scholarly journals Harmonica and Boule: Modern Python tools for geophysical gravimetry

2021 ◽  
Author(s):  
Leonardo Uieda ◽  
Santiago R. Soler ◽  
Agustina Pesce ◽  
Lorenzo Perozzi ◽  
Mark A. Wieczorek
Keyword(s):  
Community Involvement ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Point Sources ◽  
Magnetic Data ◽  
Spherical Coordinates ◽  
Forward Modelling ◽  
Free Air ◽  
Gravity Disturbances ◽  
Gravity And Magnetic Data

<p>Gravimetry is a routine part of the geophysicists toolset, historically used in geophysics following the geodetic definitions of gravity anomalies and their related “reductions”. Several authors have shown that the geodetic concept of a gravity anomaly does not align with goals of gravimetry in geophysics (the investigation of anomalous density distributions). Much of this confusion likely stems from the lack of widely available tools for performing the corrections needed to arrive at a geophysically meaningful gravity disturbance. For example, free-air corrections are completely unnecessary since analytical expressions for theoretical gravity at any point have existed for over a decade. Since this is not easily done in a spreadsheet or short script, modern tools for processing and modelling gravity data for geophysics are needed. These tools must be trustworthy (i.e., extensively tested) and designed with software development and geophysical best practices in mind.</p><p>We present the Python libraries Harmonica and Boule, which are part of the Fatiando a Terra project (https://www.fatiando.org). Both tools are open-source under the permissive BSD license and are developed in the open by a community of geoscientists and programmers.</p><p>Harmonica provides tools for processing, forward modelling, and inversion of gravity and magnetic data. The first release of Harmonica was focused on implementing methods for processing and interpolation with the equivalent source technique, as well as forward modelling with right-rectangular prisms, point sources, and tesseroids. Current work is directed towards implementing a processing pipeline for gravity data, including topographic corrections in Cartesian and spherical coordinates, atmospheric corrections, and more. The software is still in early stages of development and design and would benefit greatly from community involvement and feedback.</p><p>Boule implements reference ellipsoids (including oblate ellipsoids, spheres, and soon triaxial ellipsoids), conversions between ellipsoidal and geocentric spherical coordinates, and normal gravity calculations using analytical solutions for gravity fields at any point outside of the ellipsoid. It includes ellipsoids for the Earth as well as other planetary bodies in the solar system, like Mars, the Moon, Venus, and Mercury. This enables the calculation of gravity disturbances for Earth and planetary data without the need for free-air corrections. Boule was created out of the shared needs of Harmonica, SHTools (https://github.com/SHTOOLS), and pygeoid (https://github.com/ioshchepkov/pygeoid) and is developed with input from developers of these projects.</p><p>We welcome participation from the wider geophysical community, irrespective of programming skill level and experience, and are actively searching for interested developers and users to get involved in shaping the future of these projects.</p>

Application of gravity and magnetic methods to assess geological hazards and natural resource potential in the Mosida Hills, Utah County, Utah

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1514-1526 ◽  
Author(s):  
Alvin K. Benson ◽  
Andrew R. Floyd
Keyword(s):  
Gravity Data ◽  
Magnetic Data ◽  
Geological Hazards ◽  
Mafic Lava ◽  
Subsurface Geology ◽  
Gravity And Magnetic ◽  
Geophysical Surveys ◽  
Utah County ◽  
Gravity And Magnetic Data ◽  
Hills Area

