A MECHANICAL INTEGRATOR FOR THE COMPUTATION OF GRAVITY ANOMALIES

Geophysics ◽  
1942 ◽  
Vol 7 (4) ◽  
pp. 354-366 ◽  
Author(s):  
Arnold J. F. Siegert
Keyword(s):  
Gravity Anomaly ◽  
Indirect Method ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Closed Curve ◽  
The Body ◽  
Line Integral ◽  
Contour Lines ◽  
Terrain Corrections ◽  
Finite Body

With the instrument here described the gravity anomaly caused by an arbitrarily given finite body can be computed. The integrator is operated by tracing the contour lines representing the body in a manner similar to the operation of a planimeter. The instrument is useful mainly in the indirect method of interpretation of observed gravity anomalies, in the computation of terrain corrections, and in the evaluation of magnetic anomalies. Its design is based on a formula which expresses the gravity anomaly caused by an infinitely thin slab, bounded by a closed curve, as a line integral over this curve.

REMANENT MAGNETIZATION FROM COMPARISON OF GRAVITY AND MAGNETIC ANOMALIES

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 56-61 ◽  
Author(s):  
D. H. Shurbet ◽  
G. R. Keller ◽  
J. P. Friess
Keyword(s):  
Remanent Magnetization ◽  
Spatial Relationship ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
The Body ◽  
Gravity And Magnetic

Gravity and magnetic anomalies caused by deeply buried rock bodies in northwest Texas are compared. Interpretation of the gravity anomalies by modeling is used to locate and define the geometry of the body in a way analogous to the use of bathymetry in studies concerned with magnetization of seamounts. The direction of magnetization is then determined from the spatial relationship between the gravity and magnetic anomalies. This procedure amounts to an in‐situ determination of direction of magnetization of the body. In one example direction of magnetization indicates the time of intrusion and in another it indicates regional heating since intrusion.

Gravity anomalies of two‐dimensional bodies of irregular cross‐section with density contrast varying with depth

Geophysics ◽  
1979 ◽  
Vol 44 (9) ◽  
pp. 1525-1530 ◽  
Author(s):  
I. V. Radhakrishna Murthy ◽  
D. Bhaskara Rao
Keyword(s):  
Gravity Anomaly ◽  
Cross Section ◽  
Cross Sections ◽  
Integral Method ◽  
Gravity Anomalies ◽  
Density Contrast ◽  
Two Dimensional ◽  
Gravity Effect ◽  
Line Integral ◽  
Exponential Increase

The line‐integral method of Hubbert (1948) is extended to obtain the gravity anomalies of two‐dimensional bodies of arbitrary cross‐sections with density contrast varying linearly with depth. The cross‐section is replaced by an N‐sided polygon. The coordinates of two vertices of any given side are used to determine the associated contribution to the gravity anomaly. The gravity contribution of each side is then summed to yield the total gravity effect. The case where density contrast varies exponentially with depth is also considered. This technique is used to obtain the structure of the San Jacinto Graben, California, where sediments filling the graben have an exponential increase in density with depth.

A DIRECT COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES CAUSED BY 2- AND 3-DIMENSIONAL BODIES OF ARBITRARY SHAPE AND ARBITRARY MAGNETIC POLARIZATION BY EQUIVALENT‐POINT METHOD AND A SIMPLIFIED CUBIC SPLINE

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 610-622 ◽  
Author(s):  
Chao C. Ku
Keyword(s):  
Arbitrary Shape ◽  
Gaussian Quadrature ◽  
Magnetic Anomalies ◽  
Cubic Spline ◽  
The Body ◽  
Point Method ◽  
Magnetic Polarization ◽  
3 Dimensional ◽  
Equivalent Point ◽  
Gravity And Magnetic

