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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Experiences Using Lightweight Formal Methods for Requirements Modeling

This paper describes three case studies in the lightweight application of formal methods to requirements modeling for spacecraft fault protection systems. The case studies differ from previously reported applications of formal methods in that formal methods were applied very early in the requirements engineering process, to validate the evolving requirements. The results were fed back into the projects, to improve the informal specifications. For each case study, we describe what methods were applied, how they were applied, how much effort was involved, and what the findings were. In all three cases, formal methods enhanced the existing verification and validation processes, by testing key properties of the evolving requirements, and helping to identify weaknesses. We conclude that the benefits gained from early modeling of unstable requirements more than outweigh the effort needed to maintain multiple representations.

Easterbrook, Steve↗
NASA NTRS1983

Crustal deformation, the earthquake cycle, and models of viscoelastic flow in the asthenosphere

The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.

Cohen, S. C.↗
NASA NTRS1984

Crustal deformation, the earthquake cycle, and models of viscoelastic flow in the asthenosphere

The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.

Cohen, S. C.↗
NASA NTRS2014

Mobilization Protocols for Hybrid Sensors for Environmental AOP Sampling (HySEAS) Observations

The protocols presented here enable the proper mobilization of the latest-generation instruments for measuring the apparent optical properties (AOPs) of aquatic ecosystems. The protocols are designed for the Hybrid Sensors for Environmental AOP Sampling (HySEAS) class of instruments, but are applicable to the community of practice for AOP measurements. The protocols are organized into eleven sections beyond an introductory overview: a) cables and connectors, b) HySEAS instruments, c) platform preparation, d) instrument installation, e) cable installation, f) test deployment, g) test recovery, h) maintenance, i) shipping, j) storage, and k) smallboat operations. Each section concentrates on documenting how to prevent the most likely faults, remedy them should they occur, and accomplishing both with the proper application of a modest set of useful tools. Within the twelve sections, there are Socratic exercises to stimulate thought, and the answers to these exercises appear in Appendix A. Frequently asked questions (FAQs) are summarized in a separate section after the answers to the exercises in Appendix B. For practitioners unfamiliar with the nautical terms used throughout this document plus others likely encountered at sea, an abbreviated dictionary of nautical terms appears in Appendix C. An abbreviated dictionary of radiotelephone terms is presented in Appendix D. To ensure familiarity with many of the tools that are presented, Appendix E provides a description of the tools alongside a thumbnail picture. Abbreviated deployment checklists and cable diagrams are provided in Appendix F. The document concludes with an acknowledgments section, a glossary of acronyms, a definition of symbols, and a list of references.

Mobilizarion↗
NASA NTRS2021

NASA Engineering and Safety Center Technical Bulletin No. 19-01-1: Mitigating Risks of Single-Event Effects in Space Applications

Since most Electrical, Electronic, and Electromechanical (EEE) parts are intended for terrestrial applications, they are susceptible to a range of radiation threats in the space environment if the resulting effects are not properly characterized and mitigated. Even specially designed radiation-hardened parts may not be tolerant to all types of radiation effects. Radiation hardness is a multi-dimensional property of any part that describes intrinsic abilities to tolerate various radiation environments [1,2]. Effects to be concerned with include total ionizing dose, total non-ionizing dose, and single-event effects (SEE) – all of which depend on the mission, environment, application, and lifetime. Radiation effects concerns may be the same whether a EEE part is Commercial-Off-The-Shelf (COTS), MIL-SPEC, or some other variant, all of which are susceptible to the same radiation threats [3]. SEE consequences range from recoverable faults to catastrophic failure. Like other random faults, SEE can be mitigated with informed circuit design practices at the device, card, and/or system level.