Gravity and magnetic data were collected in the Mosida Hills, Utah County, Utah, at over 1100 stations covering an area of approximately 58 km2 (150 mi2) in order to help define the subsurface geology and assess potential geological hazards for urban planning in an area where the population is rapidly increasing. In addition, potential hydrocarbon traps and mineral ore bodies may be associated with some of the interpreted subsurface structures. Standard processing techniques were applied to the data to remove known variations unrelated to the geology of the area. The residual data were used to generate gravity and magnetic contour maps, isometric projections, profiles, and subsurface models. Ambiguities in the geological models were reduced by (1) incorporating data from previous geophysical surveys, surface mapping, and aeromagnetic data, (2) integrating the gravity and magnetic data from our survey, and (3) correlating the modeled cross sections. Gravity highs and coincident magnetic highs delineate mafic lava flows, gravity lows and magnetic highs reflect tuffs, and gravity highs and magnetic lows spatially correlate with carbonates. These correlations help identify the subsurface geology and lead to new insights about the formation of the associated valleys. At least eight new faults (or fault segments) were identified from the gravity data, whereas the magnetic data indicate the existence of at least three concealed and/or poorly exposed igneous bodies, as well as a large ash‐flow tuff. The presence of low‐angle faults suggests that folding or downwarping, in addition to faulting, played a role in the formation of the valleys in the Mosida Hills area. The interpreted location and nature of concealed faults and volcanic flows in the Mosida Hills area are being used by policy makers to help develop mitigation procedures to protect life and property.

Integrated Geophysical Interpretation of Kerio Valley Basin Stratigraphy, Kenya Rift

2016 ◽  
Author(s):  
Godfred Osukuku ◽  
Abiud Masinde ◽  
Bernard Adero ◽  
Edmond Wanjala ◽  
John Ego
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Fault System ◽  
Magnetic Data ◽  
Data Sets ◽  
Seismic Profiles ◽  
The West ◽  
Seismic Reflection Data ◽  
Basement Rocks ◽  
Western Side

Abstract This research work attempts to map out the stratigraphic sequence of the Kerio Valley Basin using magnetic, gravity and seismic data sets. Regional gravity data consisting of isotactic, free-air and Bouguer anomaly grids were obtained from the International Gravity Bureau (BGI). Magnetic data sets were sourced from the Earth Magnetic Anomaly grid (EMAG2). The seismic reflection data was acquired in 1989 using a vibrating source shot into inline geophones. Gravity Isostacy data shows low gravity anomalies that depict a deeper basement. Magnetic tilt and seismic profiles show sediment thickness of 2.5-3.5 Km above the basement. The Kerio Valley Basin towards the western side is underlain by a deeper basement which are overlain by succession of sandstones/shales and volcanoes. At the very top are the mid Miocene phonolites (Uasin Gishu) underlain by mid Miocene sandstones/shales (Tambach Formation). There are high gravity anomalies in the western and southern parts of the basin with the sedimentation being constrained by two normal faults. The Kerio Valley Basin is bounded to the west by the North-South easterly dipping fault system. Gravity data was significantly of help in delineating the basement, scanning the lithosphere and the upper mantle according to the relative densities. The basement rocks as well as the upper cover of volcanoes have distinctively higher densities than the infilled sedimentary sections within the basin. From the seismic profiles, the frequency of the shaley rocks and compact sandstones increases with depths. The western side of the basin is characterized by the absence of reflections and relatively higher frequency content. The termination of reflectors and the westward dip of reflectors represent a fault (Elgeyo fault). The reflectors dip towards the west, marking the basin as an asymmetrical syncline, indicating that the extension was towards the east. The basin floor is characterized by a nearly vertical fault which runs parallel to the Elgeyo fault. The seismic reflectors show marked discontinuities which may be due to lava flows. The deepest reflector shows deep sedimentation in the basin and is in reasonable agreement with basement depths delineated from potential methods (gravity and magnetic). Basement rocks are deeper at the top of the uplift footwall of the Elgeyo Escarpment. The sediments are likely of a thickness of about 800 M which is an interbed of sandstones and shales above the basement.

