Method for mapping of sea level undulations with applications to hydrocarbon prospecting

A method of making for an area a map or a representation of regional variations in the position of the geoid which have an amplitude less than about 1 m. and are caused by density variations in the underlying sea floor. The map or representation is intended primarily for use in the determination of part areas of the sea floor with increased probability of deposits of natural resources, the density of which part areas distinguishes from that of the surroundings. The method comprises PA0 (a) obtaining height values which indicate the sea surface height in relation to reference level and which have been calculated by means of altimeter data measured from a flying craft and by means of information about the orbits of the flying craft during measurement of the altimeter data; PA0 (b) sorting out incorrect and improbable values; and PA0 (c) adapting the height values corresponding to different orbits of the flying craft to one another, such that maximum agreement of height values is obtained in the crossing points of the orbits, whereby relative values of the geoid position are established. The method is characterised by PA0 (d) filtering off long-wave variations with a wave length exceeding about 200 km in the geoid position; PA0 (e) amplifying variations in the geoid position which have a selected spread; and PA0 (f) correcting the geoid position in respect of interference from the water depth.

BACKGROUND OF THE INVENTION 
The present invention is concerned with prospecting and relates more 
particularly to a method of making for an area a map or a representation 
of regional variations in the position of the geoid which have an 
amplitude less than about 1 m. and are caused by density variations in the 
underlying sea floor, said map or representation being intended primarily 
for use in the determination of areas of the sea floor with increased 
probability of deposits of natural resources, the density of which part 
areas distinguishes from that of the surroundings, downward bends in the 
geoid towards the sea floor indicating part areas having a density lower 
than that of the surroundings, and upward bends in the geoid from the sea 
floor indicating part areas having a density higher than that of the 
surroundings. 
Hydrocarbon deposits sufficiently rich to justify exploitation occur in 
rock traps on land and below the sea floor. The oil and/or gas in these 
traps has a slightly lower density than the surrounding bedrock. This is 
one of the facts utilised in oil prospecting operations. 
For present day offshore oil prospecting, use is made of a number of 
different techniques of which the following are the most important ones: 
(a) Seismic survey which involves the generating of acoustic impulses by 
means of an air gun and measuring of the signals reflected from certain 
geological markers below the sea floor by means of various types of 
sensors. The signals received fluctuate in time in response to density 
variations in the different layers and formations below the sea floor and 
the depth to these layers and formations. The signals thus provide a 
geological picture indicating structures and main faults which could 
contain oil/gas accumulations. 
(b) Magnetometric survey which involves measuring the intensity and the 
direction of the terrestrial magnetic field. 
(c) Gravimetric survey which involves measuring minor variations in the 
vertical component of the gravitational field at the sea surface by means 
of an instrument which, in principle, comprises a spring-suspended sinker. 
The deflection of the instrument reflects the total force of gravity from 
all mass lying vertically between the location where the survey is carried 
out and the center of the earth. In other words, large mass densifications 
can contribute considerably to the deflection of the instrument even if 
they are at very large depths, where no exploitation of the natural 
resources can be made. The measuring accuracy of present day instruments 
is about 5-10 mGal. 
(d) Geological survey and bottom samples by which it is intended, inter 
alia, to judge whether the conditions within the prospecting area during 
earlier geological times have been favourable to the formation of 
hydrocarbon-bearing areas, and it is investigated whether the rock is of 
the type in which oil/gas usually is to be found. 
(e) Electrical survey which involves investigating the character of the sea 
floor by resistivity measurements. 
(f) Geochemical survey. Hydrocarbon traps generally leak a certain amount 
of oil or gas to the overlying sediments, and in some instances it is 
possible to trace and analyse these leaks by means of bottom samples. 
All of these prior art techniques suffer from the disadvantage that they 
are not very accurate in forecasting oil deposits. Exploratory drillings 
in the areas which these techniques have indicated as promising, have 
revealed commercial quantitites of oil/gas in less than 20% of the trial 
holes, calculated on a world-wide basis. Since oil prospecting by the 
above-mentioned techniques and, especially subsequent exploratory 
drillings are extremely expensive, large sums of money could be saved if 
the forecasting accuracy could be increased, and if the areas in which 
exploratory drillings must be made could be restricted. 
In other types of prospecting, such as in ore and mineral prospecting, data 
are utilised which are collected by means of satellites for mapping areas 
with likely deposits. The techniques used for this purpose are colour 
television technique, picture analysis/processing and multispectral 
recording. 