A computational method, which combines the Gaussian quadrature formula for numerical integration and a cubic spline for interpolation in evaluating the limits of integration, is employed to compute directly the gravity and magnetic anomalies caused by 2-dimensional and 3-dimensional bodies of arbitrary shape and arbitrary magnetic polarization. The mathematics involved in this method is indeed old and well known. Furthermore, the physical concept of the Gaussian quadrature integration leads us back to the old concept of equivalent point masses or equivalent magnetic point dipoles: namely, the gravity or magnetic anomaly due to a body can be evaluated simply by a number of equivalent points which are distributed in the “Gaussian way” within the body. As an illustration, explicit formulas are given for dikes and prisms using 2 × 2 and 2 × 2 × 2 point Gaussian quadrature formulas. The basic limitation in the equivalent‐point method is that the distance between the point of observation and the equivalent points must be larger than the distance between the equivalent points within the body. By using a reasonable number of equivalent points or dividing the body into a number of smaller subbodies, the method might provide a useful alternative for computing in gravity and magnetic methods. The use of a simplified cubic spline enables us to compute the gravity and magnetic anomalies due to bodies of arbitrary shape and arbitrary magnetic polarization with ease and a certain degree of accuracy. This method also appears to be quite attractive for terrain corrections in gravity and possibly in magnetic surveys.

scholarly journals Basin Depth Mapping Beneath Wellington City Based on Residual Gravity Anomalies

2021 ◽  
Author(s):  
◽  
Alistair Stronach
Keyword(s):  
Gravity Anomaly ◽  
Sedimentary Basin ◽  
Gravity Data ◽  
Three Dimensional ◽  
Maximum Amplitude ◽  
Central Business District ◽  
Gravity Anomalies ◽  
Depth Map ◽  
Capital City ◽  
Detailed Knowledge

<p><b>New Zealand’s capital city of Wellington lies in an area of high seismic risk, which is further increased by the sedimentary basin beneath the Central Business District (CBD). Ground motion data and damage patterns from the 2013 Cook Strait and 2016 Kaikōura earthquakes indicate that two- and three-dimensional amplification effects due to the Wellington sedimentary basin may be significant. These effects are not currently accounted for in the New Zealand Building Code. In order for this to be done, three-dimensional simulations of earthquake shaking need to be undertaken, which requires detailed knowledge of basin geometry. This is currently lacking, primarily because of a dearth of deep boreholes in the CBD area, particularly in Thorndon and Pipitea where sediment depths are estimated to be greatest.</b></p> <p>A new basin depth map for the Wellington CBD has been created by conducting a gravity survey using a modern Scintrex CG-6 gravity meter. Across the study area, 519 new high precision gravity measurements were made and a residual anomaly map created, showing a maximum amplitude anomaly of -6.2 mGal with uncertainties better than ±0.1 mGal. Thirteen two-dimensional geological profiles were modelled to fit the anomalies, then combined with existing borehole constraints to construct the basin depth map. </p> <p>Results indicate on average greater depths than in existing models, particularly in Pipitea where depths are interpreted to be as great as 450 m, a difference of 250 m. Within 1 km of shore depths are interpreted to increase further, to 600 m. The recently discovered basin bounding Aotea Fault is resolved in the gravity data, where the basement is offset by up to 13 m, gravity anomaly gradients up to 8 mGal/km are observed, and possible multiple fault strands identified. A secondary strand of the Wellington Fault is also identified in the north of Pipitea, where gravity anomaly gradients up to 18 mGal/km are observed.</p>

scholarly journals Evaluation of Marine Gravity Anomaly Calculation Accuracy by Multi-Source Satellite Altimetry Data

2021 ◽  
Vol 9 ◽  
Author(s):  
Shanwei Liu ◽  
Yinlong Li ◽  
Qinting Sun ◽  
Jianhua Wan ◽  
Yue Jiao ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Gravity Anomaly ◽  
Mean Square Error ◽  
Spatial Resolution ◽  
Satellite Altimetry ◽  
Gravity Anomalies ◽  
Mean Square ◽  
Altimetry Data ◽  
Marine Gravity ◽  
Satellite Altimetry Data

