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At least 433 records · Page 24

ORCHA: A performance portability system for extreme heterogeneity

Heterogeneity is the prevalent trend in the rapidly evolving high-performance computing (HPC) landscape in both hardware and application software. The diversity in hardware platforms, currently comprising various accelerators and a future possibility of specializable chiplets, poses a significant challenge for scientific software developers aiming to harness optimal performance across different computing platforms while maintaining the quality of solutions when their applications are simultaneously growing more complex. Code synthesis and code generation can provide mechanisms to mitigate this challenge. We have developed a divide and conquer approach where different aspects of performance are handled by different stand-alone tools that are interfaced with the application through generated code. This portability system, ORCHA, enables users to configure and orchestrate their computations among available resources on a platform by specifying a high-level recipe, thereby permitting a many-to-many paradigm where each recipe results in a different variant of the application. The core design goal is to let users decide the application’s hardware mapping and orchestration by editing only the high-level recipe—without modifying the maintained source code or binding the application to a particular runtime system. Tools in ORCHA distribution are: CG-Kit for translating the recipe into an execution graph; Milhoja to execute the graph by orchestrating data and task movement among hardware resources; and Macroprocessor that enables users to define their own code-shorthand for higher composability and easier management of code variants. Additionally, the design of ORCHA permits tools to work in a plug-and-play mode where the application can build and run without CG-Kit and Milhoja, and either tool can be swapped out for other tools with similar capabilities by modifying the code generation portion of ORCHA. In this paper, we describe the design of ORCHA and the role that code-generation plays in isolating applications from tools. We demonstrate the breadth of configurations ORCHA enables with a case study in which an application configuration is realized on three distinct hardware mappings—a GPU-centric, a CPU/GPU balanced, and a CPU/GPU concurrent layouts by using different recipes.

Lee, Youngjun↗

SSME Condition Monitoring Using Neural Networks and Plume Spectral Signatures

For a variety of reasons, condition monitoring of the Space Shuttle Main Engine (SSME) has become an important concern for both ground tests and in-flight operation. The complexities of the SSME suggest that active, real-time condition monitoring should be performed to avoid large-scale or catastrophic failure of the engine. In 1986, the SSME became the subject of a plume emission spectroscopy project at NASA's Marshall Space Flight Center (MSFC). Since then, plume emission spectroscopy has recorded many nominal tests and the qualitative spectral features of the SSME plume are now well established. Significant discoveries made with both wide-band and narrow-band plume emission spectroscopy systems led MSFC to develop the Optical Plume Anomaly Detection (OPAD) system. The OPAD system is designed to provide condition monitoring of the SSME during ground-level testing. The operational health of the engine is achieved through the acquisition of spectrally resolved plume emissions and the subsequent identification of abnormal emission levels in the plume indicative of engine erosion or component failure. Eventually, OPAD, or a derivative of the technology, could find its way on to an actual space vehicle and provide in-flight engine condition monitoring. This technology step, however, will require miniaturized hardware capable of processing plume spectral data in real-time. An objective of OPAD condition monitoring is to determine how much of an element is present in the SSME plume. The basic premise is that by knowing the element and its concentration, this could be related back to the health of components within the engine. For example, an abnormal amount of silver in the plume might signify increased wear or deterioration of a particular bearing in the engine. Once an anomaly is identified, the engine could be shut down before catastrophic failure occurs. Currently, element concentrations in the plume are determined iteratively with the help of a non-linear computer code called SPECTRA, developed at the USAF Arnold Engineering Development Center. Ostensibly, the code produces intensity versus wavelength plots (i.e., spectra) when inputs such as element concentrations, reaction temperature, and reaction pressure are provided. However, in order to provide a higher-level analysis, element concentration is not specified explicitly as an input. Instead, two quantum variables, number density and broadening parameter, are used. Past experience with OPAD data analysis has revealed that the region of primary interest in any SSME plume spectrum lies in the wavelength band of 3300 A to 4330 A. Experience has also revealed that some elements, such as iron, cobalt and nickel, cause multiple peaks over the chosen wavelength range whereas other elements (magnesium, for example) have a few, relatively isolated peaks in the chosen wavelength range. Iteration with SPECTRA as a part of OPAD data analysis is an incredibly labor intensive task and not one to be performed by hand. What is really needed is the "inverse" of the computer code but the mathematical model for the inverse mapping is tenuous at best. However, building generalized models based upon known input/output mappings while ignoring details of the governing physical model is possible using neural networks. Thus the objective of the research project described herein was to quickly and accurately predict combustion temperature and element concentrations (i.e., number density and broadening parameter) from a given spectrum using a neural network. In other words, a neural network had to be developed that would provide a generalized "inverse" of the computer code SPECTRA.