Single-event effects↗
NASA NTRS2012

Turbine Engine Disk Rotor Health Monitoring Assessment Using Spin Tests Data

Detecting rotating engine component malfunctions and structural anomalies is increasingly becoming a crucial key feature that will help boost safety and lower maintenance cost. However, achievement of such technology, which can be referred to as a health monitoring remains somewhat challenging to implement. This is mostly due to presence of scattered loading conditions, crack sizes, component geometry and material properties that hinders the simplicity of imposing such application. Different approaches are being considered to assist in developing other means of health monitoring or nondestructive techniques to detect hidden flaws and mini cracks before any catastrophic events occur. These methods extend further to assess material discontinuities and other defects that have matured to the level where a failure is very likely. This paper is focused on presenting data obtained from spin test experiments of a turbine engine like rotor disk and their correlation to the development of a structural health monitoring and fault detection system. The data collected includes blade tip clearance, blade tip timing measurements and shaft displacements. The experimental results are collected at rotational speeds up to 10,000 Rpm and tests are conducted at the NASA Glenn Research Center s Rotordynamics Laboratory via a high precision spin system. Additionally, this study offers a closer glance at a selective online evaluation of a rotating disk using advanced capacitive, microwave and eddy current sensor technology.

Abdul-Aziz, Ali↗
NASA NTRS1982

Pre- and post-annealing of mechanical damage in silicon wafers

Basic properties of mechanical damage in silicon consisting of cracks and abrasion were studied using transmission electron microscopy. The crystallographic structure of mechanical damage was determined before and after high temperature annealing. The main findings include that stresses in silicon around crack tips are not plastically relieved at room temperature and that abrasion at room temperature introduces shear loops into the silicon. It was also found that cracks of micron size can be annealed out, specifically, if cleavage occurs on 111 planes. The healing products of such cracks are 60 deg and 90 deg dislocations. Submicron cracks transform into stacking faults during annealing. Likewise high concentrations of shear loops due abrasion were found to anneal into stacking faults. A one to one correlation between surface areas containing small cracks and stacking faults was made. Measurements of damage removal on silicon surfaces through chemical-mechanical etching techniques are presented. It is shown that silicon dioxide repolishes damaged silicon surfaces most effectively.

Schwottke, G. H.↗
NASA NTRS1989

Eastern Ishtar Terra: Tectonic evolution derived from recognized features

Previous analyses have recognized several styles and orientations of compressional deformation, crustal convergence, and crustal thickening in Eastern Ishtar Terra. An east to west sense of crustal convergence through small scale folding, thrusting, and buckling is reflected in the high topography and ridge-and-valley morphology of Maxwell Montes and the adjacent portion of Fortuna Tessera. This east to west convergence was accompanied by up to 1000 km of lateral motion and large scale strike-slip faulting within two converging shear zones which has resulted in the present morphology of Maxwell Montes. A more northeast to southwest sense of convergence through large scale buckling and imbrication is reflected in large, northwest-trending scarps along the entire northern boundary of Ishtar Terra, with up to 2 km of relief present at many of the scarps. It was previously suggested that both styles of compression have occurred at the expense of pre-existing tessera regions which have then been overprinted by the latest convergence event. The difference in style is attributed mostly to differences in the properties of the crust converging with the tessera blocks. If one, presumably thick, tessera block converges with another tessera region, then the widespread, distributed style of deformation occurs, as observed in western Fortuna Tessera. However, if relatively thin crust (such as suggested for the North Polar Plains converges with thicker tessera regions, then localized deformation occurs, as reflected in the scarps along Northern Ishtar Terra. The purpose is to identify the types of features observed in Eastern Ishtar Terra. Their potential temporal and spatial relationships, is described, possible origins for them is suggested, and how the interpretation of some of these features has led to the multiple-style tectonic evolution model described is shown.

