GRAVITY INTERPRETATION USING THE FOURIER INTEGRAL

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Mark E. Odegard ◽  
Joseph W. Berg
Keyword(s):  
Frequency Domain ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Fourier Integral ◽  
Numerical Techniques ◽  
Functional Representations ◽  
Gravity Interpretation ◽  
Mathematical Relations ◽  
Gravitational Anomalies

The gravitational anomalies of simple bodies (sphere, cylinder, and fault) were used to develop methods for analyzing gravity data in the frequency domain. The Fourier transforms of the functional representations of the theoretical gravitational anomalies of these bodies were obtained. Mathematical relations were formulated between the transform‐versus‐frequency relationships and the depths and sizes of the bodies. Compound gravity anomalies (multiple cylinders, fault, and cylinder) were analyzed, and the transforms were reduced to transforms of anomalies due to individual simple bodies. These methods of analysis were applied to theoretical anomalies using numerical techniques, and the accuracy of both depth and size determinations was within a few percent in all cases.

Gravity interpretation using Fourier transforms and simple geometrical models with exponential density contrast

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1074-1083 ◽  
Author(s):  
D. Bhaskara Rao ◽  
M. J. Prakash ◽  
N. Ramesh Babu
Keyword(s):  
Los Angeles ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Model Parameters ◽  
Exponential Density ◽  
Exponential Density Contrast ◽  
Gravity Interpretation

The decrease of density contrast in sedimentary basins can often be approximated by an exponential function. Theoretical Fourier transforms are derived for symmetric trapezoidal, vertical fault, vertical prism, syncline, and anticline models. This is desirable because there are no equivalent closed form solutions in the space domain for these models combined with an exponential density contrast. These transforms exhibit characteristic minima, maxima, and zero values, and hence graphical methods have been developed for interpretation of model parameters. After applying end corrections to improve the discrete transforms of observed gravity data, the transforms are interpreted for model parameters. This method is first tested on two synthetic models, then applied to gravity anomalies over the San Jacinto graben and Los Angeles basin.

THE EFFECT OF FINITE DATA LENGTH IN THE SPECTRAL ANALYSIS OF IDEAL GRAVITY ANOMALIES

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 44-55 ◽  
Author(s):  
Robert D. Regan ◽  
William J. Hinze
Keyword(s):  
Spectral Analysis ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Transformation Process ◽  
Definition Of ◽  
Horizontal Cylinders ◽  
Data Windows ◽  
Source Of Error ◽  
Data Length

The interpretation of gravity data which has been transformed from the space domain to the frequency domain is subject to limitations imposed by the transformation process and the nature of the data. One potential source of error in the spectral analysis of gravity anomalies is the incomplete definition of the anomaly due to insufficient data length. Comparison of theoretical Fourier transforms and the transforms of finite‐length segments of gravity anomalies due to two‐dimensional vertical slabs and horizontal cylinders indicates that the interpretation error can be held to less than ten percent if the profile length is at least six times the maximum depth to the source of the anomaly. This result was achieved with a rectangular data window in the transformation process. Greater error resulted from the use of the Bartlett, Parzen, and Tukey data windows.

On: “Gravity Interpretation using the Fourier Integral” by J. W. Berg, Jr., and M. E. Odegard (GEOPHYSICS, vol. 30, no. 3, p. 424–438, June 1965)

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 358-358 ◽  
Author(s):  
H. A. Meinardus
Keyword(s):  
Fourier Transform ◽  
Gravity Anomalies ◽  
Fourier Integral ◽  
Hankel Transform ◽  
Cylindrical Symmetry ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Gravity ◽  
The One ◽  
Gravity Interpretation

The authors do not state explicitly that equations (1) and (12) express gravity anomalies of the two‐dimensional cylinder and fault respectively. These structures have an infinite extension along the strike, and all the gravity profiles perpendicular to the strike are identical. For this reason it is admissible to apply the one‐dimensional Fourier transform to obtain the one‐dimensional amplitude spectra shown in Figures (1) and (5). The situation, however, is different for the sphere, which does not have a one‐dimensional gravity profile in the above sense, but rather a two‐dimensional field with cylindrical symmetry. Instead of using the one‐dimensional Fourier transform as given by (6) along a straight line, we must apply the two‐dimensional Fourier transform over the whole area. Because of the circular symmetry, one radial variable will suffice in place of the two Cartesian coordinates x and y, and the two‐dimensional Fourier transform can be expressed as Hankel transform, so that equation (6) becomes [Formula: see text]

scholarly journals Joint Gravity and Seismic Reflection Methods to Characterize the Deep Aquifers in Arid Ain El Beidha Plain (Central Tunisia, North Africa)