Furthermore, it is known that satellites are able to provide altimeter 
data, i.e. information about the distance between the satellite and the 
sea surface. A satellite revolves around the earth in a great circle 
plane. Since the earth rotates on its north-south axis, the satellite will 
gradually move back and forth within an area between specific north and 
south latitudes, the width of said area being determined by the orbital 
angle of the satellite. This area will eventually have been scanned by the 
satellite which then has passed over the area along north-western and 
south-western tracks, crossing each other and forming a deformed grid 
pattern. 
Altimeter data are measured at regular intervals along these tracks. At the 
crossing points of the tracks, the altimeter data will have been recorded 
at different times for one and the same point. Because the tidal lift is 
different at different times, because the wind force is different, because 
the satellite is at different altitudes depending upon whether it has 
travelled over land or sea before it reaches the measuring point, etc., 
the altimeter data measured at different times will differ considerably at 
the crossing points. The differences may amount to .+-.5 meters. 
By means of these altimeter data and information about the orbit of the 
satellite, it is then possible to calculate height values indicating the 
position of the sea surface in relation to a reference ellipsoid which is 
an imaginary ellipsoid representing the shape of the earth as accurately 
as possible. These height values are used to study the undulation of the 
sea surface which is not entirely globular in shape, but slightly 
undulatory. In places where the force of gravity is stronger, the sea 
bulges slightly outwardly (water masses are attracted to these places), 
and in place where the force of gravity is somewhat less, the sea bulges 
slightly inwardly. The sea surface has, in other words, adapted itself to 
the interior mass conditions of the earth. Further, if all interference 
from waves, tides, currents etc. is eliminated, the sea surface forms a 
surface with constant gravity potential, a so-called geoid. 
Up to now, the altimeter data have been utilised mainly for determining the 
position of the geoid, expressed in absolute numbers as a height above the 
reference ellipsoid. However, because of the difficulties involved in 
accurately determining the orbit of the satellite and in finding exact 
corrections for tides, waves, currents etc., only the variations in the 
geoid position which have a large spread and high amplitude could be 
determined. Scientific literature in this field gives examples of 
observations of variations in the geoid position of the order -40 m. to 
+60 m. Variations of this order are entirely without interest for 
prospecting purposes and, besides, have not been utilised therefor. 
Moreover, altimeter data have been utilised for mapping the topography of 
the sea floor. Thus, seamounts attract water from the surroundings and 
raise the sea level. 
Two papers by Richard H. Rapp, "The Determination of Geoid Undulations and 
Gravity Anomalies from Seasat Altimeter Data", Journal of Geophysical 
Research, Vol. 88, No. C3, pp. 1552-1562, Feb. 28, 1983, and "Gravity 
Anomalies and Sea Surface Heights Derived from a Combined GEOS 31 Seasat 
Altimeter Data Set", Journal of Geophysical Research, Vol. 91, No. B5, pp. 
4867-4876, Apr. 10, 1986, disclose a method of globally mapping the sea 
surface height expressed in absolute numbers above a reference ellipsoid. 
The method comprises obtaining height values which indicate the sea 
surface height in relation to a reference level and which have been 
calculated by means of altimeter data measured from a flying craft and by 
means of information about the orbits of the flying craft during 
measurement of the altimeter data; sorting out incorrect and improbable 
values; and adapting the height values corresponding to different orbits 
of the flying craft to one another, such that maximum agreement of height 
values is obtained in the crossing points of the orbits. The values 
established for the variations in the sea surface height are, in addition, 
converted into variations in the gravity acceleration expressed in mGal. 
However, such conversion causes errors in the values because it 
presupposes that all mass is concentrated in a point, which is not the 
case. 
It is the object of the present invention to determine regional variations, 
i.e. geographically limited and high-frequency variations, in the geoid 
position, said variations having an amplitude which is less than about 1 
m. and is caused by density variations in the underlying sea floor, and to 
make a map or representation of these variations, which can be used in 
prospecting for natural resources in the sea floor. 
SUMMARY OF THE INVENTION 
This object is achieved by means of a method as described above which is 
characterised by filtering off long-wave variations with a wave length 
exceeding about 200 km in the geoid position; amplifying variations in the 
geoid position which have a selected spread; and correcting the geoid 
position in respect of interference from the water depth. 