Vorderbruegge, R. W.↗
NASA NTRS2021

Cryovolcanic flooding in Viking Terra on Pluto

A prominent fossa trough (Uncama Fossa) and adjacent 28-km diameter impact crater (Hardie) in Pluto's Viking Terra, as seen in the high-resolution images from the New Horizons spacecraft, show morphological evidence of in-filling with a material of uniform texture and red-brown color. A linear fissure parallel to the trough may be the source of a fountaining event yielding a cryoclastic deposit having the same composition and color properties as is found in the trough and crater. Spectral maps of this region with the New Horizons LEISA instrument reveal the spectral signature of H2O ice in these structures and in distributed patches in the adjacent terrain in Viking Terra. A detailed statistical analysis of the spectral maps shows that the colored H2O ice filling material also carries the 2.2-μm signature of an ammoniated component that may be an ammonia hydrate (NH3·nH2O) or an ammoniated salt. This paper advances the view that the crater and fossa trough have been flooded by a cryolava debouched from Pluto's interior along fault lines in the trough and in the floor of the impact crater. The now frozen cryolava consisted of liquid H2O infused with the red-brown pigment presumed to be a tholin, and one or more ammoniated compounds. Although the abundances of the pigment and ammoniated compounds entrained in, or possibly covering, the H2O ice are unknown, the strong spectral bands of the H2O ice are clearly visible. In consideration of the factors in Pluto's space environment that are known to destroy ammonia and ammonia-water mixtures, the age of the exposure is of order ≤109 years. Ammoniated salts may be more robust, and laboratory investigations of these compounds are needed.

Pluto↗
NASA NTRS2017

The Evolution of the Deformation Substructure in a Ni-Co-Cr Equiatomic Solid Solution Alloy

The equiatomic NiCoCr alloy exhibits an excellent combination of strength and ductility, even greater than the FeNiCrCoMn high entropy alloy, and also displays a simultaneous increase in strength and ductility with decreasing the testing temperature. To systemically investigate the origin of the exceptional properties of NiCoCr alloy, which are related to the evolution of the deformation substructure with strain, interrupted tensile testing was conducted on the equiatomic NiCoCr single-phase solid solution alloy at both cryogenic and room temperatures at five different plastic strain levels of 1.5%, 6.5%, 29%, 50% and 70%. The evolution of deformation substructure was examined using electron backscatter diffraction (EBSD), transmission Kikuchi diffraction (TKD), conventional transmission electron microscopy (CTEM), diffraction contrast imaging using STEM (DCI-STEM) and atomic resolution scanning transmission electron microscopy. While the deformation substructure mainly consisted of planar dislocation slip and the dissociation of dislocations into stacking faults at small strain levels (≤6.5%), at larger strain levels, additional substructures including nanotwins and a new phase with hexagonal close packed (HCP) lamellae also appeared. The volume fraction of the HCP lamellae increases with increasing deformation, especially at cryogenic temperature. First principles calculations at 0 K indicate that the HCP phase is indeed energetically favorable relative to FCC for this composition. The effects of the nanotwin and HCP lamellar structures on hardening rate and ductility at both cryogenic and room temperature are qualitatively discussed.

Twinning↗
NASA NTRS2015

Proof-of-Concept Experiments on a Gallium-Based Ignitron for Pulsed Power Applications

