scholarly journals FRACTAL SURFACES: MEASUREMENT AND APPLICATIONS IN THE EARTH SCIENCES

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 87-115 ◽  
Author(s):  
B. LEA COX ◽  
J. S. Y. WANG
Keyword(s):  
Earth Sciences ◽  
Spatial Scales ◽  
Measurement Techniques ◽  
Heterogeneous Systems ◽  
Fractal Dimensions ◽  
Fractal Surfaces ◽  
The Earth ◽  
Power Spectral ◽  
Wide Range ◽  
Map Data

Earth scientists have measured fractal dimensions of surfaces by different techniques, including the divider, box, triangle, slit-island, power spectral, variogram and distribution methods. We review these seven measurement techniques, finding that fractal dimensions may vary systematically with measurement method. We discuss possible reasons for these differences, and point to common problems shared by all of the methods, including the remainder problem, curve-fitting, orientation of the measurement plane, size and direction of the sample. Fractal measurements have been applied to many problems in the earth sciences, at a wide range of spatial scales. These include map data of topography; fault traces and fracture networks; fracture surfaces of natural rocks, both in the field and at laboratory scales; metal surfaces; porous aggregate geometry; flow and transport through heterogeneous systems; and various microscopic surface phenomena associated with adsorption, aggregation, erosion and chemical dissolution. We review these applications and discuss the usefulness and limitations of fractal analysis to these types of problems in the earth sciences.

Uncertainty Estimation for Magnetic Maps

2021 ◽  
Author(s):  
Richard Saltus ◽  
Arnaud Chulliat ◽  
Brian Meyer ◽  
Christopher Amante
Keyword(s):  
Local Level ◽  
Uncertainty Estimation ◽  
Measured Data ◽  
Magnetic Minerals ◽  
Geochemical Environment ◽  
The Earth ◽  
Uncertainty Estimates ◽  
Wide Range ◽  
Machine Learning Applications ◽  
Map Data

<p>Magnetic maps depict spatial variations in the Earth’s magnetic field.  These variations occur at a wide range of scales and are produced via a variety of physical processes related to factors including structure and evolution of the Earth’s core field and the geologic distribution of magnetic minerals in the lithosphere.  Mankind has produced magnetic maps for 100’s of years with increasing fidelity and accuracy and there is a general understanding (particularly among the geophysicists who produce and use these maps) of the approximate level of resolution and accuracy of these maps.  However, few magnetic maps, or the digital grids that typically underpin these maps, have been produced with accompanying uncertainty quantification.  When uncertainty is addressed, it is typically a statistical representation at the grid or survey level (e.g., +- 10 nT overall uncertainty based on line crossings for a modern airborne survey) and not at the cell by cell local level.</p><p>As magnetic map data are increasingly used in complex inversions and in combination with other data or constraints (including in machine learning applications), it is increasingly important to have a handle on the uncertainties in these data.  An example of an application with need for detailed uncertainty estimation is the use of magnetic map information for alternative navigation.  In this application data from an onboard magnetometer is compared with previously mapped (or modeled) magnetic variations.  The uncertainty of this previously mapped information has immediate implications for the potential accuracy of navigation.</p><p>We are exploring the factors contributing to magnetic map uncertainty and producing uncertainty estimates for testing using new data collection in previously mapped (or modeled) map areas.  These factors include (but are likely not limited to) vintage and type of measured data, spatial distribution of measured data, expectation of magnetic variability (e.g., geologic or geochemical environment), statistics of redundant measurement, and spatial scale/resolution of the magnetic map or model.  The purpose of this talk is to discuss the overall issue and our initial results and solicit feedback and ideas from the interpretation community.</p>

scholarly journals Processes and Procedures for Data Publication: A Case Study in the Geosciences

2013 ◽  
Vol 8 (1) ◽  
pp. 193-203 ◽  
Author(s):  
Sarah Callaghan ◽  
Fiona Murphy ◽  
Jonathan Tedds ◽  
Rob Allan ◽  
John Kunze ◽  
...  
Keyword(s):  
Earth Sciences ◽  
Research Data ◽  
Academic Publishing ◽  
Data Repository ◽  
Data Publication ◽  
The Earth ◽  
Policies And Procedures ◽  
Wide Range ◽  
Key Issues ◽  
Work Done

The Peer REview for Publication and Accreditation of Research Data in the Earth sciences (PREPARDE) project is a JISC and NERC funded project which aims to investigate the policies and procedures required for the formal publication of research data, ranging from ingestion into a data repository, through to formal publication in a data journal. It also addresses key issues arising in the data publication paradigm, including, but not limited to, issues related to how one peer reviews a dataset, what criteria are needed for a repository to be considered objectively trustworthy, and how datasets and journal publications can be effectively cross-linked for the benefit of the wider research community. PREPARDE brings together a wide range of experts in the research, academic publishing and data management fields both within the Earth Sciences and in the broader life sciences with the aim of producing general guidelines applicable to a wide range of scientific disciplines and data publication types. This paper provides details of the work done in the first half of the project; the project itself will be completed in June 2013.

Measuring SHmax with Stress-Induced Anisotropy in Nonlinear Anelastic Behavior

2021 ◽  
Author(s):  
Andrew Delorey ◽  
Götz Bokelmann ◽  
Christopher Johnson ◽  
Paul Johnson
Keyword(s):  
Spatial Scales ◽  
Fundamental Property ◽  
Nonlinear Susceptibility ◽  
Induced Anisotropy ◽  
New Approach ◽  
The Earth ◽  
Wide Range ◽  
Source Mechanisms ◽  
Horizontal Compressive Stress ◽  
Stress Induced Anisotropy

Abstract Mechanical stress acting in the Earth`s crust is a fundamental property that has a wide range of geophysical applications, from tectonic movements to energy production. The orientation of maximum horizontal compressive stress, SHmax can be estimated by inverting earthquake source mechanisms and directly from borehole-based measurements, but large regions of the continents have few or no observations. Available observations often represent a variety of length scales and depths, and can be difficult to reconcile. Here we present a new approach to determine SHmax by measuring stress induced anisotropy of nonlinear susceptibility. We observe that nonlinear susceptibility is azimuthally dependent in the Earth and maximum when parallel to SHmax, as predicted by laboratory experiments. Our measurements use empirical Green’s functions that are applicable for different temporal and spatial scales. The method can quantify the orientation of SHmax in regions where no measurements exist today.

