subsurface vs ullage introduction of the gaseous oxygen flow stream as well as demonstrating a novel fiber optic sensor that measured the temperature gradients along the fluid center line within the tank.

ISRU↗

Cryogenic Fluid In-Situ Liquefaction for Landers: Prototype Demonstration

As the advancement of In-Situ Resource Utilization concepts and systems continue to develop, applicable technology development and maturation continues in parallel. While there are many different ways to use the resources found on other bodies, one of the most prevalent suggested applications is the manufacturing of propellants. One of the key technologies for the eventual use of these propellant production based ISRU systems is the liquefaction and storage of the produced propellants. The most mentioned propellant combinations include oxygen-hydrogen and oxygen-methane. The liquefaction of oxygen in these systems will be different than that on Earth, which mainly revolves around the distillation of air. These systems have been developed conceptually and many of the components have been previously tested or are in development. However, the need to demonstrate the system level operations still exists. The demonstration of a prototypical oxygen liquefaction system using tube-on-tank broad area cooling was completed to better understanding system level operations during liquefaction activities. Demonstration testing included system performance determination, constant liquefaction demonstrations, and transient liquefaction demonstrations. The demonstrations showed the operational capabilities of the tube-on-tank system with an integrated cryocooler. Additional testing explored subsurface vs ullage introduction of the gaseous oxygen flow stream as well as demonstrating a novel fiber optic sensor that measured the temperature gradients along the fluid center line within the tank.

ISRU↗

Cryogenic Fluid In-Situ Liquefaction for Landers: Prototype Demonstration

As the advancement of In-Situ Resource Utilization concepts and systems continue to develop, applicable technology development and maturation continues in parallel. While there are many different ways to use the resources found on other bodies, one of the most prevalent suggested applications is the manufacturing of propellants. One of the key technologies for the eventual use of these propellant production based ISRU systems is the liquefaction and storage of the produced propellants. The most mentioned propellant combinations include oxygen-hydrogen and oxygen-methane. The liquefaction of oxygen in these systems will be different than oxygen liquefaction systems on Earth, which mainly revolves around the distillation of air. These systems have been developed conceptually and many of the components have been previously tested or are in development. However, the need to demonstrate the system level operations still exists. The demonstration of a prototypical oxygen liquefaction system using tube-on-tank broad area cooling was completed to better understanding system level operations during liquefaction activities. Demonstration testing included system performance determination, constant liquefaction demonstrations, and transient liquefaction demonstrations. The demonstrations showed the operational capabilities of the tube-on-tank system with an integrated cryocooler. Additional testing explored subsurface vs ullage introduction of the gaseous oxygen flow stream as well as demonstrating a novel fiber optic sensor that measured the temperature gradients along the fluid center line within the tank.

ISRU↗

Advancing process-based flood frequency analysis for assessing flood hazard and population flood exposure

Recent studies have showcased the use of process-based hydrological models with Stochastic Storm Transposition (SST) techniques to conduct Flood Frequency Analysis (FFA). This framework, referred hereby FFA-SST, has proved to be a robust strategy to estimate peak flows of specific annual exceedance probability (e.g., 100-year peak flow) that can reflect natural and anthropogenic disturbances, including changes in land use and meteorological patterns. With the objective of advancing the FFA-SST framework, this study presents for the first time the use of an Integrated Surface-Subsurface Hydrological Model (ISSHM) to conduct FFA-SST by extending the analysis from peak flow responses to flood extent, enabling a unique view and analysis of flood hazard and population flood exposure at the basin scale. As a proof-of-concept, we used the ISSHM, Advanced Terrestrial Simulator (Amanzi-ATS) model, and the SST model, RainyDay, to conduct FFA-SST by simulating the flood response to 5,000 annual synthetic storm events in a 2,227 $km^2$ Southeast Texas watershed. We demonstrate that ATS, without site-specific calibration, provides a robust process-based representation of peak flows, flood extent, streamflow, evapotranspiration, soil moisture content, and water storage changes. Our results and analyses, covering frequency curves up to a 500-year return period for peak flows, basin inundation fractions, and the number of people exposed to flooding, offer a unique perspective to analyze flood impacts across spatial scales. Overall, this study provides critical insights for flood risk management by extending the FFA-SST framework to include both flood hazard and population flood exposure analyses at the basin scale. Such an approach will empower stakeholders and disaster emergency agencies with a more comprehensive understanding of flood impacts across the entire basin domain, facilitating informed decision-making for flood risk assessment and management.