Hopkins, Randall↗

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗

Dynamic and Responsive Distributed Energy Resource Education Solutions for Building, Fire, and Safety Department Officials (Final Technical Report)

From April 2021 through March 2024, the Interstate Renewable Energy Council (IREC) led a collaborative project to develop a free online clearinghouse of educational resources about solar photovoltaics (PV), energy storage systems (ESS), electric vehicle supply equipment (EVSE), and grid-interactive efficient building (GEB) technologies. Two websites—the Clean Energy Clearinghouse and CleanEnergyTraining.org—housed over 70 educational resources. Over the course of the three-year project, 154,272 unique visitors accessed the learning materials. Learner feedback was overwhelmingly positive. Even through the end of the project, there was sustained demand for education and communication. A primary innovation of the project was to drive multiple complementary audiences to the same place. Building owners, designers, installation contractors and developers, authorities having jurisdiction (AHJs), and fire service personnel all benefit from a shared understanding of clean energy technologies, including safety and code-related requirements. When considering the impact on the target audience, the project team worked with partners and advisors to inform resource creation and delivery in such a way as to address key motivational factors of the target audience and compel each user to seek additional information on the topic and return to the Clean Energy Clearinghouse website as their central location for more information. Resources were intentionally developed to be concise—five to 15 minutes—and accessible, meaning not overly technical. Providing basic information demystified the technologies and invited the professional to explore additional learning opportunities. Awardee and partner collaboration was key to project success. IREC facilitated collaboration among the other Topic 2 awardees, Southface and New Buildings Institute (NBI). The three awardees shared relevant information gained through discovery and validation questionnaires that informed product development and reduced duplication of effort by coordinating the development of complementary, and not competing, educational resources. Inspired by this collaboration, IREC brought on additional partners even in the final year of the project. Five regional energy efficiency organizations were part of the project, which expanded the connection between efficiency and distributed energy resources. We also included resources on the Clearinghouse that were developed through other federally funded projects, such as the Buildings Energy Efficiency Frontiers & Innovation Technologies (BENEFIT) program. The website was developed with the learner in mind, and not solely the funding source. Feedback from stakeholders throughout the project, and especially in its final year, indicated the need for continued education and facilitated communication among stakeholders to further the safe and widespread adoption of clean energy.

14 SOLAR ENERGY↗

Cascaded Control for Building HVAC Systems in Practice

Actuator hunting is a widespread and often neglected problem in the HVAC field. Hunting is typically characterized by sustained or intermittent oscillations, and can result in decreased efficiency, increased actuator wear, and poor setpoint tracking. Cascaded control loops have been shown to effectively linearize system dynamics and reduce the prevalence of hunting. This paper details the implementation of cascaded control architectures for Air Handling Unit chilled water valves at three university campus buildings. A framework for implementation the control in existing Building Automation software is developed that requires only a single line of additional code. Results gathered for more than a year show that cascaded control not only eliminates hunting in control loops with documented hunting issues, but provides better tracking and more consistent performance during all seasons. A discussion of efficiency losses due to hunting behavior is presented and illustrated with comparative data. Furthermore, an analysis of cost savings from implementing cascaded chilled water valve control is presented. Field tests show 2.2–4.4% energy savings, with additional potential savings from reduced operational costs (i.e., maintenance and controller retuning).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Characterization of Surface Reflectance Variation Effects on Remote Sensing

