GEOPHYSICS, VOL. 55, NO. 12 (DECEMBER 1990): P. 1558-1566, 6 FIGS
The gradient tensor of potential field anomalies:
Some implications on data collection and data
processing of maps
L. B. Pedersen* and T. M. Rasmussen*
ABSTRACT
separation between flight lines can be increased com-
The full gradients tensor is~ present!y not measured
pared with the standard mode ofoperation. !n airborne
routinely onboard airplanes or on land. This paper
surveys the distance between flight lines is normally
describes some improvements that can be made in
much larger than the height above the ground. This
strategies of data collection and in processing of po-
may introduce severe aliasing effects in the direction
tential field maps if such tensor measurements were
perpendicular to the flight lines.
By
increasing the
available. We suggest that, in addition to producing for
flight altitude, aliasing effects are reduced at the ex-
example standard total field anomaly maps, the invari-
pense of lateral resolution which, however, may be
ants of the tensor be mapped. Strikes of magnetic or
improved by mapping the tensor invariants in addition
gravimetric structures may be determined from mini-
to the magnetic field. The estimated gradient tensor
mizing the power in the first row and column of the
from total field magnetic data over the Siljan impact
tensor. Invariants can be looked upon as nonlinear
region shows that the magnetic properties of the area
filters enhancing sources with big volumes. Their
are very nonuniform even from a height of 430 m
lateral resolution is superior to that of the field proper
above the topography. The nonlinear filters discrimi-
and, for a given resolution, the flight altitude and
nate major anomalies into separate units.
INTRODUCTION
PROPERTIES OF THE GRADIENT TENSOR
The gradient tensor of potential field anomalies can be
measured either directly on the ground or onboard airplanes,
or it may be estimated from area1 coverage of the anomalous
Suppose that a volume
V
is magnetized with an excess
magnetization
J
and has an excess density p. The gravita-
tional U and the magnetic potential
A
may be defined as
gravity or from anomalies of the total magnetic field. Recent
articles by Nelson (1988a,b), Brezowski and Heller (1988),
and Vasco (1989) touch upon some of these aspects.
Some basic properties of gradient tensors are derived
in
this paper. Since they are symmetric, their eigenvalues are
real and their eigenvectors are mutually orthogonal. Their
trace is identically equal to zero, and a dimensionless ratio
between the two remaining invariants lies between zero and
unity. This ratio is zero for two-dimensional (2-D)
sources
and it is equal to one for a mass point source. Some of these
properties suggest new processing
schemes
for area1 data
and new interpretation algorithms for data collected along
lines. Aliasing effects are estimated and an example from the
Precambrian of Sweden is presented.
(1)
and
where rO and r denote observation and integration points,
respectively,
R =
(rO - r(, and G is the gravitational
constant.
Outside of sources ro, U and
A
satisfy Laplace’s equation
ViU(ro) = 0
(3a)
Manuscript
received by the Editor November 20, 1989; revised manuscript received May 10, 1990.
*Department of Geophysics, Uppsala University. Box 556, S-751 22 Uppsala, Sweden.
(” 1990 Society of Exploration Geophysicists. All rights reserved.
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