ACCURATE GRAVITY ANOMALY INTERPOLATION: A CASE-STUDY IN CAMEROON, CENTRAL AFRICA

J. Kamguia

Description

ABSTRACT
Many treatments in geodesy and geophysics require regularly gridded gravity anomalies. The gridding of gravity data needs interpolation. For the predicted data to be accurate, the smoothest type of gravity anomaly should be used along with the most indicated prediction method. This paper presents the comparison of various prediction methods applied on different types of gravity anomalies and considering the relative geological complexity of the study area. Many algorithms are tested and the suitability of each type of anomaly and each prediction method discussed in a case-study in Cameroon (Central Africa), using a set of 43,000 gravity data points to determine the must accurate prediction technique.
RESUMEN
Muchos tratamientos en geodesia y geofísica requieren que las anomalías gravimétricas se encuentren en grillas regulares. Esta disposición de los datos de gravedad requiere interpolación. Para que los datos predichos sean exactos, la anomalía gravimétrica más fina debe ser utilizada junto con el método más indicado para predicción.
Este artículo presenta la comparación de varios métodos de predicción aplicados a diversos tipos de anomalías gravimétricas y considerando la relativa complejidad geológica del área del estudio. Se probaron una gran cantidad de algoritmos y la conveniencia de cada tipo de de anomalía y método de predicción fueron discutidos en una aplicación en Camerún (África central), usando un conjunto de 43.000 datos gravimétricos para determinar la técnica de predicción más adecuada.

Sujets

• Prédiction
• Gravity anomaly
• Geophysics
• Predicción
• Geofísica

Informations

• Publié par: erevistas
• Publié le: 01 janvier 2007
• Nombre de lectures: 24
• Langue: English

Extrait

eArtH sciences
reseArcH JournAl
Earth Sci. Res. J. Vol. 11, No. 2 (December 2007): 108-116
AccurA te grA vity AnomAly interpolA tion: A cAse-study in
cAmeroon, centrAl AfricA
1 2 1 2 2J. Kamguia , c. t. tabod , J. m. tadjou , e. manguelle-dicoum , r. nouayou and l. H.
1Kande
1 National Institute of Cartography (NIC) – Cameroon, PO Box 157, Yaounde – Cameroon
2 Department of Physics, Faculty of Science, University of Yoon
Corresponding author: Joseph Kamguia: [e-mail]; [e-mail];
0023799440426
ABstrAct
Many treatments in geodesy and geophysics require regularly gridded gravity anomalies. The gridding
of gravity data needs interpolation. For the predicted data to be accurate, the smoothest type of
gravity anomaly should be used along with the most indicated prediction method. This paper presents
the comparison of various prediction methods applied on different types of gravity anomalies and
considering the relative geological complexity of the study area. Many algorithms are tested and
the suitability of each type of anomaly and each prediction method discussed in a case-study in
Cameroon (Central Africa), using a set of 43,000 gravity data points to determine the must accurate
prediction technique.
Key words: Prediction, Gravity anomaly, Residual free-air anomalies, Global geopotential model,
Complex geology, Geophysics.
resumen
Muchos tratamientos en geodesia y geofísica requieren que las anomalías gravimétricas se encuentren
en grillas regulares. Esta disposición de los datos de gravedad requiere interpolación. Para que los
datos predichos sean exactos, la anomalía gravimétrica más fna debe ser utilizada junto con el método
más indicado para predicción. Este artículo presenta la comparación de varios métodos de predicción
aplicados a diversos tipos de anomalías gravimétricas y considerando la relativa complejidad
geológica del área del estudio. Se probaron una gran cantidad de algoritmos y la conveniencia de
cada tipo de de anomalía y método de predicción fueron discutidos en una aplicación en Camerún
(África central), usando un conjunto de 43.000 datos gravimétricos para determinar la técnica de
predicción más adecuada..
Manuscript received July 15 2007.
Accepted for publication December 5 2007.