In this manner, regional undulations in the geoid can be found which are 
caused by the difference in the density in the underlying part of 
formations under the sea floor and the density in the surrounding parts of 
formations under the sea floor. In areas which lie underneath regional 
downward bends in the geoid and which thus have a lower density than the 
surroundings, the chances of finding oil/gas are, as will appear from the 
above, greater than in other locations. In areas which lie underneath 
regional upward bends in the geoid and thus have a higher density than the 
surroundings, the chances of finding oil/gas are, however, very small. 
The reverse applies to deposits of ore and minerals which have a higher 
density than the bedrock in which they occur. 
To be able to determine these regional variations in the position of the 
geoid, which are caused by density variations in formations under the sea 
floor, the height values are corrected such that any interference from 
larger-scale phenomena, such as tides, mass variations in the magma and 
other deep lying formations, etc. are eliminated. Furthermore, in order to 
achieve adequate accuracy, one merely considers relative values of the 
geoid position and disregards any absolute values of the geoid position. 
One advantage of this prospecting technique is that it is more reliable 
than conventional prospecting methods in forecasting natural resources. In 
areas where the method according to the present invention was used to 
determine that the geoid has a local downward bend of more than 25 cm, oil 
and/or gas have so far been found in about 70% of the exploratory wells 
being drilled in such areas. Generally, it may be said that downward bends 
of more than about 10 cm are of interest to prospecting for commercially 
profitable deposits. A further advantage of the invention is that one can 
predict with a high degree of accuracy in which areas there is no oil or 
gas to be found. In areas where the sea surface has an upward bend of 5 cm 
or more, almost none of hundreds of wildcats have encountered hydrocarbons 
(maximum oil/gas shows). The possibility of sorting out uninteresting 
areas is, of course, an important cost-saving factor in that exploratory 
drillings can be confined already at the outset to profitable areas. 
Another advantage of this prospecting technique is that, in contrast to 
conventional gravimetrical technique, it reflects the density variations 
solely in the outer part of the earth's crust where hydrocarbon deposits 
can be profitably exploited. Deeper lying systems affect the geoid 
position over a large area, and the effect of these systems is eliminated 
by the method according to the invention, wherein long-wave variations are 
filtered off. In this connection, long-wave variations are supposed to 
mean variations with a wave length exceeding about 200 km. 
The invention can be used universally for prospecting operations at sea. 
However, since it is extremely expensive to drill in areas with great 
depths of water, the method according to the invention is used primarily 
on the continental shelves.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
A satellite travelling in an orbit of high accuracy samples, for example 
ten times every second, the distance to the sea surface by means of a 
radar altimeter. These altimeter data are transmitted to different ground 
stations in which data associated with too noisy and weak signals are 
sorted out. The remaining data and information about the satellite orbit 
are then used for calculating height values indicating the position for 
the sea surface in relation to a reference ellipsoid. These height values 
are then compiled in data bases from which they can be obtained for 
calculation purposes. Since collection of the altimeter data and 
calculation of the height values do not form part of the present 
invention, they will not be further described. 
The height values calculated on the basis of said altimeter data, are used, 
in accordance with the present invention, for determining regional 
variations in the geoid position. These regional variations are determined 
by correcting the height values in different ways for large-scale 
phenomenon effects. The corrections preferably are made by means of a 
computer, and the final result can be presented in the form of a map of 
the area investigated showing the regional variations in the geoid 
position, or in the form of profiles indicating the density variations in 
the sea floor, or in the form of some other representation, for example in 
the form of signals recorded on a magnetic tape and containing 
corresponding information. 
The following is a description of how the method according to the invention 
is carried out by means of a computer. In the event that use is made of 
programs not commercially available, the expert in the field will have no 
difficulty in designing corresponding programs based on the information 
provided by the specification. 
In a first step, the height values obtained from a data base are stored in 
a first file. The height values in this file are then checked in different 
ways in order to find and eliminate erroneous and improbable values. 
The values are first checked for any undesired "double tracks", i.e. a 
doubled set of data from one and the same satellite track. Such double 
tracks may occur because several ground stations are receiving the same 
data. If a double track is detected, the data set associated with one of 
these tracks is removed. 
After that, measuring values subjected to interference from land are sorted 
out. Since the radar waves are scattered while travelling between the 
satellite and the sea surface, each altimeter data actually is a mean 
value for one measurement area. If there is land within this measurement 
area, the altimeter measured value will be incorrect. All height values 
based on altimeter data whose measurement areas contain land must 
therefore be sorted out, and this is done by means of maps and on the 
basis of the information available about the size of each measurement area 
associated with a specific altimeter measured value. 