Two Visions of the Earth

1999 ◽  
Author(s):  
Naomi Oreskes
Keyword(s):  
Earth Sciences ◽  
Plate Tectonics ◽  
Continental Drift ◽  
Geological Data ◽  
The Past ◽  
The Earth ◽  
Wide Range ◽  
The Face ◽  
Bohr Atom ◽  
Similar Theory

Plate tectonics is the unifying theory of modern geology. This theory, which holds that the major features of the earth’s surface are created by horizontal motions of the continents, has been hailed as the geological equivalent of the “theory of the Bohr atom in its simplicity, its elegance, and its ability to explain a wide range of observation,” in the words of A. Cox. Developed in the mid-1960s, plate tectonics rapidly took hold, so that by 1971, Gass, Smith, and Wilson could say in their introductory textbook in geology: . . . During the last decade, there has been a revolution in earth sciences . . . which has led to the wide acceptance that continents drift about the face of the earth and that the sea-floor spreads, continually being created and destroyed. Finally in the last two to three years, it has culminated in an all-embracing theory known as “plate tectonics.” The success of plate tectonics theory is not only that it explains the geophysical evidence, but that it also presents a framework within which geological data, painstakingly accumulated by land-bound geologists over the past two centuries, can be fitted. Furthermore, it has taken the earth sciences to the stage where they can not only explain what has happened in the past, and is happening at the present time, but can also predict what will happen in the future. . . . Today moving continents are a scientific fact. But some forty years before the advent of the theory of plate tectonics, a very similar theory, initially known as the “displacement hypothesis,” was proposed and rejected by the geological fraternity. In 1912, a German meteorologist and geophysicist, Alfred Wegener, proposed that the continents of the earth were mobile; in the decade that followed he developed this idea into a full-fledged theory of tectonics that was widely discussed and debated and came to be known as the theory of continental drift. To a modern geologist, raised in the school of plate tectonics, Wegener’s book, The Origin of Continents and Oceans, appears an impressive and prescient document that contains many of the essential features of plate tectonic theory.

Fractal Distribution of Snow Depth from Lidar Data

2006 ◽  
Vol 7 (2) ◽  
pp. 285-297 ◽  
Author(s):  
Jeffrey S. Deems ◽  
Steven R. Fassnacht ◽  
Kelly J. Elder
Keyword(s):  
Land Surface ◽  
Snow Depth ◽  
Multiple Scales ◽  
Driving Forces ◽  
Spatial Scales ◽  
Fractal Dimensions ◽  
Airborne Lidar ◽  
Surface Elevation ◽  
Fractal Distribution ◽  
Wide Range

Abstract Snowpack properties vary dramatically over a wide range of spatial scales, from crystal microstructure to regional snow climates. The driving forces of wind, energy balance, and precipitation interact with topography and vegetation to dominate snow depth variability at horizontal scales from 1 to 1000 m. This study uses land surface elevation, vegetation surface elevation, and snow depth data measured using airborne lidar at three sites in north-central Colorado. Fractal dimensions are estimated from the slope of a log-transformed variogram and demonstrate scale-invariant, fractal behavior in the elevation, vegetation, and snow depth datasets. Snow depth and vegetation topography each show two distinct fractal distributions over different scale ranges (multifractal behavior), with short-range fractal dimensions near 2.5 and long-range fractal dimensions around 2.9 at all locations. These fractal ranges are separated by a scale break at 15–40 m, depending on the site, which indicates a process change at that scale. Terrain has a fractal distribution over nearly the entire range of scales available in the data. Directional differences in the fractal dimensions for each parameter are also present at multiple scales, and are related to the wind direction frequency distributions at each site. The results indicate that different sampling resolutions may yield different results and allow rescaling in specific scale ranges. Resolutions of 10 m and finer are consistently self-similar, as are resolutions greater than 30 m, though the coarser resolutions show nearly random distributions.

Fractal-Regular Surface Characterization Based on Experimental Data From Atomic Force Microscopy of Hard Disks

2007 ◽  
Author(s):  
Anne Sasikanth ◽  
Shao Wang
Keyword(s):  
Experimental Data ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Surface Characterization ◽  
Hard Disks ◽  
Fractal Surfaces ◽  
Atomic Force ◽  
Regular Shape ◽  
Power Spectral ◽  
Wide Range

Engineering surfaces should be characterized as fractal-regular surfaces since they possess both a macroscopic regular shape component and a random fractal component. In the present study, surface topography measurements were conducted for magnetic hard disks with an atomic force microscope (AFM). The power spectral density data obtained reveal a regular shape region and two fractal regions, indicating bifractal-regular behavior. By combining the AFM data with previous profilometer data, a complete description of the power spectral density behavior of the measured surfaces was obtained for a wide range of scales from 2 nm to 5 mm. The fractal dimension was found to be 1.935 and 1.186 for the upper fractal region and lower fractal region, respectively. Good agreement between the AFM data and profilometer data was observed in a range of overlapping scales. A multi-section modified Weierstrass-Mandelbrot function has been proposed to simulate bi-fractal surfaces with a power spectral density trend which matches that of experimental data.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

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