The use of Monte Carlo radiative transfer codes to simulate the effects on remote sensing in visible and infrared wavelengths of variables which affect classification is examined. These variables include detector viewing angle, atmospheric aerosol size distribution, aerosol vertical and horizontal distribution (e.g., finite clouds), the form of the bidirectional ground reflectance function, and horizontal variability of reflectance type and reflectivity (albedo). These simulations are used to characterize the sensitivity of observables (intensity and polarization) to variations in the underlying physical parameters both to improve algorithms for the removal of atmospheric effects and to identify techniques which can improve classification accuracy. It was necessary to revise and validate the simulation codes (CTRANS, ARTRAN, and the Mie scattering code) to improve efficiency and accommodate a new operational environment, and to build the basic software tools for acquisition and off-line manipulation of simulation results. Initial calculations compare cases in which increasing amounts of aerosol are shifted into the stratosphere, maintaining a constant optical depth. In the case of moderate aerosol optical depth, the effect on the spread function is to scale it linearly as would be expected from a single scattering model. Varying the viewing angle appears to provide the same qualitative effect as modifying the vertical optical depth (for Lambertian ground reflectance).

Pearce, W. A.↗

Three-dimensional object recognition using similar triangles and decision trees

A system, TRIDEC, that is capable of distinguishing between a set of objects despite changes in the objects' positions in the input field, their size, or their rotational orientation in 3D space is described. TRIDEC combines very simple yet effective features with the classification capabilities of inductive decision tree methods. The feature vector is a list of all similar triangles defined by connecting all combinations of three pixels in a coarse coded 127 x 127 pixel input field. The classification is accomplished by building a decision tree using the information provided from a limited number of translated, scaled, and rotated samples. Simulation results are presented which show that TRIDEC achieves 94 percent recognition accuracy in the 2D invariant object recognition domain and 98 percent recognition accuracy in the 3D invariant object recognition domain after training on only a small sample of transformed views of the objects.

Spirkovska, Lilly↗

Design, Development and Pre-Flight Testing of the Communications, Navigation, and Networking Reconfigurable Testbed (Connect) to Investigate Software Defined Radio Architecture on the International Space Station

The Communication Navigation and Networking Reconfigurable Testbed (CoNNeCT) is a NASA-sponsored mission, which will investigate the usage of Software Defined Radios (SDRs) as a multi-function communication system for space missions. A softwaredefined radio system is a communication system in which typical components of the system (e.g., modulators) are incorporated into software. The software-defined capability allows flexibility and experimentation in different modulation, coding and other parameters to understand their effects on performance. This flexibility builds inherent redundancy and flexibility into the system for improved operational efficiency, real-time changes to space missions and enhanced reliability/redundancy. The CoNNeCT Project is a collaboration between industrial radio providers and NASA. The industrial radio providers are providing the SDRs and NASA is designing, building and testing the entire flight system. The flight system will be integrated on the Express Logistics Carrier (ELC) on the International Space Station (ISS) after launch on the H-IIB Transfer Vehicle in 2012. This paper provides an overview of the technology research objectives, payload description, design challenges and pre-flight testing results.

