Method of determining the density of substrata

A method for determining the density of substrata by means of a radiation source K comprising a collimator (1) and of a detector comprising a collimator (3), by which method the direction of radiation may optionally be changed in relation to the direction of detection, and the change of the detected signal may be measured. According to the invention the direction of radiation and the direction of detection are situated in substantially the same plane. By deducting the signal of the desirable depth of measurement from a somewhat greater depth of measurement, substantially only the signal originating from singly scattered radiation is obtained, and as a result it will be possible to measure the density at greater depth than previously. On the basis of a spectrum analysis of the spectrum originating from the measurement, the variation of the density with the depth could be obtained.

BACKGROUND OF THE INVENTION 
The present invention relates to a method of determining the density of 
substrata of a considerable thickness by means of a gamma-radiation source 
comprising a collimator and of a detector comprising a collimator, both 
located on the surface of the substratum. The direction of radiation may 
be changed in relation to the direction of detection, and the change of 
the detected signal may be measured by means of the inventive method. 
FIG. 3 illustrates an arrangement performing measurements on the basis of 
scattered gamma-radiation. The gamma-radiation emitted from the source is 
collimated to a thin beam, L, of gamma-quanta, which is damped 
exponentially during the passage of the object under measurement, said 
damping being dependent on the density of the object under measurement. 
The damping is substantially due to Compton-scattering, and the 
gamma-quanta are scattered in a direction away from the beam L in all 
directions. Some of the scattered quanta will--optionally subsequent to 
additional scatterings--be directed towards the detector. 
DESCRIPTION OF THE PRIOR ART 
The quanta detected by the detector can be divided into the following 
groups: 
Group A: The singly scattered quanta, which are only scattered in the 
reflection volume (cf. FIG. 3), and which after scattering are directed 
towards the detector. This group also comprises the quanta which are 
subjected to scatterings on its way down to the reflection volume and on 
its way up to the detector, but where the scattering angles in connection 
with all scatterings--apart from the scattering in the reflection 
volume--are very small. These quanta, which at the arrival at the detector 
have almost the same energy as the singly scattered quanta, are of great 
importance, as they dominate the result of measurement in connection with 
measurements at great depth. If the detector only detected group-A-quanta, 
the results of measurement would be an expression of the average density 
in the depth area 0 to x. 
Group B: The quanta, which are subjected to two or only a few scatterings 
with scattering angles of a considerable size, and which reach the 
detector without passing the reflection volume. Such quanta may e.g. 
follow the way L-2-M or L-3-M. These quanta, which on the average return 
at a smaller depth, have an energy which on the average is somewhat 
greater than the energy of the quanta of group A. 
Group C: The quanta, which are subjected to many scatterings usually 
without passing the reflection volume. These quanta have an average energy 
much lower than the energy of the quanta of groups A and B. However, a 
small portion of the quanta of group C have energies of the same order as 
the quanta of groups A and B. 
FIG. 5 illustrates an example of a gamma-spectrum measured by the detector. 
However, the spectrum depends on the desired depth of measurement. If this 
depth x is smaller than about 10 cm, the majority of the measuring signal 
of the detector will originate from the quanta of group A depending on the 
composition and density of the material in question. When the depth of 
measurement is increased beyond about 10 cm, the fact that the signal from 
the quanta of group A is damped exponentially, whereas the signal from the 
quanta of groups B and C is almost constant and only to a small degree 
depends on the depth of the return area, will soon implicate that the 
detector signals are dominated by the quanta of groups B and C. 
By changing the geometry in such a manner that the center line of the 
collimators of the source and the detector is no longer in the same plane, 
and the measuring signal is in principle only due to the quanta of group 
C. This method is described in U.S. Pat. No. 4,034,218. As illustrated in 
FIG. 1 of U.S. Pat. No. 4,034,218, the measuring signal will, after the 
described change of geometry, be entirely without the bulge originating 
from the quanta of groups A and B. By deducting the measuring signal after 
the described change of geometry from the measuring signal before the 
change, a signal is obtained which essentially originates from the quanta 
of groups A and B. For depths of measurement of less than about 10 cm this 
signal will as described above be dominated by quanta of group A. In 
connection with greater depths the quanta of group B will quickly be 
dominating, and the measuring signal obtained will consequently be 
practically independent of the depth of measurement. The method described 
in U.S. Pat. No. 4,034,218 is consequently not suited for measuring the 
density of layers of material with thicknesses of more than about 10 cm. 
