GIGeoscientific Instrumentation, Methods and Data SystemsGIGeosci. Instrum. Method. Data Syst.2193-0864Copernicus PublicationsGöttingen, Germany10.5194/gi-5-427-2016Muographic data analysis method for medium-sized rock overburden inspectionsTanakaHiroyuki K. M.ht@riken.jpOhshiroMichinoriEarthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo, 113-0032 Tokyo, JapanDepartment of History, Komazawa University, 1-23-1 Komazawa, Setagaya, 154-8525 Tokyo, JapanHiroyuki K. M. Tanaka (ht@riken.jp)21September2016524274352March201615March20169August201620August2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gi.copernicus.org/articles/5/427/2016/gi-5-427-2016.htmlThe full text article is available as a PDF file from https://gi.copernicus.org/articles/5/427/2016/gi-5-427-2016.pdf
Muographic measurements of rock overburdens are of particular interest
because they can be applied to natural resources and undiscovered cave
explorations, and even to searching for hidden chambers in historic
architectural structures. In order to derive the absolute density
distribution of the overburden, we conventionally needed to know accurate
information about the measurement conditions, e.g., the detector's
geometrical acceptance, detection efficiency, and measurement time, in order
to derive the absolute value of the transmitted muon flux. However, in many
cases, it is not a simple task to accurately gauge such conditions. Open-sky
muon data taken with the same detector are useful as reference data to cancel
these factors; however, if the detector is not transportable, this data
taking method is not feasible. In this work, we found that the transmitted
muon flux will follow a simple function of the areal density along the muon
path as long as the incident muon energies are below a few hundred GeV. Based
on this finding, we proposed a simple analysis method that does not require
detailed knowledge of the detector's conditions by combining the
independently measured density information for the partial volume of the
target. We anticipate that this simple method is applicable to future
muographic measurements of rock overburdens.
Introduction
Earth's subsurface density structures have been extensively measured with
muography in the last decade. High-energy muons originating from cosmic rays
have strong penetrative power to resolve the density distribution of gigantic
objects. The muography technique was first applied by Alvarez et al. (1970)
as a method to search for hidden chambers inside the second pyramid of
Chephren. Muon detectors installed inside the Belzoni chamber recorded the
arrival angles of comic ray muons after they had penetrated the pyramid and
reached the chamber. Muography utilizes the natural tendency of high-energy
muons to penetrate gigantic materials in the same way that the x-ray does;
however, while the x-ray is applicable only to objects of up to 1 m in
thickness, muography visualizes density distributions inside much larger
objects. Since George (1955) first proposed and implemented densimetric
measurements of the rock overburden above a gallery tunnel of the Snowy
Mountains Hydro Electric Authority in Australia with cosmic-ray muons,
particle detection techniques had been developed to the extent that 12 years
later, Alvarez's group could successfully apply spark chambers with digital
readout units to the technique of muography. After analyzing data collected
during several months of operation, they concluded that areal density of the
pyramid was measured with a precision of 2 % along the muon paths that
penetrated over 100 m through limestone in the pyramid. This pioneering
experiment was a crucial step that eventually led to recent muographic
experiments that explored inside volcanoes (Tanaka et al., 2007, 2008, 2009;
Lesparre et al., 2012; Cârloganu et al., 2012; Carbone et al., 2013;
Kusagaya and Tanaka, 2015a, b), industrial plants (Tanaka, 2013; Ambrosino et
al., 2015), seismic faults (Tanaka et al., 2011; Tanaka, 2015),
and caves (Caffau et al., 1997; Barnaföldi et al., 2012; Oláh et al.,
2012).
Cosmic-ray muons are generated in the Earth's atmosphere as secondary cosmic
rays and the integrated vertical open-sky muon flux ISKY is known
to be ∼ 70 m-2 sr-1 s-1. Since the first discovery of muons by Neddermeyer and
Anderson (1936), the differential flux of these particles has been precisely
measured (Olive et al., 2014). The muon flux is
reduced after passing through matter. This reduction can be theoretically
calculated by integrating the differential flux over the energy range between
the cutoff energy, Ec, and infinity, where Ec is the
minimum energy required for muons to penetrate the target object.