Over, Ann P.↗

Evaluation of Novel Liner Concepts for Fan and Airframe Noise Reduction

This paper presents a review of four novel liner concepts: soft vanes, over-the-rotor liners, external liners, and flap side-edge liners. A number of similarities in the design and evaluation of these concepts emerged during these investigations. Since these were the first attempts to study these particular liner concepts, there was limited information to guide the design process. In all cases, the target frequencies (or frequency range) were known, but the optimum acoustic impedance and optimum liner placement were typically not known. For these cases, the maximum available surface was used and a c-impedance was targeted based on the assumption the sound field impinges on the surface at normal incidence. This choice proved fruitful for every application. An impedance prediction model was used to design variable-depth liner configurations, and a graphical design code (ILIAD) was developed to aid in this process. The ability to build increasingly complex liner configurations via additive manufacturing was key, such that multiple designs could quickly be tested in a normal incidence impedance tube. The Two-Thickness Method was used to evaluate available bulk materials, such that bulk liners could also be considered for each application. These novel liner concepts provide sufficient noise reduction to warrant further investigations.

Jones, M. G.↗

Feasibility of Varying Geo-Fence Around an Unmanned Aircraft Operation Based on Vehicle Performance and Wind

Managing trajectory separation is critical to ensuring accessibility, efficiency, and safety in the unmanned airspace. The notion of geo-fences is an emerging concept, where distance buffers enclose individual trajectories and areas of operation in order to manage the airspace. Currently, the Air Traffic Management system for commercial travel defines static distance buffers around the aircraft; however, commercial UASs are envisioned to operate in significantly closer proximity to other UAS requiring a geo-fence for spacing operations. The geo-fence size can be determined based on vehicle performance characteristics, state of the airspace, weather, and other unforeseen events such as emergency or disaster response. Calculation of the geo-fence size could be determined as part of pre-flight planning and during real-time operations. A largely non-homogeneous fleet of UASs will be operating in low altitude and will likely be commercially developed. Due to intellectual property concerns, the operators may not provide detailed specifications of the control system to UTM. In addition, the huge variety of UAS makes modeling each control system prohibitive and flight data for these vehicles may not exist. Therefore, a generalized, simple geo-fence sizing algorithm must be developed such that it does not rely on detailed knowledge of the vehicle control system, accounts for the presence of urban winds, and is sufficiently accurate. In this work, two simple models are investigated to determine its feasibility as an adequate means for calculating the geo-fence size. The vehicle data used in this work are provided by UAS manufactures who have partnered with NASA's UTM project and some publicly available websites. The first model utilizes wind data processed from the NOAA HRRR (Hourly Rapid Refresh) product and Sonar Annemometer data provided by San Jose State. The second model utilizes OpenFOAM which is a CFD code used to generate a wind field for flow around a single building. The key vehicle performance parameters can include UAS response time to disturbances, command to actuation latency, control system rate limits, time to recovery to desired path, and aerodynamics. It was found that the first model provides an initial understanding of geo-fence sizing, but does not provide enough accuracy to provide UTM with an efficient means of scheduling vehicles. The results of the second model reveal that modeling UAS controls systems with a linearized plant and gain scheduled PID controller does not allow capture the UAS flight dynamics within a significant envelope of the wind disturbances.

uncertainty↗

Microstructure & Mechanical Properties of Scaled Thermally Aged LPBF 316H SS Builds

As part of the US Department of Energy’s Advanced Materials and Manufacturing Technologies program’s mission to accelerate qualification of advanced manufacturing pathways for nuclear applications, laser powder bed fusion (LPBF) 316H stainless steel (SS) has been selected as a model system to develop a rapid code case framework. This effort directly addresses the grand challenges of (1)expanding the limited portfolio of materials currently codified for elevated-temperature nuclear structural service under Section III, Division 5of the American Society of Mechanical Engineers’ Boiler and Pressure Vessel Code; and (2) significantly reducing qualification timelines that traditionally exceed a decade. The strategic importance of LPBF 316H lies in its immediate industrial relevance, existing data foundation from wrought 316H, and alignment with ongoing code case development for LPBF 316L.Prior work revealed accelerated precipitation of deleterious secondary phases and reduced creep ductility in as-printed LPBF 316H. Building on that prior research, FY2025activities focused on establishing an understanding of the key failure mechanisms of crept 316H specimens to aid in code case development and on evaluating stress relief (SR) parameters on the high-temperature performance and thermal aging-induced degradation of tensile and fracture behavior in LPBF316H.