58 GEOSCIENCES↗

The Nature of Martian Flow Ejecta Craters

Ejecta with flow features and discrete termini surround many fresh Martian craters. Several morphologies of the flow-like ejecta are observed; they are found globally and in nearly all terrains. It is suggested that the morphology of flow ejecta craters is related to the amount of subsurface volatiles and/or to atmospheric drag effects. It was attempted to constrain factors which could contribute to the ejecta morphology such as latitude, elevation, and terrain unit, however, they involved only one or two constrained variables or used global data sets based on Mariner 9 information. Viking-based data sets are becoming available and may provide a better base from which an understanding of the factors which governs ejecta morphology may be obtained. Block sizes of Martian flow ejecta may provide clues to the ejecta emplacement process.

Horner, V. M.↗

Evaluating integrated surface/subsurface permafrost thermal hydrology models in ATS (v0.88) against observations from a polygonal tundra site

Numerical simulations are essential tools for understanding the complex hydrologic response of Arctic regions to a warming climate. However, strong coupling among thermal and hydrological processes on the surface and in the subsurface and the significant role that subtle variations in surface topography have in regulating flow direction and surface storage lead to significant uncertainties. Careful model evaluation against field observations is thus important to build confidence.We evaluate the integrated surface/subsurface permafrost thermal hydrology models in the Advanced Terrestrial Simulator (ATS) against field observations from polygonal tundra at the Barrow Environmental Observatory. ATS couples a multiphase, 3D representation of subsurface thermal hydrology with representations of overland nonisothermal flows, snow processes, and surface energy balance. We simulated thermal hydrology of a 3D ice-wedge polygon with geometry that is abstracted but broadly consistent with the surface microtopography at our study site. The simulations were forced by meteorological data and observed water table elevations in ice-wedge polygon troughs. With limited calibration of parameters appearing in the soil evaporation model, the 3-year simulations agreed reasonably well with snow depth, summer water table elevations in the polygon center, and high-frequency soil temperature measurements at several depths in the trough, rim, and center of the polygon. Upscaled evaporation is in good agreement with flux tower observations. The simulations were found to be sensitive to parameters in the bare soil evaporation model, snowpack, and the lateral saturated hydraulic conductivity.Timing of fall freeze-up was found to be sensitive to initial snow density, illustrating the importance of including snow aging effects. The study provides new support for an emerging class of integrated surface/subsurface permafrost simulators.

54 ENVIRONMENTAL SCIENCES↗

Stratigraphic Identification with Airborne Electromagnetic Methods at the Hanford Site, Washington

Stratigraphic units can influence the fate and transport of subsurface contaminants within groundwater. Units having coarse-grained sediments act as preferential flow pathways, and therefore can accelerate the transport of contaminants to reach human and ecological receptors. At legacy waste sites, detailed knowledge of subsurface stratigraphy can be used for effective monitoring and remediation planning to help minimize risk to human health and the environment. Airborne electromagnetic (AEM) methods can non-invasively provide information on kilometer-scale or larger subsurface stratigraphic features and fill informational gaps in directly sampled data from sparsely located boreholes. In this paper, we present inversion results of a 412 line-km frequency-domain AEM survey to delineate subsurface stratigraphic features at the Hanford Site, located in southeastern Washington State. The inversion was performed using a massively parallel 3D electromagnetic modeling and inversion code, where the modeling is based on solving frequency-domain Maxwell’s equations using an unstructured-mesh finite-element method and the inversion employs a Gauss-Newton optimization scheme. The results are compared to an underlying geologic framework model (GFM), built by interpolating contact depths of stratigraphic units interpreted from site borehole datasets. In areas with good borehole coverage, the inversion results show a good match with the GFM to a depth of about 60 m. Outside of these areas, the inversion results exhibit inconsistencies from the assumptions made to create the GFM, demonstrating that the AEM survey results can be used to improve the understanding of the geological conceptual model.

47 OTHER INSTRUMENTATION↗

Idaho National Laboratory Integrated Multisite SSHAC Level 3: Probabilistic Volcanic Hazards Assessment