Ec can be precisely derived with Monte Carlo simulations, which are
based on our knowledge of the standard model of particle physics; therefore,
there are almost no uncertainties in these theories (Groom et al., 2001).
Once muons are irradiated to the surface of the rock overburden, they are
detected and recorded by the detector underneath the overburden to generate
the histogram of the number of muon events as a function of the muon's
arriving angle.
Muography has the capability to derive an areal density along the muon path.
George (1955) compared the muon flux inside and outside of the
Guthega–Munyang tunnel, Australia, to calculate the muon's transmission
rate, and measured the areal density of the rock overburden of
163 ± 8 m water equivalent (m w.e.), which was consistent with the
result of the drilling and sampling at the same site: 175 ± 6 m w.e.
However, the open-sky muon counts are not always available as reference data,
particularly when the observation system is not transportable. For example,
Alvarez et al. (1970) constructed their observation system inside the Belzoni
chamber of the Chephren Pyramid. Their entire system weighed more than
10 ton, and thus it was not realistic to transport the system to the outside
of the pyramid to take the reference data without changing the configuration.
In this work, we proposed a new method of muographic data analysis for
deriving the density distribution of the middle-scale rock overburden (up to
a few hundred meters in thickness). With our proposed technique, by combining
the value of the density independently measured for a partial volume of the
target, we can derive the areal density along the muon path without detailed
knowledge about the muon detector. In this paper, we formulated this method
and re-analyzed the data presented by Alvarez et al. (1970), Caffau et
al. (1997), and Liu et al. (2012) as examples in order to test the method.
PrincipleCosmic-ray muons
High-energy muons are produced when primary cosmic rays interact with nuclei
in the Earth's atmosphere. The energy spectrum of the primary cosmic ray is
expressed with the following power law that has an index of -2.7
(γ= 1.7) and is almost constant with energies up to 106 GeV.
dNdE=AE-(γ+1)
Consequently, the muon spectrum also closely obeys the power law as the
secondary particles of the primaries. Up to this date, several authors have
derived the analytical expressions for the differential atmospheric muon
spectra in the reaction between primaries and atmospheric nuclei (Bull et
al., 1965; Matsuno et al., 1984; Bugaev et al., 1998; Gaisser and Stanev, 2008).
The parameters in their models have been adjusted by comparing these with
the observed spectrum of muons taken from experiments made at sea level
(Jokisch et al., 1979; Matsuno et al., 1984; Allkofer et al., 1985; Haino et
al., 2004; Achard et al., 2004). The integrated vertical muon flux is
proportional to E-2.2 in the energy region between 50 and 200 GeV.
The geomagnetic deflection depends on the geomagnetic latitude, and has a
significant effect on the muon flux with energies up to 10 GeV (Haeshim and
Bludman, 1988), while Hansen et al. (2005) reported that the east–west
effect is negligible in the vertical cosmic-ray muon flux. Kamiya et
al. (1976) reported that the muon charge ratio measured by the MUTRON
spectrometer had to be modified with correction factors of 1.35 and 0.75 for
muons in the N–W and S–E directions, respectively, indicating a strong
geomagnetic effect even on high-energy horizontal muons.
Muon range
The processes through which muons interact with matter can be divided into
two types: continuous and stochastic. The rate of the muon's energy loss
through matter is expressed by
-dEdX=a(E)+b(E)E,
where E is the muon's energy and X is an areal density
along the muon path. a(E) is the energy loss caused by the
continuous process, and b(E)E is the energy loss
caused by the stochastic process.
Via the continuous process, the muon has frequent encounters with atoms, each
losing a very small fraction of its energy via the ionization process.
Fluctuations in range arise from stochastic processes: bremsstrahlung, direct
pair production, and photonuclear interactions. In these processes, the muon
loses a large but random fraction of its energy. However, if the muon's
energy is much lower than the critical energy, 708 GeV in SiO2, the
continuous process is the main process in muon's energy loss, and thus muons
of a given energy would have almost a unique range. For example, an energy
loss rate of 100 GeV muons via the continuous and stochastic processes is
2.46 and 0.11 MeV cm2 g-1, respectively. The 100 GeV muons have
a range of 406 m w.e.