36 MATERIALS SCIENCE↗

Community-scale interaction of energy efficiency and demand flexibility in residential buildings

Demand-side management (DSM) strategies, including energy efficiency (EE) and demand flexibility (DF), contribute to cost-effective operation of the electricity grid. From a system-level perspective, such programs reduce costs, enhance reliability, and reduce network issues. Similarly, DSM programs help participating customers reduce utility bills while maintaining occupant comfort. Understanding the relationship between EE and DF is key to realizing the full potential of DSM programs. In this study, we modeled an all-electric residential community based on a 498-home community that is planned for construction in Fort Collins, Colorado in the United States. We used this community model to study the relationship between different EE measures, including building envelope upgrades and smart appliances, and DF enabled by a home energy management system (HEMS) responding to a time-varying tariff. Various EE levels in the homes – code-minimum, zero energy ready, and even higher levels of envelope efficiency – were simulated. DF is enabled by the HEMS, which coordinates behind-the-meter resources, including flexible building loads, PV, and home battery systems, to minimize utility bills while maintaining occupant comfort. When comparing to the code-minimum homes, EE upgrades alone reduce HVAC energy use during peak hours by up to 50% and the HVAC utility bill by up to $312/year. With the addition of HEMS, the average daily peak demand can be reduced by up to 0.58 MW or 1.2 kW/home in the higher envelope efficiency homes. The combination of EE upgrades, HEMS, and home battery systems is expected to save homeowners up to $590/year while increasing community load flexibility. However, HEMS and home battery systems are less effective in increasing the DF in the more efficient homes due to the lower load.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Microstructure and Mechanical Properties of Scaled Thermally Aged LPBF 316H SS Builds

As part of the US Department of Energy’s Advanced Materials and Manufacturing Technologies program’s mission to accelerate qualification of advanced manufacturing pathways for nuclear applications, laser powder bed fusion (LPBF) 316H stainless steel (SS) has been selected as a model system to develop a rapid code case framework. This effort directly addresses the grand challenges of (1) expanding the limited portfolio of materials currently codified for elevated-temperature nuclear structural service under Section III, Division 5 of the American Society of Mechanical Engineers’ Boiler and Pressure Vessel Code; and (2) significantly reducing qualification timelines that traditionally exceed a decade. The strategic importance of LPBF 316H lies in its immediate industrial relevance, existing data foundation from wrought 316H, and alignment with ongoing code case development for LPBF 316L. Prior work revealed accelerated precipitation of deleterious secondary phases and reduced creep ductility in as-printed LPBF 316H. Building on that prior research, FY 2025 activities focused on establishing an understanding of the key failure mechanisms of crept 316H specimens to aid in code case development and on evaluating stress relief (SR) parameters on the high-temperature performance and thermal aging induced degradation of tensile and fracture behavior in LPBF 316H.

36 MATERIALS SCIENCE↗

JAE: A Jupiter Atmospheric Entry Probe Heating Code

The strong gravitational attraction of Jupiter on probes approaching the planet results in very high atmospheric entry velocities. The values relative to the rotating atmosphere can vary from about 47 to 60 km/sec, depending on the latitude of the entry. Therefore, the peak heating rates and heat shield mass fractions exceed those for any other atmospheric entries. For example, the Galileo probe's heat shield mass fraction was 50%, of which 45% was devoted to the forebody. Although the Galileo probe's mission was very successful, many more scientific questions about the Jovian atmosphere remain to be answered and additional probe missions are being planned. Recent developments in microelectronics have raised the possibility of building smaller and less expensive probes than Galileo. Therefore, it was desirable to develop a code that could quickly compute the forebody entry heating environments when performing parametric probe sizing studies. The Jupiter Atmospheric Entry (JAE) code was developed to meet this requirement. The body geometry consists of a blunt-nosed conical shape of arbitrary nose and base radius and cone angles up to about 65 deg at zero angle of attack.