Towards an updated, enhanced regional gravity field solution for Antarctica

2021 ◽  
Author(s):  
Mirko Scheinert ◽  
Philipp Zingerle ◽  
Theresa Schaller ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Data Set ◽  
Gravity Field Model ◽  
Terrestrial Gravity ◽  
Field Solution ◽  
Gravity Disturbances ◽  
Regional Gravity

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).</p><p>We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).</p><p>We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

Gravity and Magnetic Methods

2000 ◽  
Author(s):  
Richard M. Carruthers ◽  
John D. Cornwell
Keyword(s):  
Large Scale ◽  
Gravity Data ◽  
Integrated Approach ◽  
Rock Properties ◽  
Magnetic Data ◽  
Satellite Gravity ◽  
Fully Integrated ◽  
Continental Shelves ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Data

Lateral variations in the density and magnetization of the rocks within the crust give rise to "anomalies" in the Earth's gravity and magnetic fields. These anomalies can be measured and interpreted in terms of the geology both in a qualitative sense, by mapping out trends and changes in anomaly style, and quantitatively, by creating models of the subsurface which reproduce the observed fields. Such interpretations are generally less definitive in themselves than the results from seismic surveys (see chapter 12), but the data are widely available and can provide information in areas where other methods are ineffective or have not been applied. As the different geophysical techniques respond to specific rock properties such as density, magnetization, and acoustic velocity, the results are complementary, and a fully integrated approach to data collection and interpretation is generally more effective than the sum of its parts assessed on an individual basis. Gravity and magnetic data have been acquired, at least to a reconnaissance scale, over most of the world. In particular, the release into the public domain of satellite altimetry information (combined with improved methods of data processing) means that there is gravity coverage to a similar standard for most of the offshore region to within about 50 km of the coast. Magnetic anomalies recorded from satellites provide global coverage, but the high altitude of the observations means that only large-scale features extending over many 10s of kilometers are delineated. Reconnaissance aeromagnetic surveys with flight lines 10-20 km apart provide a lateral anomaly resolution similar to that of the satellite gravity data. Oceanographic surveys undertaken by a variety of academic and research institutions are another valuable source of data in remote regions offshore which supplement and extend the more detailed coverage obtained over the continental shelves, for example, by oil companies in areas of hydrocarbon interest. Surveys over land vary widely in terms of acquisition parameters and quality, but some form of national compilation is available from many countries. A number of possible applications of the potential field (i.e., gravity and magnetic) data follow from the terms set out by UNCLOS. Paragraph 4(b) of article 76 states, "In the absence of evidence to the contrary, the foot of the continental slope is to be determined as the point of maximum change in the gradient at its base" (italics added).

The calculation of deflexions of the vertical from gravity anomalies

1950 ◽  
Vol 204 (1078) ◽  
pp. 374-395 ◽  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Sources Of Error ◽  
Free Air ◽  
Gravity Measurements ◽  
Standard Deviations ◽  
The Difference ◽  
Different Sources

The theory of the application of gravity measurements to geodetic calculations is discussed, and the errors involved in calculating deflexions of the vertical are estimated. If the gravity data are given as free air anomalies from Jeffreys’s (1948) formula, so thdt the second and third harmonics of gravity are assumed known, the orders of magnitude of the standard deviations of the different sources of error are the following: Single deflexion: neglect of gravity outside 20° 1" Difference of deflexions: neglect of gravity outside 5° 0"·5 Calculation of effects of gravity from 0º·05 to 5° 0"·1 Calculation of effects of gravity within 0º·05 between 0"·1 and 0"·5 Estimates of the deflexions are made for Greenwich, Herstmonceux, Southampton and Bayeux, and the difference between Greenwich and Southampton is compared with the astronomical and geodetic amplitudes.