After that, the height values are checked with respect to wave height, wind 
and standard deviation. In areas where the waves have been very high 
and/or the wind has been very strong when the altimeter data were 
recorded, corresponding height values are removed. Waves that are too high 
and winds that are too strong are reflected in that the standard deviation 
of the altitude values will be large. 
Furthermore, the height values are checked with respect to 
.DELTA.-altitude, i.e. the difference between two successive values, and 
ripple, i.e. the acuteness of the bend in the water surface. The reason 
for this correction is that there are physical limits to how much a water 
surface can incline. Optionally, and simultaneously with this correction, 
also a tidal correction is effected by means of known values of the tidal 
lift. 
Finally, a check is made of individual points and interruptions in tracks. 
In those cases where a satellite approaches land and passes over many 
islands, it may occur that only one measuring point at a great distance 
from the remaining measuring points from the track remains after removal 
of height values based on altimeter data subject to interference from 
land. Such a measuring point is then of slight value and is sorted out. It 
is also checked that the tracks contain no longer interruptions. In such a 
case, the tracks are sorted out. 
After these corrections have been effected, the remaining height values are 
stored in a second base file. If desired, the computer can be used for 
plotting the height values associated with the different satellite tracks, 
which preferably is done by utilising different colours in order to mark 
different heights above the reference ellipsoid. Such a graphic 
representation also provides an opportunity for subjective assessment of 
the height values. The plotting shows that height values based on 
altimeter data measured in the same point but at different times differ 
considerably because of several factors, as has been explained above. 
However, none of these factors is associated with the required density 
variations in the sea floor. The tracks may therefore be raised, lowered 
and angled such that maximum agreement is established at the crossing 
points, while maintaining the information about the density variations in 
the sea floor intact. For this reason, the above-mentioned elimination of 
incorrect and improbable values is followed by a step in which the tracks 
are adapted to one another such that maximum agreement between height 
values for different tracks is obtained at the crossing points. 
This adaptation step is initiated by dividing the tracks into south-western 
and north-western tracks, whereupon the latitude and longitude of the 
crossing points as well as the time between the start of the track and 
each crossing point are calculated, the time calculation being based upon 
exact information about the time interval between each measuring point. 
After the positions of the crossing points have been determined, a main 
track and a control track are selected. The main track is selected among 
the south-west tracks and preferably should extend as far as possible 
through the search area, i.e. essentially diagonally. The control track is 
selected among the north-west tracks and should also extend as far as 
possible through the search area. If there is no sufficiently long control 
track, two control tracks may be selected. During the subsequent 
adaptation of the track positions to one another, the main track is 
maintained fixed, and neither its height nor its angular position is 
changed. The angular position of the control track also remains unchanged 
during the subsequent adaptation, but its height may be changed such that 
the control track will intersect the main track. 
The main track and the control track define a plane to which the remaining 
tracks are adapted in the best possible way in that they are raised or 
lowered as well as angled. This adaptation is based upon the least square 
method and can be carried out by means of a commercially available 
calculation program from the NAG library. The input data to this 
calculation program are a matrix containing the latitude and longitude of 
the crossing points, the height difference for each crossing point and the 
time from the start of the track to the crossing point, as well as 
information about which track is the main track and which is the control 
track. From this calculation program, a result file is obtainable which 
indicates the height difference between the tracks at the crossing points 
and the mean height difference for all crossing points. By studying these 
data, individual points or whole tracks may be found which obviously are 
incorrect and should be eliminated. The adaptation is repeated until a 
satisfactory result has been obtained. 
The output data from the calculation program are in the form of a 
correction file containing the magnitude of the angling and of the raising 
or lowering that must be carried out for each track. The height values in 
base file 2 are corrected by means of the corrections in the correction 
file, and the corrected height values are stored in base file 3. 
Then, all superfluous data are sorted out, and merely latitude, longitude 
and the corrected height value for each crossing point are retained and 
stored in a fourth base file. Upon adaptation of the satellite tracks to 
the main track and the control track, the height values have been made 
independent of the original reference ellipsoid. The height values thus 
are no longer absolute values in relation to the reference ellipsoid, but 
merely are relative values. 