Wercinski, Paul F.↗

Build-up Approach to Updating the Mock Quiet Spike(TM)Beam Model

A crucial part of aircraft design is ensuring that the required margin for flutter is satisfied. A trustworthy flutter analysis, which begins by possessing an accurate dynamics model, is necessary for this task. Traditionally, a model was updated manually by fine tuning specific stiffness parameters until the analytical results matched test data. This is a time consuming iterative process. The NASA Dryden Flight Research Center has developed a mode matching code to execute this process in a more efficient manner. Recently, this code was implemented in the F-15B/Quiet Spike (Gulfstream Aerospace Corporation, Savannah, Georgia) model update. A build-up approach requiring several ground vibration test configurations and a series of model updates was implemented to determine the connection stiffness between aircraft and test article. The mode matching code successfully updated various models for the F-15B/Quiet Spike project to within 1 percent error in frequency and the modal assurance criteria values ranged from 88.51-99.42 percent.

Herrera, Claudia Y.↗

A Novel Partitioned Approach for Reduced Order Model—Finite Element Model (ROM-FEM) and ROM-ROM Coupling

Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and multiscale applications. In this work, we consider a scenario in which one or more of the “codes” being coupled are projection-based reduced order models (ROMs), introduced to lower the computational cost associated with a particular component. We simulate this scenario by considering a model interface problem that is discretized independently on two non-overlapping subdomains. Here we then formulate a partitioned scheme for this problem that allows the coupling between a ROM “code” for one of the subdomains with a finite element model (FEM) or ROM “code” for the other subdomain. The ROM “codes” are constructed by performing proper orthogonal decomposition (POD) on a snapshot ensemble to obtain a low-dimensional reduced order basis, followed by a Galerkin projection onto this basis. The ROM and/or FEM “codes” on each subdomain are then coupled using a Lagrange multiplier representing the interface flux. To partition the resulting monolithic problem, we first eliminate the flux through a dual Schur complement. Application of an explicit time integration scheme to the transformed monolithic problem decouples the subdomain equations, allowing their independent solution for the next time step. We show numerical results that demonstrate the proposed method’s efficacy in achieving both ROM-FEM and ROM-ROM coupling.

de Castro, Amy↗

A methodology to generate crystal-based molecular structures for atomistic simulations

Abstract We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal ‘slabs’ with periodic boundary conditions (PBCs) and non-periodic solids such as Wulff structures. We also introduce a method to build crystal slabs with orthogonal PBC vectors. These methods are integrated into our code, Los Alamos Crystal Cut ( LCC ), which is open source and thus fully available to the community. Examples showing the use of these methods are given throughout the manuscript.

42 ENGINEERING↗

Estimating an airborne dipole source using 3-D wavefield simulations and seismic receivers on the ground

Acoustic signals can couple to the ground, providing an opportunity to use seismic stations to investigate airborne sources. The study of Bishop et al. used wavefield simulations in a fluid-solid medium to quantify the role of topography on the seismic (ground) recordings of a monopole source in the air. We build upon this study by linking wavefield forward modelling with the source estimation code MTUQ, which can accommodate point forces or moment tensors in a solid medium, as well as sources in the air (or water) if they are enabled by the forward-modelling solver. We perform a series of synthetic numerical experiments to demonstrate that a dipole airborne source can be estimated using ground-based receivers, even within the presence of realistic topography. We investigate the influence of receiver coverage, topography, and assumed source location on the estimated results. The established capabilities raise the prospects for future efforts to estimate dipole sources in 3-D models that include heterogeneity in the air and the earth in addition to topography.

58 GEOSCIENCES↗