Ignitrons are electrical switching devices that operate at switching times that are on the order of microseconds, can conduct high currents of thousands of amps, and are capable of holding off tens of thousands of volts between pulses. They consist of a liquid metal pool within an evacuated tube that serves both the cathode and the source of atoms and electrons for an arc discharge. Facing the liquid metal pool is an anode suspended above the cathode, with a smaller ignitor electrode tip located just above the surface of the cathode. The ignitron can be charged to significant voltages, with a potential difference of thousands of volts between anode and cathode. When an ignition pulse is delivered from the ignitor electrode to the cathode, a small amount of the liquid metal is vaporized and subsequently ionized, with the high voltage between the anode and cathode causing the gas to bridge the gap between the two electrodes. The electrons and ions move rapidly towards the anode and cathode, respectively, with the ions liberating still more atoms from the liquid metal cathode surface as a high-current plasma arc discharge is rapidly established. This arc continues in a self-sustaining fashion until the potential difference between the anode and cathode drops below some critical value. Ignitrons have been used in a variety of pulsed power applications, including the railroad industry, industrial chemical processing, and high-power arc welding. In addition, they might prove useful in terrestrial power grid applications, serving as high-current fault switches, quickly shunting dangerous high-current or high-voltage spikes safely to ground. The motivation for this work stemmed from the fact that high-power, high-reliability, pulsed power devices like the ignitron have been used for ground testing in-space pulsed electric thruster technologies, and the continued use of ignitrons could prove advantageous to the future development and testing of such thrusters. Previous ignitron designs have used mercury as the liquid metal cathode, owing to its presence as a liquid at room temperatures and a vapor pressure of 10 Pa (75 mtorr) at room temperature. While these are favorable properties, there are obvious environmental and personal safety concerns with the storage, handling, and use of mercury and its compounds. The purpose of the present work was to fabricate and test an ignitron that used as its cathode an alternate liquid metal that was safe to handle and store. To that end, an ignitron test article that used liquid gallium as the cathode material was developed and tested. Gallium is a metal that has a melting temperature of 29.76 C, which is slightly above room temperature, and a boiling point of over 2,300 C at atmospheric pressure. This property makes gallium the element with the largest relative difference between melting and boiling points. Gallium has a limited role in biology, and when ingested, it will be subsequently processed by the body and expelled rather than accumulating to toxic levels. The next section of this Technical Memorandum (TM) provides background information on the development of mercury-based ignitrons, which serves as the starting point for the development of the gallium-based variant. Afterwards, the experimental hardware and setup used in proof-of-concept testing of a basic gallium ignitron are presented. Experimental data, consisting of discharge voltage and current waveforms as well as high-speed imaging of the gallium arc discharge in the gallium ignitron test article, are presented to demonstrate the efficacy of the concept. Discussion of the data and suggestions on improvements for future iterations of the design are presented in the final two sections of this TM.

Ali, H. K.↗
NASA NTRSDate not supplied

In-Time Safety Assessment & Risk Prediction for Unmanned Aerial Systems

One of the critical challenges in emerging autonomous systems is timely mitigation of hazards encountered during operation which may not be known or accounted for at the time of design. Efficient execution of unmanned systems therefore demands a paradigm shift from scheduled periodic maintenance to predictive risk analysis that includes condition-based-monitoring, real-time reliability assessment and hazard mitigation. Particularly, the state-of-health parameters needs to be computed at the component level, unit level as well as the integrated system level. While in the former two levels, the physics of health propagation may be based on underlying electro-mechanical properties, system level prognostics often relies on data-driven models. Further, uncertainty from model, measurements and input sources should be accurately quantified to generate meaningful prediction results that can be fed into reliable decision making processes. Finally, the expected risk and time to failure has to be computed based on the current state-of-health of the overall system. This talk presents a conceptual design of such an in-time safety assurance approach for unmanned aerial vehicles (UAV) operating at low altitudes near and over populated areas. Typical in-flight hazard incidents include unplanned detour, proximity to obstacles, mid-flight component faults, limited battery life and poor quality of GPS measurements. Safety assessment therefore comprises trajectory generation and re-plan, battery RUL computation, distributed fault diagnostics and uncertainty management of predicted trajectory based on GPS measurement noise. The entire monitoring framework will be demonstrated on simulated as well as real UAV flight experiments conducted at the NASA Langley Research Center. This tutorial will therefore guide the audience through a step-by-step tracking of an autonomous system with focus on in-time risk prediction in the presence of unforeseen hazards and uncertain environment.