The purpose of this paper is to analyze the influence of satellite altimetry data accuracy on the marine gravity anomaly accuracy. The data of 12 altimetry satellites in the research area (5°N–23°N, 105°E–118°E) were selected. These data were classified into three groups: A, B, and C, according to the track density, the accuracy of the altimetry satellites, and the differences of self-crossover. Group A contains CryoSat-2, group B includes Geosat, ERS-1, ERS-2, and Envisat, and group C comprises T/P, Jason-1/2/3, HY-2A, SARAL, and Sentinel-3A. In Experiment I, the 5′×5′ marine gravity anomalies were obtained based on the data of groups A, B, and C, respectively. Compared with the shipborne gravity data, the root mean square error (RMSE) of groups A, B, and C was 4.59 mGal, 4.61 mGal, and 4.51 mGal, respectively. The results show that high-precision satellite altimetry data can improve the calculation accuracy of gravity anomaly, and the single satellite CryoSat-2 enables achieving the same effect of multi-satellite joint processing. In Experiment II, the 2′×2′ marine gravity anomalies were acquired based on the data of groups A, A + B, and A + C, respectively. The root mean square error of the above three groups was, respectively, 4.29 mGal, 4.30 mGal, and 4.21 mGal, and the outcomes show that when the spatial resolution is satisfied, adding redundant low-precision altimetry data will add pressure to the calculation of marine gravity anomalies and will not improve the accuracy. An effective combination of multi-satellite data can improve the accuracy and spatial resolution of the marine gravity anomaly inversion.

Mapping of induced polarization using natural fields

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Erika Gasperikova ◽  
H. Frank Morrison
Keyword(s):  
Electric Field ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Induced Polarization ◽  
The Body ◽  
Electromagnetic Response ◽  
Frequency Dependent ◽  
Finite Body ◽  
Electric Field Profile ◽  
Measured Response

The observed electromagnetic response of a finite body is caused by induction and polarization currents in the body and by the distortion of the induction currents in the surrounding medium. At a sufficiently low frequency, there is negligible induction and the measured response is that of the body distorting the background currents just as it would distort a direct current (dc). Because this dc response is not inherently frequency dependent, any observed change in response of the body for frequencies low enough to be in this dc limit must result from frequency‐dependent conductivity. Profiles of low‐frequency natural electric (telluric) fields have spatial anomalies over finite bodies of fixed conductivity that are independent of frequency and have no associated phase anomaly. If the body is polarizable, the electric field profile over the body becomes frequency dependent and phase shifted with respect to a reference field. The technique was tested on data acquired in a standard continuous profiling magnetotelluric (MT) survey over a strong induced polarization (IP) anomaly previously mapped with a conventional pole‐dipole IP survey. The extracted IP response appears in both the apparent resistivity and the normalized electric field profiles.

Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 730-741 ◽  
Author(s):  
M. Okabe
Keyword(s):  
Gravitational Potential ◽  
Computing Time ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Two Dimensions ◽  
First Derivative ◽  
Second Derivatives ◽  
Analytical Expressions ◽  
Derivatives Of ◽  
The Magnetic Field

Complete analytical expressions for the first and second derivatives of the gravitational potential in arbitrary directions due to a homogeneous polyhedral body composed of polygonal facets are developed, by applying the divergence theorem definitively. Not only finite but also infinite rectangular prisms then are treated. The gravity anomalies due to a uniform polygon are similarly described in two dimensions. The magnetic potential due to a uniformly magnetized body is directly derived from the first derivative of the gravitational potential in a given direction. The rule for translating the second derivative of the gravitational potential into the magnetic field component is also described. The necessary procedures for practical computer programming are discussed in detail, in order to avoid singularities and to save computing time.