SUMMARY OF THE INVENTION 
According to the invention of said patent specification the centerlines of 
the collimators of source and detector will always be in the same plane. 
By using for this geometrical configuration the difference between the 
result of measurement corresponding to the desirable depth of measurement 
and the result of measurement corresponding to a somewhat greater depth of 
measurement, a signal is obtained, which is practically only determined by 
the quanta of group A, which are scattered in the desirable depth of 
measurement. The contributions of the quanta of groups B and C will, in 
the two measuring signals, be of practically equal size and thus 
neutralize each other, whereas the contribution of the quanta of group A 
which are scattered at a greater depth will be very small due to the 
additional exponential damping, to which these quanta are subjected on 
account of the greater depth. This method makes it possible to measure the 
density at considerably greater depth than previously. 
Information as to the variation of the density with the depth is 
furthermore obtainable on the basis of the measured gamma-spectrum.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
An example of the use of gamma-density measurements are described in the 
following. 
In road building it is of great importance that the road substratum is 
compacted sufficiently, and considerable means are used for compacting 
control. It is known to perform this control by means of the so-called 
"sand replenishment method". By this method a 15 cm deep hole is dug, 
whereafter the density and the water content of the material dug up are 
determined by packing the hole with sand of a well-defined density and by 
drying the sand dug up. This method requires, however, much work. 
Furthermore, the result of the determination of the water content will not 
be available until the next day. 
It is also known to use nuclear probes for determining the density and the 
water content of a road substratum. These probes yield a quick result with 
a modest performance. 
The surface density of the stratum of earth is determined by means of 
nuclear probes either by the back-scattering method or by the transmission 
method. 
In the usual back-scattering method (with the use of collimators) a 
gamma-source on the surface emits gamma-quanta into the stratum, where 
said quanta are scattered, whereafter they are able to reach a 
gamma-detector also located on the surface. The gamma-detector is shielded 
against direct radiation from the gamma-source. In connection with 
densities above about 1 g/cm.sup.3, the counting velocity of the detector 
decreases concurrently with increasing earth density. An increased number 
of atoms per volume unit will prevent the gamma-quanta from reaching the 
detector, and simultaneously the absorption probability of the 
gamma-quanta will be increased. The advantage of the back-scattering 
method is that it does not disturb the road surface. On the other hand the 
usual back-scattering only indicates the density of the upper 4-6 cm, 
which is not sufficient in earth compacting tests. 
In the transmission method--cf. FIG. 1--a spear with a gamma-source in the 
head is lead 15-20 cm down into the stratum. From here the gamma-quanta of 
the source are able to reach the gamma-detector. The registered counting 
velocity depends on the damping of the stratum, which in turn is 
determined by the density of the stratum. The greater the density is, the 
lower is the counting velocity due to the greater damping. The advantage 
of the transmission method is that it measures the average value of the 
density in the earth from source to detector. The insertion of the spear 
may on the other hand be difficult, optionally impossible, if the stratum 
contains many stones, which is normally the case in connection with road 
building materials. The method is furthermore inapplicable, if the 
measurements are to be performed on e.g. asphalt, concrete or other solid 
materials. 
The method here described is based on Compton-scattering of gamma-quanta. 
In the method a collimated gamma-luminous beam is emitted into the medium 
in question, where the gamma-quanta are scattered--cf. FIG. 2. By 
measuring only the quanta of group A scattered in a depth of up to about 
25 cm, a counting velocity is obtained, which is a standard for the 
average density of the medium down to this depth. The energy of the quanta 
of group A is close to the value calculated by Compton's formula: 
##EQU1## 
E.sub.o is the energy of the gamma-quanta emitted by the source and 
.theta. is the angle shown in FIG. 2. This method ensures that only the 
quanta of group A with an energy of about E.sub..gamma. are measured. 
The measuring arrangement used is as illustrated in FIG. 2. The 
gamma-radiation from the source K (about 30 mCi.sup.137 Cs) is emitted 
uniformly in all directions. The collimator of the source has an aperture 
angle of about 3.times.6.degree., whereas the collimator of the detector 
has an aperture angle of about 3.times.8.degree.. The gamma-quanta will 
only reach the surroundings, if they are directed out through the 
collimator. The remaining quanta are absorbed by the shield A. 
