Critique of terrain corrections for gravity stations

Geophysics ◽  
1982 ◽  
Vol 47 (5) ◽  
pp. 839-840 ◽  
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.

A note on airborne gravity terrain corrections

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 396-399 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Essential Feature ◽  
Terrain Correction ◽  
Airborne Gravity ◽  
Narrow Beam ◽  
Contour Map ◽  
General Behavior ◽  
Topographic Information ◽  
Correction Problem ◽  
Terrain Corrections ◽  
Square Array

Terrain corrections for airborne gravity surveying have been a cause of some concern in the exploration industry (Hammer, 1974). Some skepticism still persists that the problem may be troublesome. As a matter of fact, an essential feature of the present field procedure in airborne gravity surveying is to make observations in a more or less square array of intersecting lines, along which narrow beam radar recordings of the terrain clearance provide topographic information to calculate the terrain corrections (Navazio and Gumert, 1981). In addition, this yields a topographic contour map of the area which is very useful for many other purposes. What has not been generally appreciated is that taking observations in the air, at some distance above the topography, actually is a major advantage with respect to the terrain corrections. The magnitude and general behavior of the terrain correction problem in airborne gravity is demonstrated herein by very simple simulated calculations.

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

Geosciences ◽  
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.

TERRAIN CORRECTIONS FOR BOREHOLE GRAVIMETRY

Geophysics ◽  
1968 ◽  
Vol 33 (2) ◽  
pp. 361-362 ◽  
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.

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.

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),

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.

Airborne gravity gradiometry: Terrain corrections and elevation error

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. I37-I42 ◽  
Author(s):  
Mark Dransfield ◽  
Yi Zeng
Keyword(s):  
Power Law ◽  
Data Interpretation ◽  
Relative Magnitude ◽  
Terrain Correction ◽  
Flying Height ◽  
Airborne Gravity ◽  
Gravity Gradiometry ◽  
Correction Error ◽  
Terrain Corrections ◽  
Airborne Gravity Gradiometry

Terrain corrections for airborne gravity gradiometry data are calculated from a digital elevation model (DEM) grid. The relative proximity of the terrain to the gravity gradiometer and the relative magnitude of the density contrast often result in a terrain correction that is larger than the geologic signal of interest in resource exploration. Residual errors in the terrain correction can lead to errors in data interpretation. Such errors may emerge from a DEM that is too coarsely sampled, errors in the density assumed in the calculations, elevation errors in the DEM, or navigation errors in the aircraft position. Simple mathematical terrains lead to the heuristic proposition that terrain-correction errors from elevation errors in the DEM are linear in the elevation error but follow an inverse power law in the ground clearance of the aircraft. Simulations of the effect of elevation error on terrain-correction error over four measured DEMs support this proposition. This power-law relation may be used in selecting an optimum survey flying height over a known terrain, given a desired terrain-correction error.

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.

scholarly journals Fast-Fourier-based error propagation for the gravimetric terrain correction

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. G71-G76 ◽  
Author(s):  
J. C. McCubbine ◽  
W. E. Featherstone ◽  
J. F. Kirby
Keyword(s):  
Digital Elevation Model ◽  
Error Propagation ◽  
Terrain Correction ◽  
Mathematical Framework ◽  
Model Errors ◽  
Spatially Correlated ◽  
Digital Elevation ◽  
Australian Continent ◽  
Terrain Corrections ◽  
Elevation Model

We have identified a gap in the literature on error propagation in the gravimetric terrain correction. Therefore, we have derived a mathematical framework to model the propagation of spatially correlated digital elevation model errors into gravimetric terrain corrections. As an example, we have determined how such an error model can be formulated for the planar terrain correction and then be evaluated efficiently using the 2D Fourier transform. We have computed 18.3 billion linear terrain corrections and corresponding error estimates for a 1 arc-second ([Formula: see text]) digital elevation model covering the whole of the Australian continent.

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