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1310
Author(s):  
Hajer Azaiez ◽  
Hakim Gabtni ◽  
Mourad Bédir
Keyword(s):  
Seismic Reflection ◽  
Large Scale ◽  
Seismic Analysis ◽  
Gravity Data ◽  
Geophysical Methods ◽  
Gravity Anomalies ◽  
Integrated Approach ◽  
Central Tunisia ◽  
Deep Aquifers ◽  
Advanced Analysis

Electric resistivity sounding and tomography, as well as electromagnetic sounding, are the classical methods frequently used for hydrogeological studies. In this work, we propose the development and implementation of an original integrated approach using the unconventional hydro–geophysical methods of gravity and seismic reflection for the fast, large–scale characterization of hydrogeological potential using the Ain El Beidha plain (central Tunisia) as an analogue. Extending the values of vintage petroleum seismic reflection profiles and gravity data, in conjunction with available geological and hydrogeological information, we performed an advanced analysis to characterize the geometry of deep tertiary (Oligocene and Eocene) aquifers in this arid area. Residual and tilt angle gravity maps revealed that most gravity anomalies have a short wavelength. The study area was mainly composed of three major areas: the Oued Ben Zitoun and Ain El Beidha basins, which are both related to negative gravity trends corresponding to low–density subsiding depocenters. These basins are separated by an important NE–SW trend called “El Gonna–J. El Mguataa–Kroumet Zemla” gravity high. Evaluation of the superposition of detected lineaments and Euler deconvolution solutions’ maps showed several NE–SW and N–S relay system faults. The 3D density inversion model using a lateral and vertical cutting plane suggested the presence of two different tectonic styles (thin VS thick). Results from the gravity analysis were in concordance with the seismic analysis. The deep Oligocene and Eocene seismic horizons were calibrated to the hydraulic wells and surrounding outcrops. Oligocene and Eocene geological reservoirs appear very fractured and compartmented. The faulting network also plays an important role in enhancing groundwater recharge process of the Oligocene and Eocene aquifers. Finally, generated isochron maps provided an excellent opportunity to develop future comprehensive exploration surveys over smaller and more favorable areas’ sub–basins.

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 Basement Mapping of the Fucino Basin in Central Italy by ITRESC Modeling of Gravity Data

Geosciences ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 398
Author(s):  
Federico Cella ◽  
Rosa Nappi ◽  
Valeria Paoletti ◽  
Giovanni Florio
Keyword(s):  
Seismic Activity ◽  
Site Response ◽  
Gravity Data ◽  
A Priori ◽  
Central Italy ◽  
Gravity Anomalies ◽  
Gravity Modeling ◽  
Ground Shaking ◽  
Sedimentary Evolution ◽  
Fucino Basin

Sediments infilling in intermontane basins in areas with high seismic activity can strongly affect ground-shaking phenomena at the surface. Estimates of thickness and density distribution within these basin infills are crucial for ground motion amplification analysis, especially where demographic growth in human settlements has implied increasing seismic risk. We employed a 3D gravity modeling technique (ITerative RESCaling—ITRESC) to investigate the Fucino Basin (Apennines, central Italy), a half-graben basin in which intense seismic activity has recently occurred. For the first time in this region, a 3D model of the Meso-Cenozoic carbonate basement morphology was retrieved through the inversion of gravity data. Taking advantage of the ITRESC technique, (1) we were able to (1) perform an integration of geophysical and geological data constraints and (2) determine a density contrast function through a data-driven process. Thus, we avoided assuming a priori information. Finally, we provided a model that honored the gravity anomalies field by integrating many different kinds of depth constraints. Our results confirmed evidence from previous studies concerning the overall shape of the basin; however, we also highlighted several local discrepancies, such as: (a) the position of several fault lines, (b) the position of the main depocenter, and (c) the isopach map. We also pointed out the existence of a new, unknown fault, and of new features concerning known faults. All of these elements provided useful contributions to the study of the tectono-sedimentary evolution of the basin, as well as key information for assessing the local site-response effects, in terms of seismic hazards.

scholarly journals DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

2021 ◽  
Vol 6 (24) ◽  
pp. 213-225
Author(s):  
Shazad Jamal Jalal ◽  
Tajul Ariffin Musa ◽  
Ami Hassan Md Din ◽  
Wan Anom Wan Aris
Keyword(s):  
Gravity Data ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Gravity Survey ◽  
Mountainous Areas ◽  
Entire Study ◽  
Terrestrial Gravity ◽  
The Past ◽  
Regional Gravity ◽  
Entire Study Area

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

scholarly journals Structural model of the Northern Latium volcanic area constrained by MT, gravity and aeromagnetic data