108ACCuRATE GRAVITy ANoMALy INTERPoLATIoN: A CASE-STuDy IN CAMERooN, CENTRAL AFRICA
Palabras claves: Predicción, Anomalía Gravimétrivca, Anomalías Residuales Libres de Aire, Modelo
Geopotencial Global, Geología Compleja, Geofísica.
introduction anomalies are now easily computed using the
spherical harmonic coeffcients of a global
Interpolation is a process widely used in geopotential model (GGM) (Kamguia et al.,
earth science. It estimates the value of a parameter 2007).
at a point from neighbourings. The process may This paper presents the results of
be extrapolation in some areas (Heiskanen and comparison of various types of gravity anomaly
Moritz, 1967). In Geodesy, gravity anomalies predicted with some methods commonly and in
are interpolated when computing geoid different areas of Cameroon. These anomalies
undulations or the quasi-geoid height anomalies. were computed from a homogeneous database
In Geophysics, prediction is used to compute containing 43,000 data points. The aim is to give
regular grids of gravity anomalies required for some hints as to the most appropriate gravity
presentation purposes or further treatments. The anomaly prediction strategy according to the
accuracy of the predicted gravity anomalies density of the gravity net, their geographical
depends mainly on their smoothness and on the distribution and the relative complexity of the
method used. It also depends the data density, geology of the study area. To achieve this, four
their geographical distribution and the grid areas with different geological characteristics
intervals. In general, the smoother the gravity are chosen. In these areas of different extension
anomalies, the more accurate the predicted and gravity net density, six prediction algorithms
values. Many interpolation methods are now are tested: the Minimum Curvature Splines in
proposed (El Abbas et al., 1990), with some Tension (Smith and Wessel, 1990); the Least
algorithms available in open sources such as the Square Polynomial Fitting (two variants);
Generic Mapping Tools or GMT (Wessel and Krigging (Krige, 1978) and the inverse distance
Smith, 1995). to a power method (two variants).
Comparisons have already been made
between surface ftting algorithms, in order to 2. Gravity anomaly prediction
check their reliability in predicting Bouguer
gravity anomalies (El Abbas et al., 1990). 2.1. Characteristics of gravity anomalies
However, many types of gravity anomalies are Different types of gravity anomaly are
routinely used in geodesy and in geophysics. It used in earth sciences. Gravity data recorded
may sometimes be diffcult to determine which on land must be adjusted for elevation above or
type is a priori suited for prediction. A constant below sea level to yield the free-air anomalies
crustal density value generally used in different (FAA). They are nearly equivalent to what
computations might be too far from the reality would be observed if all the topographic masses
below the earth topographic surface in complex were condensed onto this reference surface
geological areas. Residual anomalies that are (Blakely, 1996). Simple and complete Bouguer
deduced from free-air (FAA), simple Bouguer gravity anomalies (BA and CBA) are obtained
(BA), complete Bouguer (CBA) and isostatic by completely removing the masses that exist
(IA) anomalies might also be smoother than between the level of observation and sea level.
the original anomalies in some areas. These They are in theory smoother and then more

109Kamguia et al. ESRJ Vol. 11, No. 2. December 2007
(i) (ii)
Data point
Grid node with a reference point of gridded data
(i) Input data in gridding algorithms
(ii) Gridded cells waiting for gridded data at nodes
figure 1. Choice of reference points of gridded data
suitable for prediction than the FAA (Heiskanen (r, l ,q)constant; the spherical coordinates of
and Moritz, 1967). However, in complex gthe computation point; the normal gravity on
geological contexts, the gravity feld may have athe reference ellipsoid; the equatorial radius
special characteristics. Therefore, BA and CBA
P (sinq )nmof the earth; the fully normalized may be rougher than FAA. The isostatic reduction
nassociated Legendre functions for degree regularizes the earth’s crust according to a model
∆C ∆Sof isostasy. Depending on the complexity of the n m n mmand order ; and the normalized
geology of the study area, these anomalies may
EGM-GGM harmonic coeffcients, reduced for
be less or more suited in prediction processes
the even zonal for the ellipsoid and
than FAA, BA and CBA. N = 360maxcomplete to degree and order .
From spherical harmonic coeffcients
of global geopotential models (GGM), the long
2.2. Prediction of gravity anomalies and statistical
wavelength components of FAA, BA, CBA and
analysis
IA are easily computed. After subtraction from
The gravity is a regionalized feld, since
respective total feld gravity anomalies, the
it varies from place to place in a continuous
residual anomalies obtained may be smoother
manner but with no possibility of associating
in some areas. The long wavelength anomalies
a specifed mathematical function. The most ( ∆g)
GGM are computed from the harmonic
accurate gravity anomaly prediction technique is
coeffcients of the GGM using equation (1) and
the one that maintains the broad and fne features
subtracted from the total feld gravity anomalies
of the original gravity data processed, without
( ∆g) (Heiskanen and Moritz, 1967): introducing undue distortions. Therefore, the
nN max n predicted and the measured values must at the GM  a
g  (n1)Cc osm  S sinm P( s in )GGM  n m n m n m2 r r n2 m0 same point should be mathematically and/or
(1) physically related. To achieve this, the criterion
GMwhere is the geocentric gravitational of Crain and Bhattacharyya (1967) is important.

110ACCuRATE GRAVITy ANoMALy INTERPoLATIoN: A CASE-STuDy IN CAMERooN, CENTRAL AFRICA
To apply the criterion, some data points must be processes. Their selection is based on the
selected to serve as reference points (Fig. 1). A differences in geological characteristics, the
reference point is a data point with coordinates density and distribution of the data points, and
nearly coinciding with those of a grid node. the relative roughness of the topography relief
The predicted and known values are therefore of the area. The principal characteristics of these
comparable in a simple statistical analysis of areas are summarized in Table 2.
their differences.
Table 2: Characteristics of the four test areas
3. A case-study in Cameroon (Central Africa) Num ber of
Test area Data m ean densit ypoi ntsusedcont rolpoi nt s
2Z13  E    16  E ; 8  N    11  N1 2179 36 1 poi nt per 5 km
2Z13 E 