The Idaho National Laboratory (INL) resides on the eastern Snake River Plain (ESRP), part of the Snake River Plain (SRP) with a complex origin and geologic history of volcanism. Much of the Quaternary (last 2.58 million years) volcanism within 400 km of INL is genetically associated with a major thermal anomaly referred to as the Yellowstone hotspot, which is currently located more than 180 km northeast of INL. Near INL, local volcanic sources include silicic domes near its southern border, and numerous dike-fed basaltic vents of the ESRP, some of which are near or within the INL boundaries. Quantitative probabilistic assessments of screened-in volcanic hazardous phenomena for nine different facility complexes at the INL are presented for a Senior Seismic Hazard Analysis Committee (SSHAC) Level 3 (SL3) study. The comprehensive, integrated multisite SSHAC study consists of a single regional Probabilistic Volcanic Hazards Assessment (PVHA) that pertains to all nine INL facility complexes, with site-specific information developed at each respective area of interest (AOI), referred to as the "INL facility AOI" (Figure ES-1). Hazard products are generated for specified INL facility AOIs for use by multiple stakeholders from different agencies in risk-informed decision-making regarding site selection, operations, and design of nuclear facilities at INL, consistent with U.S. Department of Energy (DOE) and U.S. Nuclear Regulatory Commission (NRC) regulatory guidance. The study also serves as the basis for future periodic safety assessments required for existing DOE facilities, such as 10-year evaluations of natural-phenomena hazards. Elements of the INL PVHA including initial characterization, screening, quantitative assessments of eruption and hazard potential, and consideration of facility needs are conducted using the three phases of the SSHAC process: evaluation, integration, and documentation. As per regulatory guidance, the SSHAC framework provided the necessary processes and procedures for the PVHA Technical Integration (TI) team, at three workshops, five formal working meetings and many TI team remote meetings, to conduct initial characterization, screen the volcanic hazards, create PVHA model inputs, exercise those models in the PVHA, consider facility-specific volcanic hazard needs, and perform final hazard calculations. The Participatory Peer Review Panel (PPRP) provided independent oversight and performed process and technical reviews of the PVHA throughout its duration. The study included an extensive New Data Collection and Analyses (NDCA) program developed by the PVHA TI team to reduce uncertainties in hazard-significant elements in the PVHA model. NDCA activities generated 20 reports providing important contributory datasets and results to the project database for characterizing the ESRP. For example, a report compiling the dimensions of ESRP shield volcanoes and lava fields was used to construct volcanic footprints (areas of impact), was compared with data from INL subsurface cores, and was used to validate the results of lava-flow inundation modeling on the contemporary terrain. Another example is the acquisition of aeromagnetic data over INL and its surrounding area, with maps of buried magmatic features (e.g., subsurface volcanoes and swarms of feeder dikes) that informed the PVHA conceptual model of volcanism. The SSHAC evaluation process was used to conduct all elements of the PVHA including initial characterization and screening. Existing data and NDCA activities provided the foundation to develop the tectonomagmatic conceptual model of volcanism for the region of geographical interest in the SRP and Yellowstone hotspot volcanic system, and for considering volcanoes in the western US. Considering Quaternary volcanic sources active during this period, the screening approach identified and evaluated magma compositions, types of eruptive and intrusive phenomena, types of hazardous phenomena, and proximity of sources to INL. The PVHA TI team evaluated 18 types of magmatic sources in terms of 20 potentially hazardous phenomena, resulting in 360 screening decisions. The screening process resulted in 140 screened-in hazardous volcanic phenomena for Quaternary volcanic sources 1) proximal to INL facility complexes in the ESRP (64 basaltic and 54 silicic), 2) regional sources associated with the Yellowstone caldera system and Blackfoot Reservoir volcanic field (7), and 3) more distal sources from thirteen Cascade volcanoes and two volcanoes at Long Valley caldera (CA).

58 GEOSCIENCES↗

Quantification of the Impact of Acidified Brine on Fracture-Matrix Transport in a Naturally Fractured Shale Using in Situ Imaging and Modeling

Understanding flow, transport, chemical reactions, and hydromechanical processes in fractured geologic materials is key for optimizing a range of subsurface processes including carbon dioxide and hydrogen storage, unconventional energy resource extraction, and geothermal energy recovery. Flow and transport processes in naturally fractured shale rocks have been challenging to characterize due to experimental complexity and the multiscale nature of quantifying continuum scale descriptions of mass exchange between micrometer-scale fractures and nanometer-scale pores. In this study, we use positron emission tomography (PET) to image the transport of a conservative tracer in a naturally fractured Wolfcamp shale core before and after the core was exposed to low pH brine conditions. Image-based experimental observations are interpreted by fitting an analytical transport model to fracture-containing voxels in the core. Results of this analysis indicate subtle increases in matrix diffusivity and a slightly more uniform fracture velocity distribution following exposure to low pH conditions. These observations are compared with a multicomponent one-dimensional reactive transport model that indicates the capacity for a 10% increase in porosity at the fracture-matrix interface as a result of the low pH brine exposure. This porosity change is the result of the dissolution of carbonate minerals in the shale matrix to low pH conditions. Further, this image-based workflow represents a new approach for quantifying spatially resolved fracture-matrix transport processes and provides a foundation for future work to better understand the role of coupled transport, reaction, and mechanical processes in naturally fractured rocks.

58 GEOSCIENCES↗

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