TERRAIN CORRECTIONS FOR AN INCLINED PLANE IN GRAVITY COMPUTATIONS

Geophysics ◽  
1958 ◽  
Vol 23 (4) ◽  
pp. 701-711 ◽  
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.

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

Geophysics ◽  
1981 ◽  
Vol 46 (7) ◽  
pp. 1054-1056 ◽  
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.

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

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1110-1115 ◽  
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.

EXTENDED TERRAIN CORRECTION TABLES FOR GRAVITY REDUCTIONS

Geophysics ◽  
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),

Gravity terrain corrections calculated using digital elevation models

Geophysics ◽  
1990 ◽  
Vol 55 (1) ◽  
pp. 102-106 ◽  
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.

scholarly journals Gravity terrain correction for mainland territory of Vietnam

2017 ◽  
Vol 17 (4B) ◽  
pp. 145-150
Author(s):  
Pham Nam Hung ◽  
Cao Dinh Trieu ◽  
Le Van Dung ◽  
Phan Thanh Quang ◽  
Nguyen Dac Cuong
Keyword(s):  
Gravity Data ◽  
Computing Time ◽  
Terrain Correction ◽  
Bouguer Gravity ◽  
Mountainous Region ◽  
Terrain Effect ◽  
Rugged Topography ◽  
Terrain Corrections ◽  
Gravity Map

Terrain corrections for gravity data are a critical concern in rugged topography, because the magnitude of the corrections may be largely relative to the anomalies of interest. That is also important to determine the inner and outer radii beyond which the terrain effect can be neglected. Classical methods such as Lucaptrenco, Beriozkin and Prisivanco are indeed too slow with radius correction and are not extended while methods based on the Nagy’s and Kane’s are usually too approximate for the required accuracy. In order to achieve 0.1 mGal accuracy in terrain correction for mainland territory of Vietnam and reduce the computing time, the best inner and outer radii for terrain correction computation are 2 km and 70 km respectively. The results show that in nearly a half of the Vietnam territory, the terrain correction values ≥ 10 mGal, the corrections are smaller in the plain areas (less than 2 mGal) and higher in the mountainous region, in particular the correction reaches approximately 21 mGal in some locations of northern mountainous region. The complete Bouguer gravity map of mainland territory of Vietnam is reproduced based on the full terrain correction introduced in this paper.

TERRAIN CORRECTIONS FOR GRAVIMETER STATIONS

Geophysics ◽  
1939 ◽  
Vol 4 (3) ◽  
pp. 184-194 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Gravitational Effect ◽  
Relative Accuracy ◽  
Terrain Correction ◽  
Gravitational Attraction ◽  
Gravity Station ◽  
Terrain Corrections ◽  
Instrumental Precision

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.

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

Geophysics ◽  
1980 ◽  
Vol 45 (1) ◽  
pp. 109-112 ◽  
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.

Gravity modeling of the volcanic island of Surtsey, Iceland

2020 ◽  
Author(s):  
Sara Sayyadi ◽  
Magnús T.Gudmundsson ◽  
Thórdís Högnadóttir ◽  
James White ◽  
Marie D. Jackson
Keyword(s):  
Sedimentary Rocks ◽  
Thin Layers ◽  
Gravity Modeling ◽  
Minor Components ◽  
Scientific Drilling ◽  
Gravity Station ◽  
Effusive Activity ◽  
Terrain Corrections ◽  
Lapilli Tuff ◽  
Additional Formation

<p>The formation of the oceanic island Surtsey in the shallow ocean off the south coast of Iceland in 1963-1967 remains one of the best-studied examples of basaltic emergent volcanism to date. The island was built by both explosive, phreatomagmatic phases and by effusive activity forming lava shields covering parts of the explosively formed tuff cones.   A detailed gravity survey was carried out on Surtsey in July 2014 with a gravity station spacing of ~100 m.  We analyse these data in order to refine a 2.5D-structural and density model of the internal structure for this type locality of Surtseyan volcanism.  We carry out a complete Bouguer correction of these data using total terrain corrections based on detailed DEMs of the island and the submarine bathymetry.  The principal components of the island are the two tuff cones composed principally of lapilli tuff; this was originally phreatomagmatic tephra formed in the explosive phases of the eruption. Lapilli tuff can be subdivided into (1) submarine lapilli tuff and (2) lapilli tuff above sea level. Other units are (3) subaerial lava, and (4) subaqueous lava deltas. Minor components that are volumetrically insignificant are small intrusions, and unconsolidated and unaltered tephra, still found in thin layers flanking the tuff cones.  An additional formation, relevant for any analysis of the subsurface structure of Surtsey, is (5) the sedimentary rocks making up the seafloor, being at least 100 m thick but probably much thicker.  Using measurements of the density of all the above components, and subdividing the island into different units based on its pattern of growth, we specifically attempt to constrain the width and depth of diatreme structures proposed by Moore (1985) and confirmed in the ICDP SUSTAIN drilling of Surtsey in 2017 (Jackson et al., 2019).  Our forward modeling is aided by a detailed subdivision of the island into units (1) to (4) based on repeated mapping of the island during 1964-1967.</p><p> </p><p>Moore, J. G., 1985, Geological Magazine 122, 649–661</p><p>Jackson, M. D., et al. 2019, Scientific Drilling 25, 35–46.</p>

THE USE OF NONLINEAR FUNCTIONAL EXPANSIONS IN CALCULATION OF THE TERRAIN EFFECT IN AIRBORNE AND MARINE GRAVIMETRY AND GRADIOMETRY

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Leroy M. Dorman ◽  
Brian T. R. Lewis
Keyword(s):  
Exact Result ◽  
Expansion Method ◽  
Gravity Gradient ◽  
Nonlinear Functional ◽  
Expansion Technique ◽  
Nonlinear Functionals ◽  
Terrain Effect ◽  
Convolution Kernels ◽  
Terrain Corrections ◽  
Expansion Coefficients

The terrain corrections for gravity and gravity gradient data are nonlinear functionals of the surrounding topography. We show how to approximate these corrections by use of Volterra‐Wiener functional expansion, which is a sum of linear convolutions using the topography, the square of the topography, etc. The convolution kernels are like Taylor expansion coefficients which depend upon the distance from the source point to the field point. As an example, we compute the field [Formula: see text] for a two‐dimensional ridge by the expansion method and compare the result with the exact result. We then show how the expansion technique can be used to propagate statistical properties through nonlinear functionals. As an example of this, we compute the rms terrain correction for [Formula: see text] as a function of the flight elevation and terrain relief.

A sloping wedge technique for calculating gravity terrain corrections

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1061-1063 ◽  
Author(s):  
L. J. Barrows ◽  
J. D. Fett
Keyword(s):  
High Precision ◽  
Field Data ◽  
Open Space ◽  
Gravity Station ◽  
Topographic Features ◽  
Original Field ◽  
Rugged Topography ◽  
Terrain Corrections ◽  
Wedge Technique

Gravity terrain corrections account for the upward pull of topographic features which are higher than a gravity station (hills) and the lack of downward pull from open space which is lower than the station (valleys). In areas of rugged topography or in high precision surveys, the magnitude of the terrain corrections can be comparable to the anomalies being sought and the uncertainties in the terrain corrections can limit the accuracy of the survey. Also, calculating the corrections can require more time and effort than gathering the original field data. Even if terrain corrections are not made, it is necessary to show that their omission does not compromise the integrity of the survey.

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