TERRAIN CORRECTIONS FOR GRAVIMETER STATIONS

In this paper the correction for the gravitational attraction of the topography on a gravity station is considered as consisting of two parts; (1) the restricted but conventional “Bouguer correction” which postulates as a convenient approximation that the topography consists of an infinite horizontal plain, and (2) the “Terrain correction” which is a supplementary correction taking into account the gravitational effect of the undulations of the terrain about the plane through the gravity station. The paper illustrates the necessity of making terrain corrections if precise gravity surveys are desired in hilly country and presents terrain correction tables with which this quantity may be determined to a relative accuracy of one‐tenth milligal. This accuracy is required to fully utilize the high instrumental precision of modern gravimeters.

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THE GRAVITATIONAL ATTRACTION OF A RIGHT RECTANGULAR PRISM

Geophysics ◽

10.1190/1.1439779 ◽

1966 ◽

Vol 31 (2) ◽

pp. 362-371 ◽

Cited By ~ 292

Author(s):

Dezsö Nagy

Keyword(s):

Gravity Field ◽

Dimensional Analysis ◽

Three Dimensional ◽

Vertical Component ◽

Gravitational Effect ◽

Rectangular Prism ◽

Gravitational Attraction ◽

Closed Expression ◽

Building Element ◽

Terrain Corrections

The derivation of a closed expression is presented to calculate the vertical component of the gravitational attraction of a right rectangular prism, with sides parallel to the coordinate axis. As any configuration can be expressed as the sum of prisms of various sizes and densities, the computation of the total gravitational effect of bodies of arbitrary shapes at any point outside of or on the boundary of the bodies is straightforward. To calculate the gravitational effect of the “unit” building element a subroutine called Prism has been developed, tested, and incorporated, in one program to calculate terrain corrections, and in another program for three‐dimensional analysis of a gravity field.

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Improvement of the conic prism model for terrain correction in rugged topography

Geophysics ◽

10.1190/1.1441243 ◽

1981 ◽

Vol 46 (7) ◽

pp. 1054-1056 ◽

Cited By ~ 13

Author(s):

Raymond J. Olivier ◽

Réjean G. Simard

Keyword(s):

Gravity Anomalies ◽

Terrain Correction ◽

Field Calculation ◽

Bouguer Gravity ◽

New Model ◽

Gravity Station ◽

Rugged Terrain ◽

Rugged Topography ◽

Terrain Corrections ◽

Prism Model

Terrain corrections for Bouguer gravity anomalies are generally obtained from topographic models represented by flat‐topped compartments of circular zones, utilizing the so‐called Hayford‐Bowie (1912), or Hammer’s (1939) method. Some authors have introduced improved relief models for taking uniform slope into consideration (Sandberg, 1958; Kane, 1962; Takin and Talwani, 1966; Campbell, 1980). We present a new model that increases the accuracy of the calculation of terrain correction close to the gravity station in rugged terrain, especially when conventional templates with few zones are used in field calculation.

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A method to compute terrain corrections for gravimeter stations using a digital elevation model

Geophysics ◽

10.1190/1.1487059 ◽

2001 ◽

Vol 66 (4) ◽

pp. 1110-1115 ◽

Cited By ~ 11

Author(s):

J. Garca‐Abdeslem ◽

B. Martn‐Atienza

Keyword(s):

Numerical Methods ◽

Digital Elevation Model ◽

Mass Density ◽

Model Solution ◽

Gravitational Attraction ◽

Gravity Effect ◽

Gravity Station ◽

Digital Elevation ◽

Terrain Corrections ◽

Elevation Model

A description is given of a method to compute the terrain corrections for a gravity survey using a digital elevation model. This method is based upon a new forward model solution to compute the gravity effect due to a rectangular prism of uniform mass density that is flat at its base but has a nonflat top. The gravitational attraction of such a prism is evaluated at the gravity station locations by combining analytic and numerical methods of integration. Two simple synthetic examples are provided that show the accuracy of this numerical method, and its performance is illustrated in a field example.