diagnostics↗
NASA NTRS2003

System Modeling and Diagnostics for Liquefying-Fuel Hybrid Rockets

A Hybrid Combustion Facility (HCF) was recently built at NASA Ames Research Center to study the combustion properties of a new fuel formulation that burns approximately three times faster than conventional hybrid fuels. Researchers at Ames working in the area of Integrated Vehicle Health Management recognized a good opportunity to apply IVHM techniques to a candidate technology for next generation launch systems. Five tools were selected to examine various IVHM techniques for the HCF. Three of the tools, TEAMS (Testability Engineering and Maintenance System), L2 (Livingstone2), and RODON, are model-based reasoning (or diagnostic) systems. Two other tools in this study, ICS (Interval Constraint Simulator) and IMS (Inductive Monitoring System) do not attempt to isolate the cause of the failure but may be used for fault detection. Models of varying scope and completeness were created, both qualitative and quantitative. In each of the models, the structure and behavior of the physical system are captured. In the qualitative models, the temporal aspects of the system behavior and the abstraction of sensor data are handled outside of the model and require the development of additional code. In the quantitative model, less extensive processing code is also necessary. Examples of fault diagnoses are given.

Poll, Scott↗
NASA NTRS2005

Real-Time System Verification by Kappa-Induction

We report the first formal verification of a reintegration protocol for a safety-critical, fault-tolerant, real-time distributed embedded system. A reintegration protocol increases system survivability by allowing a node that has suffered a fault to regain state consistent with the operational nodes. The protocol is verified in the Symbolic Analysis Laboratory (SAL), where bounded model checking and decision procedures are used to verify infinite-state systems by k-induction. The protocol and its environment are modeled as synchronizing timeout automata. Because k-induction is exponential with respect to k, we optimize the formal model to reduce the size of k. Also, the reintegrator's event-triggered behavior is conservatively modeled as time-triggered behavior to further reduce the size of k and to make it invariant to the number of nodes modeled. A corollary is that a clique avoidance property is satisfied.

Pike, Lee S.↗
NASA NTRS1991

Venus tectonics - Initial analysis from Magellan

The styles of lithospheric deformation, the inferred mechanical properties of the lithosphere, and their implications for the tectonic history of Venus are discussed on the basis of radar imaging and altimetry data from Magellan. Observations of the planet plains reveal a superposition of different episodes of deformation and volcanism, strain both distributed and concentrated into zones of extension and shortening, and features reflecting a crustal response to mantle dynamic processes. Lithospheric shortening and crustal thickening are represented by ridge belts and mountain belts. The latter show the evidence for extension and collapse both during and following crustal compression. Venus displays quasi-circular coronae and broad rises with linear rift zones, associated with significant volcanism. Large-offset strike-slip faults have not been observed, although horizontal shear is accommodated across broad zones of crustal shortening. On Venus strain is distributed across zones that are one to a few hundred kilometers wide, and separated by stronger and less deformed blocks hundreds of kilometers in width, as in actively deforming continental regions on earth.

Solomon, Sean C.↗
NASA NTRS1994

Tartarus Colles: A sampling of the Martian highlands

Several of the most fundamental issues about the geology of Mars can be addressed using information on composition and structure of the plateau plains ('highlands') that cover approximately half the planet. The units that compose the highlands are interpreted as a mixture of volcanic, fluvial, lacustrine, and impact ejecta deposits. A more precise inventory of differing of igneous and sedimentary lithologies in highland rock units would not only lead to a better understanding of how the plateau plains formed, but would also clarify the nature of the surface environment during the first 800 m.y. of martian history. Structural features including bedforms, joints, and small faults that are unresolved from orbit record a history of the emplacement and deformation of the highlands. In addition, weathering products present in this very ancient terrain represent a mineralogic record of past climate and of the pathways by which bedrock is altered chemically. Their similarity or dissimilarity to bright soils observed spectroscopically and in situ at the Viking Lander sites will be evidence for the relative roles of regional sources and global eolian transport in producing the widespread cover of 'dust.' Unfortunately, these issues are difficult to address in the plateau plains proper, because bedrock is covered by mobile sand and weathering products, which dominate both surface composition and remotely measurable spectral properties. However, the 'Tartarus Colles' site, located at 11.41 deg N, 197.69 deg W at an elevation of -1 km, provides an excellent opportunity to address the highland geology within the mission constraints of Mars Pathfinder. The site is mapped as unit HNu, and consists of knobby remnants of deeply eroded highlands. It contains rolling hills, but lacks steep escarpments and massifs common in most highland remnants, and is free of large channels that would have removed colluvium from eroded upper portions of the stratigraphic column. These characteristics indicate that variety of bedrock types from throughout the Noachian-Hesperian stratigraphic column may remain at the site.