A monochromatic luminous beam is thus emitted from the source within a 
narrow solid angle. The direction of radiation may be changed by adjusting 
a handle H. There are N different adjustments corresponding to N different 
depths of measurement, e.g. N=3, 6, 10, 15, 25, and 35. As illustrated in 
the Figure, the luminous beam is emitted into the material, the density of 
which should be determined. During the passage through the material, a 
portion of the gamma-quanta in the luminous beam will be scattered or 
absorbed. The scattered part is to a substantial degree dependent on the 
density of the scattered material. 
When the radiation reaches the desirable depth of measurement it will be 
damped to a certain degree depending on the density of the material. 
During the passage of the reflection volume V, a portion of the 
gamma-quanta is scattered away from the luminous beam depending on the 
density of the substance. A smaller portion of the radiation scattered in 
V will be directed towards the gamma-detector. On its way the radiation is 
damped further depending on the density of the material. The intensity of 
the radiation reaching the detector will thus depend strongly on the 
density (almost exponentially) of the object to be measured. 
As mentioned the radiation of gamma-quanta away from the luminous beam 
during passage of a material depends on the density of the material. The 
dependency is the same for all materials, except materials containing 
hydrogen as well as heavy atoms. This is due to the fact that gamma-quanta 
are scattered by electrons, and the scattering probability is proportional 
to the electron density N.sub.e in the material. N.sub.e is indicated by 
the formula: 
##EQU2## 
in which N.sub.Av is Avogadro's number, .rho. the density, Z the atom 
number, and A the mass number. Apart from hydrogen it applies for all not 
too heavy atoms that Z/A.perspectiveto.0.5, for which reason N is 
proportional to .rho.. For hydrogen it applies that Z/A.perspectiveto.1. 
This involves that for water (H.sub.2 O) 
##EQU3## 
i.e. 10% greater. In connection with gamma-radiation calculations it is 
thus necessary to correct for the abnormally great ability of water to 
scatter gamma-radiation by using in the calculations a corrected density 
of 1100 kg/m.sup.3. 
The radiation to be measured are the quanta of group A, which are scattered 
in the reflection volume V. The intensity of this radiation is 
substantially determined by the average density along the radiation path 
in the material. 
The detector is provided with a collimator serving to filter off all 
gamma-radiation apart from the radiation having the correct direction, 
i.e. the direction from the reflection volume to the detector. 
By means of shield and collimators the majority of the undesirable 
radiation is filtered off. It is, however, not possible by geometry alone 
to sort out all undesirable gamma-quanta. Quanta, which have been 
scattered twice or more (groups B and C), which do not reach far into the 
material, but which at the last scattering is directed up through the 
collimator of the detector (cf. FIG. 3), will also be detected, but they 
only contain information as to density down to the depth which they have 
reached. 
The following method is used for measuring the quanta of group A alone. 
By the measuring arrangement illustrated in FIG. 3 a thin luminous beam L 
is emitted from the collimator of the source, said beam being damped 
exponentially during passage of the object under measurement. 
This damping is substantially due to the Compton-scattering, by which the 
gamma-quanta are scattered away from the luminous beam L. As the quanta 
are emitted in all directions, some of them will be directed towards the 
detector. Due to the detector collimator only the quanta following the 
collimator line M will reach the detector and transmit a signal. 
If the detector only detects quanta of group A the result of measurement 
will be an expression of the average density in the depth area from 0 to 
x. 
An emitted gamma-quantum can, however, also follow the way L-2-M or L-3-M. 
These quanta are scattered more than once (here two and three times). If 
measurements were only performed on these quanta it is obvious that only 
information as to the density from 0 to x.sub.1 will be obtained, and not 
as desired from 0 to x. 
It can be illustrated that if the desired depth of measurement is less than 
about 10 cm, the majority of the measuring signal at normal densities and 
compositions will originate from quanta of group A. This is due to the 
slight probability of quanta of group B reaching the detector when 
subjected to two or more scatterings and thereafter ending in the correct 
direction. 
When the depth of measurement x is increased, the fact that the signal from 
quanta of group A is damped exponentially, whereas the signal from quanta 
of groups B and C is almost constant, will soon lead to the detector 
signal being dominated by the signal from the undesirable quanta of groups 
B and C, which do not reach the desired depth. 