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Gravity terrain corrections for stations on a uniform slope—A power law approximation

Geophysics ◽

10.1190/1.1441035 ◽

1980 ◽

Vol 45 (1) ◽

pp. 109-112 ◽

Cited By ~ 6

Author(s):

David L. Campbell

Keyword(s):

Power Law ◽

Terrain Correction ◽

Gravity Station ◽

Rule Of Thumb ◽

Terrain Corrections ◽

Special Case ◽

Hand Calculator

A hand calculator program for gravity terrain corrections should include functions to (1) calculate the standard terrain correction due to topography of constant elevation throughout a given sector of a terrain correction graticule, and (2) calculate the terrain correction due to topography that slopes uniformly throughout the graticule sector. Equations for function (1) and for a special case of function (2) were given by Hammer (1939). Hammer’s equation covers the useful case where the uniform slope extends in azimuth a full 360 degrees around the gravity station. Using this equation, Sandburg (1958) published tables of gravity terrain corrections for stations on complete (360 degree) uniform slopes of slope angles 0 degrees to 30 degrees. This note points out that Hammer’s equation, as well as the corresponding equation for the incomplete uniform slope (one extending under a single graticule sector only), may both be approximated by a square‐power law. The resulting forms are particularly convenient for hand calculator use. A particular application gives a new rule of thumb for estimating Hammer inner‐zone terrain corrections.

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Necessity of Terrain Correction in Magnetotelluric Data Recorded from Garhwal Himalayan Region, India

Geosciences ◽

10.3390/geosciences11110482 ◽

2021 ◽

Vol 11 (11) ◽

pp. 482

Author(s):

Dharmendra Kumar ◽

Arun Singh ◽

Mohammad Israil

Keyword(s):

Real Data ◽

Terrain Correction ◽

Himalayan Region ◽

General Character ◽

Period Range ◽

Magnetotelluric Data ◽

Heterogeneous Models ◽

Corrected Data ◽

Terrain Corrections ◽

And Inversion

The magnetotelluric (MT) method is one of the useful geophysical techniques to investigate deep crustal structures. However, in hilly terrains, e.g., the Garhwal Himalayan region, due to the highly undulating topography, MT responses are distorted. Such responses, if not corrected, may lead to the incorrect interpretation of geoelectric structures. In the present paper, we implemented terrain corrections in MT data recorded from the Garhwal Himalayan Corridor (GHC). We used AP3DMT, a 3D MT data modeling and inversion code written in the MATLAB environment. Terrain corrections in the MT impedance responses for 39 sites along the Roorkee–Gangotri profile in the period range of 0.01 s to 1000 s were first estimated using a synthetic model by recording the topography and locations of MT sites. Based on this study, we established the general character of the terrain and established where terrain corrections were necessary. The distortion introduced by topography was computed for each site using homogenous and heterogeneous models with actual topographic variations. Period-dependent, galvanic and inductive distortions were observed at different sites. We further applied terrain corrections to the real data recorded from the GHC. The corrected data were inverted, and the inverted model was compared with the corresponding inverted model obtained with uncorrected data. The modification in electrical resistivity features in the model obtained from the terrain-corrected response suggests the necessity of terrain correction in MT data recorded from the Himalayan region.

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TERRAIN CORRECTIONS FOR AN INCLINED PLANE IN GRAVITY COMPUTATIONS

Geophysics ◽

10.1190/1.1438517 ◽

1958 ◽

Vol 23 (4) ◽

pp. 701-711 ◽

Cited By ~ 12

Author(s):

C. H. Sandberg

Keyword(s):

Inclined Plane ◽

Gravity Station ◽

Terrain Effect ◽

Terrain Corrections ◽

Inclined Planes

In many instances an inclined‐plane approximation represents more accurately the terrain near a gravity station than does the conventional block‐cylinder approximation. Combinations of the terrain effect of inclined planes through various terrain zones, as represented in the accompanying tables, can be used to approximate easily and quickly such familiar land forms as valleys, ridges, and hillsides.

