GRAVITY ANOMALIES OF A FAULT CUTTING A SERIES OF BEDS

Geophysics ◽  
1970 ◽  
Vol 35 (4) ◽  
pp. 708-712 ◽  
Author(s):  
Bijon Sharma ◽  
Mahesh P. Vyas
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Simple Expression ◽  
Uniform Density ◽  
Arbitrary Angle ◽  
Single Block ◽  
Inclined Fault ◽  
Unusual Situation

The gravity anomaly due to a single horizontal semi‐infinite block terminated by a vertical or dipping fault has been discussed by several authors previously. Geldart, Gill, and Sharma (1966) gave a new and simple expression for calculating the gravity anomaly due to a block cut by an inclined fault at an arbitrary angle and used this expression to obtain the gravity anomaly due to a fault cutting a single bed. In their derivation the effects of both the upthrown and the downthrown blocks were taken into consideration. It is, however, only in the unusual situation that faults cut a single bed of uniform density. More often, faults cut a series of beds of different densities and thicknesses. If the densities and the thicknesses of the various beds differ greatly, an interpretation based upon replacement of the series of beds by a single bed of uniform density may be highly erroneous. Starting from the single block expression given by Geldart et al, an expression can be derived giving the gravity anomaly due to a fault cutting a series of beds having different densities and thicknesses.

A GENERAL EXPRESSION FOR THE FOURIER TRANSFORM OF THE GRAVITY ANOMALY DUE TO A FAULT

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1458-1461 ◽  
Author(s):  
Bijon Sharma ◽  
T. K. Bose
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
General Expression ◽  
Fault Plane ◽  
Gravity Anomalies ◽  
Arbitrary Angle ◽  
Vertical Fault ◽  
The Fourier Transform

The application of the method of the Fourier transform in interpreting gravity anomalies of faults has so far been based upon the Fourier transform of the gravity anomaly due to a single semi‐infinite block cut by a vertical fault. A general expression for the Fourier transform of the fault anomaly is here derived which is valid for an arbitrary angle of inclination of the fault plane. For deriving the general expression, the gravity anomaly of the fault is first separated into a constant and a variable term. The transforms of the two terms are calculated separately and then added to give the general expression for the Fourier transform of the fault anomaly.

THE CORRELATION BETWEEN PRE‐CAMBRIAN ROCK DENSITIES AND BOUGUER GRAVITY ANOMALIES NEAR PARRY SOUND, ONTARIO

Geophysics ◽  
1954 ◽  
Vol 19 (1) ◽  
pp. 76-88
Author(s):  
C. H. G. Oldham
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Canadian Shield ◽  
Gravity Survey ◽  
Uniform Density ◽  
Bouguer Gravity ◽  
Geological Evidence ◽  
Bouguer Gravity Anomaly ◽  
Bouguer Gravity Anomalies

A gravity survey and a survey of rock densities have been carried out over an area of two thousand square miles near Parry Sound. A closed positive Bouguer gravity anomaly of thirty milligals was delineated, and a considerable variation was found to exist in the densities of pre‐Cambrian gneisses. In most previous interpretations of gravity over the Canadian Shield the gneisses have been assumed to possess a uniform density and anomalies have been attributed to changes in the thickness of horizontal crustal layers. In this paper it is shown that the Parry Sound anomaly can be explained in terms of structures within the crust taking the form of projections downward of the density variations found at the surface. The postulated structure is a nearly circular basin of dense gneisses. The shape is reasonable and agrees with such geological evidence as is available.

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.

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.

Linear inversion of gravity data using the spectral expansion method

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 820-824 ◽  
Author(s):  
Rene E. Chavez ◽  
George D. Garland
Keyword(s):  
Inverse Problem ◽  
Gravity Data ◽  
Linear Equations ◽  
Thin Sheet ◽  
Gravity Anomalies ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Uniform Density ◽  
Linear Inversion ◽  
Prismatic Structure

Inversion of gravity anomalies in terms of an anomalous mass distribution with irregular outline but uniform density leads to a nonlinear inverse problem. An alternative approach based on the thin‐sheet approximation can, however, be formulated as a linear inverse problem provided the structures are two‐dimensional. The anomalous mass is represented by a thin sheet, which is located at a depth [Formula: see text] and is divided into M strips with N < M data points. Thus, an underdetermined system of linear equations is obtained which is solved by the spectral expansion method for the surface density distribution of each segment. This set of parameters is then transformed into a prismatic structure with variable depth but uniform density. The modeling procedure involves a noniterative method. A gravity problem is investigated, and the solution obtained compares well with previous interpretations.

scholarly journals On the topographic effects by Stokes’ formula

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
L.E. Sjöberg
Keyword(s):  
Gravity Anomaly ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Topographic Effects ◽  
Gravimetric Geoid ◽  
Bouguer Gravity ◽  
The Third ◽  
Stokes Formula ◽  
The Difference

AbstractTraditional gravimetric geoid determination relies on Stokes’ formula with removal and restoration of the topographic effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth’s surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator,which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes’ formula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals.

An analysis of the crust–mantle boundary in Hudson Bay from gravity and seismic observations

1968 ◽  
Vol 5 (5) ◽  
pp. 1297-1303 ◽  
Author(s):  
J. R. Weber ◽  
A. K. Goodacre
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Gravitational Effect ◽  
Compressional Wave ◽  
Seismic Survey ◽  
Hudson Bay ◽  
Mantle Boundary ◽  
Crustal Velocity ◽  
Velocity Variations ◽  
Crustal Density

A study of the results of the gravity and seismic surveys in Hudson Bay in 1965 has shown that the gravitational effect of a two-layer model based on the seismically determined depths has no correlation with the observed gravity anomalies. On the profile from Churchill to Povungnituk the gravity and seismic observations can be reconciled by postulating lateral variations of the acoustic compressional wave velocity within the crust. A crustal model has been calculated—using the same time-terms and the same mean crustal velocity—whose gravitational effect fits the observed gravity. The velocity varies from 6.15 to 6.56 km/s and the postulated depths are almost entirely within the confidence limits of the original model.In order to test the hypothesis, the postulated velocity variations have been compared with the lower refractor velocities of the shallow seismic survey, based on the assumption that the crustal velocities ought to be systematically higher than the crystalline surface velocities and that there may be a correlation between variations in crustal and surface velocities. The test is inconclusive because bottom refractor velocities are higher than crustal velocities in two areas where volcanic flows and high-velocity sediments may be present.The case of linearly related velocity (V) and density (ρ) variations has been analyzed and it is shown that the gravitational effect of the crust–mantle boundary undulations may be completely masked or even overbalanced by density changes in the crust if [Formula: see text]. The crust can be characterized by having dominant velocity variations (in which case the gravity anomaly reflects the undulations of the crust–mantle boundary) or dominant density variations (in which case the gravity anomaly inversely reflects the crust–mantle boundary undulations) depending on the relationship between average crustal density and average crustal velocity.

Regional‐residual gravity anomaly separation using the minimum‐curvature technique

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 279-283 ◽  
Author(s):  
K. L. Mickus ◽  
C. L. V. Aiken ◽  
W. D. Kennedy
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Bouguer Gravity ◽  
Bouguer Gravity Anomaly ◽  
Residual Gravity ◽  
Residual Gravity Anomaly ◽  
Gravity Interpretation ◽  
Minimum Curvature

One of the most difficult problems in gravity interpretation is the separation of regional and residual gravity anomalies from the Bouguer gravity anomaly. This study discusses the application of the minimum‐curvature method to determine the regional and residual gravity anomalies.

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