Different types of gravity prediction methods for local and regional gravity evaluation are developed, tested, and compared. Four different test areas were particularly selected in view of different prediction requirements. Also different parts of the spectrum of the gravity field were considered

Becker, M.

Euler, H.-J.

Groten, E.

Hausch, W.

Kling, TH.

English

NASA Technical Reports Server

N9o- o53 
The Use of High-Resolution Terrain Data in Gravity Field Prediction
E. Groten, M. Becker, H.-J. Euler, W. Hausch, Th. Kling
Institut fur Physikalische Geod_sie, Technische Hochschule Darmstadt,
F.R.G.
A_STRACT
The aim of this paper is to develop, test and, to some extent, compare
different types of gravity prediction methods for local and regional gra-
vity evaluation. Four different test areas have particularly been selected
in view of different prediction requirements. Also different parts of the
spectrum of the gravity field were considered.
I. INTRODUCTION
From modern seismic tomography and other results it is known that
lateral density variations have been underestimated in the past. Conse-
quently, gravity variations at the surface of the earth are difficult to
predict. On the other hand, modern photogrammetric and altimetric measure-
ments give way to very detailed models of the terrain for estimating
gravity in continental areas. Four different areas were selected in order
to test various aspects of regional and local gravity modeling. Different
mathematical tools have been used in order to test their ability to predict
gravity under various conditions.
2. DESCRIPTION OF PREDICTION TESTS
Test area one comprises a 500 by 300 km area in Northern Argentina,
Southern Bolivia and Northern Chile in the high Andes. Based on a recent
terrestrial gravity survey (Goetze et al., 1988) which could be assumed to
be free of errors in that comparison a study of the accuracy of Rapp's
(1981, 1986) global gravity models was possible in a zone where very scarce
surface gravity data was available to the global models. The area is a
typical subduction zone and was recently studied in detail by Isacks
(1988). This is one of the few areas where the geophysical structure is
relatively well known from seismic results even though details of the
gravity field are not well known. Nevertheless, the comparison was based on
a regular Airy-Heiskanen model using a compensation depth of 40 and 50 km,
respectively. The investigation in terms of isostatic anomalies was done in
order to reduce the effect of erroneous elevation data and local effects.
The two data sets could be assumed to be independent of each other.
Basically, wave lengths up to degree n = 180 were considered. The compari-
son was made in terms of free air, Bouguer and isostatic gravity. The com-
parison indicates a surprisingly good agreement of large scale phenomena
whereas smaller phenomena of the gravity field reveal discrepancies of the
order of ±i0 mgal, as expected.
A second test area is characterized by alpine overthrust, leading to
strongly varying anomalous regression of free air gravity with elevation.
Therefore, Nettleton type prediction does not lead to good free air or Bou-
guer gravity estimates as in the case of homogeneous parts of the Northern
Alps. The area was chosen in order to demonstrate the difficulties asso-
ciated with overthrust and similar density variations in mountain areas
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CROTEN ET AL.: THE USE OF HIGH-RESOLUTION TERRAIN DATA ...
which can make local gravity prediction quite erroneous unless precise geo-
logical information is available. But there are few areas where detailed
density information is available where gravity is unsurveyed. In the area
under consideration the density values determined by the Nettleton method
differ about 0.i to 0.2 gr/cm 3 from that determined by geological means.
For details see (Kling et al., 1987).
The overwhelming part of the investigation is related to the third
area in the Odenwald close to the Rhinegraben where extremely dense (from
ten to fifty meter grid spacing) terrain data were available. The area is
dominated by paleocoic mountains and deep (4 km) sediments, in the grahen
zone, and magmatic rocks of different kind leading to quite discontinuous
and significant density variations. Fig. 1 shows a small part of the third
test area on the eastern Rhinegraben shoulder (Odenwald) where the majority
of the prediction tests were carried out. In order to get a meaningful
illustration a grid distance of i00 m was chosen instead of I0 to 50 m as
was used in the computations themselves. The figure should illustrate the
type of topography for which gravity prediction, based on various mathe-
matical techniques, was carried out using high-resolution terrain, sparse
density and a few gravity data. As mean gravity values for blocks of a few
kilometer side length are of primary interest to geodesy the smoothing or
"smearing" effects inherent in least-squares adjustment of terrain models
with respect to relatively few gravity data is not too perturbing.
The fourth test area is located off central Italy close to Sardinia
island in the Tyrrhennian Sea which is characterized by extremely thin (I0
km) lithosphere. Various types of gravity data including altimetric results
were available. Mainly terrain, regional density and gravity data were used
for prediction based on various types of spectral analysis.
As a relatively dense gravity net was available the application of
various mathematical procedures could be tested. Flat twodimensional
Fourier methods (FFT) were used to represent local digital terrain models.
Freeden's (1982) well known spherical spline techniques were modified in
order to solve strictly local prediction and transformation (conversion of
gravity into potential etc.) problems. Pellinen's (1964) classical methods
by which he solved Molodensky's linear integral equation approach using
terrain data was adapted to regionally varying coefficients for the linear
regression of free air gravity with elevation. As a great variety of geo-
physical parameters such as (i) thickness and density variations in the
crust, (2) various types of Moho depths, (3) thickness and density variati-
ons in the lithosphere, (4) thickness of sediment layers etc. have been
derived for Western Europe from seismic and gravity data this information
(which is usually not available for gravity prediction in unsurveyed areas)
could be fully exploited for our test areas (2) to (4). These parameters
clearly reveal variations of totally different wave lengths s down to s <
30 km. Consequently, by fully exploiting modern digital terrain models
errors of > 5 mgal in smooth hill areas occur which do not average out over
distances of I0 to 20 km unless geophysical detail information is
available. Deviations from standard isostatic and similar models are of
non-isotropic and non-random character so that stochastic or similar re-
gression techniques can only be used reliably if trends can be well estima-
ted from existing (scarce) gravity or similar information.
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3, CONCLUSIONS
This study which focuses on four primary aspects of modern prediction
of gravity in unsurveyed or weakly determined areas reveals the efficiency
and limitations of gravity prediction using high-resolution terrain models.
It also shows the accuracy of global gravity models in (almost) "unsur-
veyed" areas characterized by strongly varying irregular gravity fields. It
demonstrates the consequences of lateral density variations in the crust
and lithosphere. By comparing these results with prediction results earlier
derived by others or by us it becomes clear that quite favorable prediction
results obtained e.g. in the Northern Alps where homogeneous density pre-
vails should be generalized with great care or should better not be genera-
lized at all. The necessity to supplement global gravity models to be dedu-
ced from satellite gradiometry for degrees n ! 180 by other measurements
was shown. In spite of the fact that static models prevail in modeling
local and regional gravity for harmonics of degrees 180 _ n _ 1800 the use
of strong correlation of free air gravity with terrain is perturbed by a
great variety of significant local and regional effects.
"Jt_
Typical digital terrain model in third test area
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GROTEN ET AL . : THE USE OF HIGH-R_soLUTION TERRAIN DATA . . .
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The use of high-resolution terrain data in gravity field prediction

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