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
P. Capuano ◽  
G. Florio ◽  
P. Gasparini
Keyword(s):  
Structural Model ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Volcanic Area ◽  
Aeromagnetic Data ◽  
Geothermal Exploration ◽  
Magnetotelluric Soundings ◽  
Aeromagnetic Anomalies ◽  
Deep Boreholes

The results of about 120 magnetotelluric soundings carried out in the Vulsini, Vico and Sabatini volcanic areas were modeled along with Bouguer and aeromagnetic anomalies to reconstruct a model of the structure of the shallow (less than 5 km of depth) crust. The interpretations were constrained by the information gathered from the deep boreholes drilled for geothermal exploration. MT and aeromagnetic anomalies allow the depth to the top of the sedimentary basement and the thickness of the volcanic layer to be inferred. Gravity anomalies are strongly affected by the variations of morphology of the top of the sedimentary basement, consisting of a Tertiary flysch, and of the interface with the underlying Mesozoic carbonates. Gravity data have also been used to extrapolate the thickness of the neogenic unit indicated by some boreholes. There is no evidence for other important density and susceptibility heterogeneities and deeper sources of magnetic and/or gravity anomalies in all the surveyed area.

scholarly journals New insights on the dynamics of the Sumatra and Mariana complexes inferred from the comparative analysis of gravity data and model predictions

2020 ◽  
Author(s):  
Arcangela Bollino ◽  
Anna Maria Marotta ◽  
Federica Restelli ◽  
Alessandro Regorda ◽  
Roberto Sabadini
Keyword(s):  
Comparative Analysis ◽  
Gravity Field ◽  
Wide Spectrum ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Phase Changes ◽  
Wide Range ◽  
Model Predictions ◽  
Dip Angle ◽  
The Masses

&lt;p&gt;Subduction is responsible for surface displacements and deep mass redistribution. This rearrangement generates density anomalies in a wide spectrum of wavelengths which, in turn, causes important anomalies in the Earth's gravity field that are visible as lineaments parallel to the arc-trench systems. In these areas, when the traditional analysis of the deformation and stress fields is combined with the analysis of the perturbation of the gravity field and its slow time variation, new information on the background environment controlling the tectonic loading phase can be disclosed.&lt;/p&gt;&lt;p&gt;Here we present the results of a comparative analysis between the geodetically retrieved gravitational anomalies, based on the EIGEN-6C4 model, and those predicted by a 2D thermo-chemical mechanical modeling of the Sumatra and Mariana complexes.&lt;/p&gt;&lt;p&gt;The 2D model accounts for a wide range of parameters, such as the convergence velocity, the shallow dip angle, the different degrees of coupling between the facing plates. The marker in cell technique is used to compositionally differentiate the system. Phase changes in the crust and in the mantle and mantle hydration are also allowed. To be compliant with the geodetic EIGEN-6C4 gravity data, we define a model normal Earth considering the vertical density distribution at the margins of the model domain, where the masses are not perturbed by the subduction process.&lt;/p&gt;&lt;p&gt;Model predictions are in good agreement with data, both in terms of wavelengths and magnitude of the gravity anomalies measured in the surroundings of the Sumatra and Marina subductions. Furthermore, our modeling supports that the differences in the style of the gravity anomaly observed in the two areas are attributable to the different environments &amp;#8211; ocean-ocean or ocean-continental subduction &amp;#8211; that drives a significantly different dynamic in the wedge area.&lt;/p&gt;

scholarly journals Grid preparation for magnetic and gravity data using fractal fields

2012 ◽  
Vol 19 (2) ◽  
pp. 291-296 ◽  
Author(s):  
M. Pilkington ◽  
P. Keating
Keyword(s):  
Potential Field ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Fractal Model ◽  
Data Sets ◽  
Spectral Character ◽  
Aeromagnetic Survey ◽  
Fractal Method ◽  
Gravity Measurements ◽  
Interpretive Method

Abstract. Most interpretive methods for potential field (magnetic and gravity) measurements require data in a gridded format. Many are also based on using fast Fourier transforms to improve their computational efficiency. As such, grids need to be full (no undefined values), rectangular and periodic. Since potential field surveys do not usually provide data sets in this form, grids must first be prepared to satisfy these three requirements before any interpretive method can be used. Here, we use a method for grid preparation based on a fractal model for predicting field values where necessary. Using fractal field values ensures that the statistical and spectral character of the measured data is preserved, and that unwanted discontinuities at survey boundaries are minimized. The fractal method compares well with standard extrapolation methods using gridding and maximum entropy filtering. The procedure is demonstrated on a portion of a recently flown aeromagnetic survey over a volcanic terrane in southern British Columbia, Canada.

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