The crossing points do not cover the search area completely. In some parts 
of the area, the crossing points lie close together, whereas in other 
parts they are fairly sparsely arranged. To make the global or large-scale 
trend within the area quite clear, an interpolation is made by means of an 
interpolation method known as GINTP1, whereby a first matrix is obtained. 
If desired, the first matrix may then be plotted by means of a printer or 
on the screen of the computer. FIG. 1 illustrates a simulated 
three-dimensional graphic representation of the first matrix, in which the 
x axis indicates longitude values, the y axis latitude values, and the z 
axis height values in meter above a reference level, i.e. the variation in 
height for the geoid position. The Figure clearly shows that the global 
trend resides in an inclination downwards in a direction toward greater 
longitude values. 
After that, the fourth base file is corrected for the global trend by 
filtering off interference from long-wave phenomena, such as tides. 
Filtration may be accomplished by, for example, calculation of a 
regression plane which is subtracted from the height values. Filtration 
may also be compared to a straightening-out of the entire search area, 
such that the altitude values will lie within the smallest possible 
interval, without on that account changing their interrelationship. The 
operation may be compared to having a crumpled and sloping or warped 
paper, the folds of which correspond to the regional variations in the 
geoid position, and the slope or warp of the paper corresponding to the 
global trend within the search area. If the paper is straightened up, i.e. 
if the global trend is removed, no information about the regional 
variations has been lost, but these regional variations will be more 
readily comparable. In FIG. 1, the correction for the global trend implies 
that the plane is inclined such that the left-hand short end is lowered 
and the right-hand short end is raised. 
After the global trend has thus been eliminated, a further interpolation is 
carried out in the manner described above, and a second matrix is 
obtained. 
The second matrix is illustrated graphically in FIG. 2 in which the x axis 
indicates longitude values, the y axis indicates latitude values, and 
height values within different intervals are illustrated by different 
rasterings. In the Figure altitude curves having a distance of 0.15 m have 
been drawn to make the height position of the geoid within the area appear 
more clearly. These curves and the rasterings show that the geoid has a 
downward bend in an area between long 19.degree.-20.degree. and lat 
61.0.degree.-61.5.degree.. 
In subsequent steps, phenomena of the order which is of interest for 
oil/gas prospecting are studied and amplified. Amplification is achieved 
in the following manner. First, a square size is selected which depends 
upon the size of the phenomena to be studied. The square size may extend 
from about 10 km.times.10 km and upwards, and the squares need not be 
equilateral, but may just as well be rectangular. After the square size 
has been selected, a mean value of all height values within each square is 
formed, whereupon the mean value matrix is interpolated up to the same 
matrix size as the second matrix and is subtracted therefrom. The result 
is a third matrix showing variations in the geoid position of the size 
which is of interest to oil/gas prospecting. 
The third matrix is illustrated graphically in FIG. 3 in which, as in FIG. 
2, the x axis indicates longitude values, the y axis indicates latitude 
values, and altitude values within different intervals are shown by 
different rasterings. The distance between the altitude curves in this 
Figure is 0.05 m. If FIG. 3 is compared to FIG. 2, it will be found that 
regional bends not seen in FIG. 2 will appear in FIG. 3. In FIG. 3, for 
example, a regional downward bend is shown at long 17.degree., lat 
60.0.degree.-60.5.degree., a bend which is not to be seen in FIG. 2. 
The step of mean value formation within squares of a selected size, and the 
subsequent upward interpolation, may be repeated for squares of different 
sizes, whereby phenomena of different sizes may be studied. This is shown 
in FIG. 4 which is a view corresponding to FIG. 3 and graphically 
illustrates the third matrix when said mean value formation within squares 
has been carried out with a smaller square size than in FIG. 3. In FIG. 4, 
the distance between the altitude curves is but 0.025 m, and this means 
that bends having a smaller geographical extent than in FIG. 3 are shown. 
As already mentioned, the third matrix produced in this manner will reflect 
regional variations in the geoid position. These variations depend upon 
the density conditions at the sea floor below the water surface, but also 
on the water depth (i.e. the sea floor topography). In order to refine 
variations in the geoid position depending upon density variations at the 
sea floor, it will therefore be necessary to eliminate the effect of the 
water depth, and this is done in the next step. 
The water surface may be regarded as an undulating surface which is 
composed of several superimposed functions, one of which represents the 
water depth. The objective is to find the function which best represents 
the interference of the water depth with the undulating surface and to 
subtract this function from the undulating surface, such that it only 
reflects density variations in the sea floor. This objective is achieved 
by means of regression analysis utilising the water depth as the input 
value. 