Murchie, Scott↗
NASA NTRS2016

International Docking Standard (IDSS) Interface Definition Document (IDD) : Revision - E

This International Docking System Standard (IDSS) Interface Definition Document (IDD) is the result of a collaboration by the International Space Station membership to establish a standard docking interface to enable on-orbit crew rescue operations and joint collaborative endeavors utilizing different spacecraft. This IDSS IDD details the physical geometric mating interface and design loads requirements. The physical geometric interface requirements must be strictly followed to ensure physical spacecraft mating compatibility. This includes both defined components and areas that are void of components. The IDD also identifies common design parameters as identified in section 3.0, e.g., docking initial conditions and vehicle mass properties. This information represents a recommended set of design values enveloping a broad set of design reference missions and conditions, which if accommodated in the docking system design, increases the probability of successful docking between different spacecraft. This IDD does not address operational procedures or off-nominal situations, nor does it dictate implementation or design features behind the mating interface. It is the responsibility of the spacecraft developer to perform all hardware verification and validation, and to perform final docking analyses to ensure the needed docking performance and to develop the final certification loads for their application. While there are many other critical requirements needed in the development of a docking system such as fault tolerance, reliability, and environments (e.g. vibration, etc.), it is not the intent of the IDSS IDD to mandate all of these requirements; these requirements must be addressed as part of the specific developer's unique program, spacecraft and mission needs. This approach allows designers the flexibility to design and build docking mechanisms to their unique program needs and requirements. The purpose of the IDSS IDD is to provide basic common design parameters to allow developers to independently design compatible docking systems. The IDSS is intended for uses ranging from crewed to autonomous space vehicles, and from Low Earth Orbit (LEO) to deep-space exploration missions.The purpose of the IDSS IDD is to provide basic common design parameters to allow developers to independently design compatible docking systems. The IDSS is intended for uses ranging from crewed to autonomous space vehicles, and from Low Earth Orbit (LEO) to deep-space exploration missions. The purpose of the IDSS IDD is to provide basic common design parameters to allow developers to independently design compatible docking systems. The IDSS is intended for uses ranging from crewed to autonomous space vehicles, and from Low Earth Orbit (LEO) to deep-space exploration missions.

docking↗
NASA NTRS1991

Application of Hapke photometric model to three geologic surfaces using PARABOLA bidirectional reflection data

The Geologic Remote Sensing Field Experiment (GRSFE) was conducted in July and September of 1989 to collect data with both ground and airborne instrumentation. A major objective of GRSFE was to collect data which could be used to test radiative transfer models for the extraction of composition and textural surface properties from remotely acquired data. Reported here are the initial results from an application of the Hapke photometric model, using data from the Portable Apparatus for Remote Acquisition of Bidirectional Observations of Land and Atmosphere (PARABOLA), a ground based radiometer with three spectral channels. PARABOLA data was collected in the Lunar Crater Volcanic Field in Nevada, specifically from the region of Lunar Lake, a playa. The Hapke model was found to be inadequate for three relatively common geologic surfaces (a clay-rich, hard packed surface with decimeter sized mudcracks; a cobble site, similar to a playa site, but strewn with basaltic cobbles and pebbles; and a surface mantled basalt lava flow). The model is not at fault; rather, the complexity of most geologic surfaces is not accounted for in the initial assumptions.

Shepard, Michael K.↗