Sea floor topography modeling by cumulating different types of gravity information

2020 ◽  
Author(s):  
Lucia Seoane ◽  
Benjamin Beirens ◽  
Guillaume Ramillien
Keyword(s):  
New England ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Extended Kalman Filtering ◽  
Sea Floor ◽  
Single Beam ◽  
Free Air ◽  
Free Air Gravity ◽  
Great Meteor Seamount

<p>We propose to cumulate complementary gravity data, i.e. geoid height and (radial) free-air gravity anomalies, to evaluate the 3-D shape of the sea floor more precisely. For this purpose, an Extended Kalman Filtering (EKF) scheme has been developed to construct the topographic solution by injecting gravity information progressively. The main advantage of this sequential cumulation of data is the reduction of the dimensions of the inverse problem. Non linear Newtonian operators have been re-evaluated from their original forms and elastic compensation of the topography is also taken into account. The efficiency of the method is proved by inversion of simulated gravity observations to converge to a stable topographic solution with an accuracy of only a few meters. Real geoid and gravity data are also inverted to estimate bathymetry around the New England and Great Meteor seamount chains. Error analysis consists of comparing our topographic solutions to accurate single beam ship tracks for validation.</p>

A better strategy for interpolating gravity and magnetic data

2020 ◽  
Author(s):  
Santiago Rubén Soler ◽  
Leonardo Uieda
Keyword(s):  
Observation Point ◽  
Point Sources ◽  
Source Distribution ◽  
Magnetic Data ◽  
Relative Depth ◽  
Regular Grid ◽  
Gravity And Magnetic ◽  
Layer Technique ◽  
Gravity And Magnetic Data ◽  
Equivalent Layer

<p>We present a new strategy for gravity and magnetic data interpolation and processing. Our method is based on the equivalent layer technique (EQL) and produces more accurate interpolations when compared with similar EQL methods. It also reduces the computation time and memory requirements, both of which have been severe limiting factors.</p><p>The equivalent layer technique (also known as equivalent source, radial basis functions, or Green’s functions interpolation) is used to predict the value of gravity and magnetic fields (or transformations thereof) at any point based on the data gathered on some observation points. It consists in estimating a source distribution that produces the same field as the one measured and using this estimate to predict new values. It generally outperforms other general-purpose 2D interpolators, like the minimum curvature or bi-harmonic splines, because it takes into account the height of measurements and the fact that these fields are harmonic functions. Nevertheless, defining a layout for the source distribution used by the EQL is not trivial and plays an important role in the quality of the predictions.</p><p>The most widely used source distributions are: (a) a regular grid of point sources and (b) one point source beneath each observation point. We propose a new source distribution: (c) divide the area into blocks, calculate the average location of observation points inside each block, and place one point source beneath each average location. This produces a smaller number of point sources in comparison with the other source distributions, effectively reducing the computational load. Traditionally, the source points are located: (i) all at the same depth or (ii) each source point at a constant relative depth beneath its corresponding observation point. Besides these two, we also considered (iii) a variable relative depth for each source point proportional to the median distance to its nearest neighbours. The combination of source distributions and depth configurations leads to seven different source layouts (the regular grid is only compatible with the constant depth configuration).</p><p>We have scored the performance of each configuration by interpolating synthetic ground and airborne gravity data, and comparing the interpolation against the true values of the model. The block-averaged source layout (c) with variable relative depth (iii) produces more accurate interpolation results (R² of 0.97 versus R² of 0.63 for the traditional grid layout) in less time than the alternatives (from 2 to 10 times faster on our test cases). These results are consistent between ground and airborne survey layouts. Our conclusions can be extrapolated to other applications of equivalent layers, such as upward continuation, reduction-to-the-pole, and derivative calculation. What is more, we expect that these optimizations can benefit similar spatial prediction problems beyond gravity and magnetic data.</p><p>The source code developed for this study is based on the EQL implementation available in Harmonica (fatiando.org/harmonica), an open-source Python library for modelling and processing gravity and magnetic data.</p>