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TERRAIN CORRECTIONS FOR BOREHOLE GRAVIMETRY

Geophysics ◽

10.1190/1.1439936 ◽

1968 ◽

Vol 33 (2) ◽

pp. 361-362 ◽

Cited By ~ 5

Author(s):

J. R. Hearst

Keyword(s):

First Principles ◽

Surface Density ◽

Gravitational Constant ◽

Terrain Correction ◽

Correction Formula ◽

Free Air ◽

Terrain Corrections

The measurement of in‐situ density by borehole gravimetry has now become a commonly accepted, if not commonly used, practice (McCulloh, 1965, 1967; Howell et al., 1966; Hammer 1950). The expression for density as a function of gravity difference at two depths is given in a general form by McCulloh (1967) as [Formula: see text] [Formula: see text] where ρ is the density, F the free air gradient, [Formula: see text] the measured gravity difference between two depths, [Formula: see text] a correction for the effect of sub surface density differences (according to McCulloh, generally negligible), [Formula: see text] the terrain correction, [Formula: see text] a borehole correction, and k the gravitational constant. This equation can be obtained from first principles using Gauss’ law.

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EXTENDED TERRAIN CORRECTION TABLES FOR GRAVITY REDUCTIONS

Geophysics ◽

10.1190/1.1440266 ◽

1972 ◽

Vol 37 (2) ◽

pp. 377-379

Author(s):

Jesse K. Douglas ◽

Sidney R. Prahl

Keyword(s):

Computer Program ◽

Rocky Mountain ◽

Terrain Correction ◽

Western Montana ◽

Inclined Plane ◽

Plane Model ◽

Mountain Area ◽

Terrain Corrections

This note extends the gravity terrain corrections for elevation differences beyond the tables originally published by Hammer (1939). Experience in the Rocky Mountain area has demonstrated to us the need for such an extension. The frustration encountered by the authors led to a computer program to calculate the terrain correction tables presented in this article. The mountain topography in western Montana is typical of an area not sufficiently regular to allow use of the less tedious inclined‐plane model presented by Sandberg (1958). The inclined‐plane and the cylinder models are designed for calculating the effects of local terrain and do not include a correctional factor for earth curvature. Large regional surveys require the Hayford‐ Bowie terrain correction zones. However, local surveys can be easily incorporated into these larger studies by Hammer to Hayford‐Bowie transition tables (Sandberg, 1959),

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Gravity terrain corrections calculated using digital elevation models

Geophysics ◽

10.1190/1.1442762 ◽

1990 ◽

Vol 55 (1) ◽

pp. 102-106 ◽

Cited By ~ 24

Author(s):

Allen H. Cogbill

Keyword(s):

High Precision ◽

The Other ◽

Mountainous Areas ◽

Data Set ◽

Gravity Station ◽

Digital Terrain ◽

Terrain Effects ◽

Digital Elevation ◽

Gravity Measurements ◽

Terrain Corrections

Corrections for terrain effects are required for virtually all gravity measurements acquired in mountainous areas, as well as for high‐precision surveys, even in areas of low relief. Terrain corrections are normally divided into two parts, one part being the correction for terrain relatively close to the gravity station (the “inner‐zone” correction) and the other part being the correction for more distant, say, >2 km, terrain. The latter correction is normally calculated using a machine procedure that accesses a digital‐terrain data set. The corrections for terrain very close to the gravity station are done manually using Hammer’s (1939) procedures or a similar method, are guessed in the field, or simply are neglected. Occasionally, special correction procedures are used for the inner‐zone terrain corrections (e.g., LaFehr et al., 1988); but such instances are uncommon.

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Critique of terrain corrections for gravity stations

Geophysics ◽

10.1190/1.1441352 ◽

1982 ◽

Vol 47 (5) ◽

pp. 839-840 ◽

Cited By ~ 12

Author(s):

Sigmund Hammer

Keyword(s):

Radial Distance ◽

Terrain Correction ◽

Recent Issue ◽

Correction Problem ◽

Terrain Corrections ◽

Explicit Discussion

The terrain correction problem for gravity stations continues to attract perennial interest. Since the publication of Hayford and Bowie’s method (1912) and Hammer’s detailed tables (1939), no fewer than 35 papers have reported changes and improvements (in various languages, including Russian) the latest by Olivier and Simard (1981) in a recent issue of Geophysics. However, in none of these papers is there explicit discussion of the weighting for topography within the radial distance across a topographic compartment. This is not a negligible factor, especially for inner topographic zones.

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