Comoros – New Evidence and Arguments for Continental Crust

2016 ◽  
Author(s):  
John Milsom ◽  
Phil Roach ◽  
Chris Toland ◽  
Don Riaroh ◽  
Chris Budden ◽  
...  
Keyword(s):  
Continental Crust ◽  
Fracture Zone ◽  
Seismic Data ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
The West ◽  
Sea Floor ◽  
Inappropriate Use ◽  
Sea Floor Spreading

ABSTRACT As part of an ongoing exploration effort, approximately 4000 line-km of seismic data have recently been acquired and interpreted within the Comoros Exclusive Economic Zone (EEZ). Magnetic and gravity values were recorded along the seismic lines and have been integrated with pre-existing regional data. The combined data sets provide new constraints on the nature of the crust beneath the West Somali Basin (WSB), which was created when Africa broke away from Gondwanaland and began to move north. Despite the absence of clear sea-floor spreading magnetic anomalies or gravity anomalies defining a fracture zone pattern, the crust beneath the WSB has been generally assumed to be oceanic, based largely on regional reconstructions. However, inappropriate use of regional magnetic data has led to conclusions being drawn that are not supported by evidence. The identification of the exact location of the continent-ocean boundary (COB) is less simple than would at first sight appear and, in particular, recent studies have cast doubt on a direct correlation between the COB and the Davie Fracture Zone (DFZ). The new high-quality reflection seismic data have imaged fault patterns east of the DFZ more consistent with extended continental crust, and the accompanying gravity and magnetic surveys have shown that the crust in this area is considerably thicker than normal oceanic and that linear magnetic anomalies typical of sea-floor spreading are absent. Rifting in the basin was probably initiated in Karoo times but the generation of new oceanic crust may have been delayed until about 154 Ma, when there was a switch in extension direction from NW-SE to N-S. From then until about 120 Ma relative movement between Africa and Madagascar was accommodated by extension in the West Somali and Mozambique basins and transform motion along the DFZ that linked them. A new understanding of the WSB can be achieved by taking note of newly-emerging concepts and new data from adjacent areas. The better-studied Mozambique Basin, where comprehensive recent surveys have revealed an unexpectedly complex spreading history, may provide important analogues for some stages in WSB evolution. At the same time the importance of wide continent-ocean transition zones marked by the presence of hyper-extended continental crust has become widely recognised. We make use of these new insights in explaining the anomalous results from the southern WSB and in assessing the prospectivity of the Comoros EEZ.

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

&lt;p&gt;In the frame of the IAG Subcommission 2.4f &amp;#8220;Gravity and Geoid in Antarctica&amp;#8221; (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).&lt;/p&gt;&lt;p&gt;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).&lt;/p&gt;&lt;p&gt;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&amp;#8217;s interior (cf. the contribution of Schaller et al. in session G4.3).&lt;/p&gt;

Empirical Determination of the Gravity Anomaly Covariance Function in Mountainous Areas

1980 ◽  
Vol 34 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Gerard Lachapelle ◽  
K. P. Schwarz
Keyword(s):  
Gravity Anomaly ◽  
Covariance Function ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Mountainous Areas ◽  
The North ◽  
Regression Parameters ◽  
Free Air ◽  
Vening Meinesz ◽  
Free Air Gravity

An evaluation of the empirical gravity anomaly covariance function using over 95 000 surface gravity anomalies in the North American Western Cordillera was carried out. A regression analysis of the data exhibits a strong and quasi-linear correlation of free air gravity anomalies with heights. This height correlation is removed from the free air anomalies prior to the numerical evaluation of the gravity anomaly covariance function. This covariance function agrees well with that evaluated previously by the authors for the remainder of Canada. A possible use for such a covariance function of ‘height independent’ gravity anomalies in mountainous areas is described. First, the height independent gravity anomaly at a point of known height is evaluated by least squares prediction using neighboring measured height independent gravity anomalies. Secondly, the part caused by the height correlation is calculated using linear regression parameters estimated previously and added to the predicted height independent gravity anomaly to obtain a predicted standard free air anomaly. This technique can be used to densify the coverage of free air anomalies for subsequent use in integral formulas of physical geodesy, e.g., those of Stokes and Vening Meinesz. This method requires that point topographic heights be given on a grid.

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