On the continental shelves where it is economically feasable to drill for 
hydrocarbons, the sea floor topography has been carefully mapped on 
nautical charts. In this step, use is made of a chart covering the search 
area, and for this chart water depth data are taken which are digitalised. 
The water depth matrix produced in this manner is then interpolated to the 
same matrix size as the water surface matrix. By means of the water 
density and the water volume, it is then calculated how the water mass 
affects the shape of the water surface. This calculation results in a 
matrix having correction values for how the water mass or the water depth 
affects the surface. Then a mean value formation according to the same 
model as for the water surface is carried out, and for this the same 
square size as before is, of course, selected. In this manner, a fourth 
matrix for correction of the regional effect of the water depth is 
obtained. To correct the third matrix, the fourth matrix is added to the 
third matrix, and this gives a fifth matrix showing how the geoid is 
regionally affected by underlying geological phenomena, i.e. by density 
variations in the underlying sea floor. Calculation is repeated for 
different density values, and for each density value the height values in 
the fifth matrix are summed-up. Finally, that density value is selected 
which gives the lowest sum of the height values because this value 
provides for optimum reflection of the interference of the sea floor 
topography with the surface. The fifth matrix is the finished matrix which 
shows regional variations in the geoid position above a reference level 
and downwardly, i.e. when the density at the sea floor is lower than in 
the surroundings. In areas where the sea surface has an upward bend, i.e. 
where the density at the sea floor is higher than that of the 
surroundings, the prospects of finding oil or gas are very low. To 
minerals and ores, the reverse applies. 
If desired, the fifth matrix may then be processed by calculating how the 
geoid is affected by known geological systems (salt lentils, salt plugs, 
high density systems, etc.). 
FIGS. 5a and 5b, finally, illustrate a comparison between the method 
according to the invention and prior art gravimetrical technique for an 
assumed part area, the density of which distinguishes from that of the 
surroundings and which is in the form of a square block having a thickness 
of 200 m. 
The interference of the part area with the geoid position is calculated by 
means of the formula 
##EQU1## 
wherein .DELTA.h is the change in the geoid position caused 
by the assumed deposit; 
G is Newton's gravitation constant=6.67.multidot.10.sup.-11 Nm.sup.2 
/kg.sup.2 ; 
.DELTA.b is the density difference between the surroundings and the deposit 
and has been set at 0.25 kg/dm.sup.3 ; 
.DELTA.V.sub.i is a volume element in the form of a cube whose side is 100 
m; 
g.sub.o is the normal gravity acceleration=9.80m/s.sup.2 ; 
R.sub.i is the radial distance expressed in meters from said volume element 
to the point on the water surface for which .DELTA.h is determined; 
and the summation is carried out for all volume elements .DELTA.V.sub.i. 
The interference of the part area with the gravity acceleration is 
calculated by means of the formula 
##EQU2## 
wherein .DELTA.g is the change in the gravity acceleration caused by the 
interference from the part area, .alpha..sub.i is the angle between the 
vertical line and the radial line to said volume element .DELTA.V.sub.i, 
the remaining parameters have the same significance as in the above 
formula, and the summation is carried out for all volume elements 
.DELTA.V.sub.i. 
The result is plotted in the diagrams shown in FIGS. 5a and 5b, .DELTA.h 
being given in centimeters and .DELTA.g in mGal on the ordinate, and the 
extension of the part area being given in kilometers on the abscissa. The 
diagram clearly shows that .DELTA.h increases essentially linearly with 
the extension of the part area, while .DELTA.g relatively quickly attains 
a given value which it then retains regardless of the extension of the 
deposit. Even if .DELTA.h and .DELTA.g are not directly comparable, the 
calculations clearly indicate that .DELTA.h gives more reliable 
indications of widespread density variations and accordingly possibilities 
for the existence of large and commercially profitable deposits of natural 
resources. The reason for this is that the part area merely affects the 
vertical component at gravimetrical measurements, whereas the water 
surface in each point is affected by the entire gravitation and thereby 
forms an equipotential surface. For part areas of large extension, the 
contribution to .DELTA.g by the volume element .DELTA.V.sub.i with a large 
angle .alpha..sub.i will be very low, while .DELTA.h is affected to a far 
greater extent.