The Origin of Lunar Mascon Basins

Science ◽  
2013 ◽  
Vol 340 (6140) ◽  
pp. 1552-1555 ◽  
Author(s):  
H. J. Melosh ◽  
Andrew M. Freed ◽  
Brandon C. Johnson ◽  
David M. Blair ◽  
Jeffrey C. Andrews-Hanna ◽  
...  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Element Model ◽  
Isostatic Adjustment ◽  
Melt Pool ◽  
Free Air ◽  
Free Air Gravity ◽  
Bull's Eye ◽  
Gravity Recovery ◽  
The Impact

High-resolution gravity data from the Gravity Recovery and Interior Laboratory spacecraft have clarified the origin of lunar mass concentrations (mascons). Free-air gravity anomalies over lunar impact basins display bull’s-eye patterns consisting of a central positive (mascon) anomaly, a surrounding negative collar, and a positive outer annulus. We show that this pattern results from impact basin excavation and collapse followed by isostatic adjustment and cooling and contraction of a voluminous melt pool. We used a hydrocode to simulate the impact and a self-consistent finite-element model to simulate the subsequent viscoelastic relaxation and cooling. The primary parameters controlling the modeled gravity signatures of mascon basins are the impactor energy, the lunar thermal gradient at the time of impact, the crustal thickness, and the extent of volcanic fill.

A geological interpretation of gravity and magnetic data, northwest Saskatchewan

1970 ◽  
Vol 7 (3) ◽  
pp. 858-868 ◽  
Author(s):  
R. H. Wallis
Keyword(s):  
Gravity Data ◽  
Magnetic Data ◽  
Early Proterozoic ◽  
Geological Interpretation ◽  
Metasedimentary Rocks ◽  
Lower Proterozoic ◽  
Gravity And Magnetic ◽  
Northern Saskatchewan ◽  
Gravity And Magnetic Data ◽  
Sedimentary Unit

The striking 'fit' of aeromagnetic and gravity data from the Precambrian of northwest Saskatchewan, combined with known and nearby analogous, geological relationships, suggests the presence of a northeast-trending belt, 250 × 20 miles (400 × 30 km), of early Proterozoic (?) metasedimentary rocks, probably magnetite-bearing meta-arkoses. This structural–sedimentary unit might have economic possibilities analogous to other northeast-striking, Precambrian, lower Proterozoic (?), metasedimentary belts of northern Saskatchewan, the Virgin River Belt, and the Wollaston Trend.

A GEOLOGICAL AND GEOPHYSICAL STUDY OF PILOT KNOB (SOUTH), TRAVIS COUNTY, TEXAS

Geophysics ◽  
1954 ◽  
Vol 19 (3) ◽  
pp. 438-454 ◽  
Author(s):  
Frederick Romberg ◽  
Virgil E. Barnes
Keyword(s):  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Complete Picture ◽  
Magnetic Data ◽  
Strong Gravity ◽  
Local Setting ◽  
Gravity And Magnetic ◽  
Geophysical Study ◽  
Gravity And Magnetic Data ◽  
First Time

Pilot Knob is an exhumed volcano of Cretaceous age, composed of “serpentinized” pyroclastics and minor amounts of basalt in both intrusive and extrusive masses. The geology of Pilot Knob was re‐examined, and gravity and magnetic observations made and interpreted, in order to present a complete picture of the feature itself, its history, its relation to the region and area surrounding it, and the resemblances between it and the serpentine plugs in the neighborhood, to which it is geologically related. Some of these plugs have been discovered by geophysical means, and some so discovered have produced oil; the application of gravity and magnetic data to such discoveries is analyzed. The extrusive masses are here reported for the first time, and other evidence is given for the age and volcanic nature of Pilot Knob. The observations reveal 1) strong gravity and magnetic anomalies over the central basalt mass, 2) a pattern of weaker anomalies probably caused by flows and dikes and suggesting that Pilot Knob is situated near the intersection of two sets of fractures, and 3) evidence that “serpentinized” pyroclastics show weak magnetic anomalies and (in the local setting) no visible gravity anomalies.

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