By using Compton's formula on quanta of groups A and B it is illustrated 
that quanta of group B normally have more energy than the quanta of group 
A. The quanta of group C will normaly have considerably less energy. 
A typical gamma-spectrum as registered by the detector is illustrated in 
FIG. 4. The part of the spectrum containing information as to the density 
from 0 to x is hatched. The arrow indicates the energy of the quanta of 
group A according to Compton's formula. It appears that the peak is 
displaced towards higher energies. This is due to the fact that the quanta 
of group B have energies in the same interval (somewhat higher) and 
actually drown the desired signal. 
The spectrum of FIG. 4 may be understood as composed of three portions as 
illustrated in FIG. 5. The area A indicates the desired measuring signal 
from the quanta of group A. The area B indicates the signal from the 
quanta of group B (multiple scattering) and quanta of photo-electric 
emission in the detector collimator and from natural background radiation. 
By adopting two measurements, one having the depth of measurement x and 
one having the depth of measurement x+y, in which y is typically 10 cm, it 
is obtained that in the case where the depth of measurement is x+y the 
signal from the quanta of group A will in practice disappear, as the 
signal is damped during the passage of the further 2.times.10 cm. In x+y 
measurements the signal from the quanta of groups B and C will then on the 
other hand be practically unchanged as they move at considerably lower 
depth, and as their geometry is almost unchanged. As a result, by taking 
the difference between the results of the two measurements (x and x+y), a 
result of measurement is obtained merely determined by the quanta of group 
A (cf. FIG. 6), and on the basis hereof it is possible to determine the 
average density of the object of measurement from depth 0 to depth x. 
SPECTRUM ANALYSIS OF THE RESULT OF MEASUREMENT 
Out of a spectrum analysis of the peak A+B information is obtained as to 
the variation of the density with the depth at greater depths. This is 
also the case when adopting measurements of smaller depths. 
In the following a spectrum analysis means an analysis of the shape of the 
spectrum originating from the measurement (energy-spectrum versus 
gamma-energy). FIG. 5 illustrates that the part of the spectrum, in which 
the area A is situated, is only partly congruent with the energy interval, 
within which the area B is situated. The average energy of the area B is 
higher than the average energy of the area A. 
The number of countings in the area B depends on the average density in the 
depth interval from 0 to x.sub.1 (cf. FIG. 3). Greater counting velocities 
within the area B are obtained in connection with a lower average density 
from 0 to x.sub.1. 
It is thus possible from the number of countings in the energy interval, in 
which B dominates, to calculate the average density from the depth 0 to 
x.sub.1, .rho.(0-x.sub.1) (cf. FIG. 4). 
As described above the average density from the depth 0 to x.sub.1, 
.rho.(0-x.sub.1) may be determined by determination of the number of 
countings in the area A. On the basis of .rho.(0-x.sub.1) and .rho.(0-x) 
the average density of the substratum in the depth x.sub.1 to x, 
.rho.(x.sub.1 -x), may be determined by the formula 
##EQU4## 
On the basis of Compton's formula it can be illustrated that a 
gamma-quantum scattered as shown at "3" of FIG. 3 (three scatterings) will 
have a higher energy that a quantum scattered as shown at "2" of FIG. 3 
(two scatterings). Both quanta will belong to the quanta of group B. It 
can be illustrated that the three times scattered quanta of group B 
detected have on the average obtained a smaller maximum depth than the 
corresponding twice scattered quanta. It generally applies that the N 
times scattered quanta reaching the detector will originate from a greater 
average depth than the N+1 times scattered quanta. 
The signal originating from the quanta of group B can consequently be 
divided into energy intervals. The number of countings of each interval 
contains information as to the density down to a certain depth, and the 
higher the energy of the intervals is, the lower is the corresponding 
depth. 
By dividing the energy area of the quanta of group B into a suitable number 
of intervals and analyzing the associated number of countings it is 
possible to calculate the average density in the corresponding depth 
intervals from the surface to the total depth of measurement. 
By using the method of the least squares a suitably chosen function may be 
approximated to the gamma-spectrum of the quanta of group B. The values 
achieved of the adapter constants contain information as to the variation 
of the density with the depth. By means of the constants it is possible to 
estimate the density at a desirable depth, and the variation of the 
density with the depth can be calculated continuously. 
The analyzing method here described is in practice applicable at all depths 
of measurement.