The cutoff energy (Ec) is defined as the minimum energy that a
muon can penetrate for a given areal density of rock (X) and is
derived by finding the value at which the muon's continuous slowing down
approximation (CSDA) range matches X (Fig. 3). The Ec
solely depends on an areal density along the muon path in matter, and its
material dependence is small. In order to derive the muon flux after passing
through matter, the zenith-angular dependence of the muon flux and the
continuous slowing down approximation (CSDA) range (Groom et al., 2001) are
utilized. The CSDA range is derived by integrating Eq. (2) over a muon's
energy E within a range between 0 and the incident energy E0.
Inversely, once an areal density is determined along the
muon paths, the minimum energy that a muon can penetrate through the path is
uniquely determined if the muon's energy is much lower than the critical energy.
Results
In this work, we modeled muographic observations of the rock overburden. We
divided the overburden into two horizontal layers (Layer 0 and Layer 1). The
muon detector was assumed to be located underneath this overburden. The areal
density was then calculated by assuming a uniform density along the muon
paths and multiplying it by the geometrically exploited muon path lengths as
follows:
X=ρ0×ℓ0+ρ1×ℓ1,
where ρ0 and ρ1 are assumed densities for Layer 0 and
Layer 1, respectively. Both ℓ0 and
ℓ1 are the path lengths averaged over the
elevation angle (θ) and azimuth angle (ϕ), according to an
angular resolution of the muogram when it is generated. Most muons traverse
matter in a linear trajectory. Therefore, the path length of muons can be
precisely determined by reading the outer geometry of the target volume. To
calculate the CSDA range, the muon's ionization, bremsstrahlung, direct pair
production and photonuclear processes are considered. In Fig. 1, the CSDA
range of muons in SiO2 is shown. The Monte Carlo calculation results are
based on the publication by Groom et al. (2001).
In order to derive the transmitted muon intensity (I) (the muon flux after
passing through the overburden), the number of muon events counted in each
histogram bin (N) is divided by the detector's active area (S) detection
efficiency (Aeff) solid angle (Ω) and measurement
time (t). I is compared with the theoretical muon intensity (i) to
derive the areal density along the muon path (X), where i is calculated
by integrating the muon energy spectrum over a range between the muon's
cutoff energy (Ec) and infinity. In this work, we proposed the flux
ratio I0/I1 to cancel S, Aeff, Ω, and t, where
I0 and I1 are the measured intensity after passing through Layer 0
and Layer 1, respectively.
CSDA range of muons in units of meter water equivalent in SiO2.
When the muon's energy is less than 100 GeV, corresponding to a muon range
of 400 m w.e., the contribution of the stochastic energy loss (b(E)E) is
less than 10 % to the total energy loss. Furthermore, the energy loss rate
due to the ionization process (a(E)) does not have a strong energy
dependence. For example, a(E)= 2.3 MeV cm2 g-1 when the
muon energy is 20 GeV (which corresponds to the muon range of 90 m w.e.),
and it becomes 2.5 MeV cm2 g-1 when muon energy is 200 GeV
(which corresponds to the muon range of 740 m w.e.). Therefore, we can
expect that the CSDA range can be fit by a near-linear function within this
energy range.
In order to confirm this assumption, the CSDA range reported by
Groom et al. (2001) was fit by the following equation:
Ec=AXε,
where X is the CSDA range. A and ε are parameters.
Ec is measured in GeV and X in meter water equivalent (m w.e.).
The results of the fitting five data points (40, 80, 100, 140, and 200 GeV)
are shown in Eq. (5).
A=0.1224,ε=1.1176.
The fitting accuracy was about 0.7 %. Within this energy range the muon
range varies from 180 to 740 m w.e. As can be seen in Eq. (5b), the
cutoff energy (Ec) has an almost linear relationship with the
areal density. Therefore, we approximated the muon flux ratio (I0/I1) as follows:
I0I1≈X0X1-2.2,
where I0 and I1 is the transmitted muon flux after passing through
Layer 0 and Layer 1, respectively. X0 and
X1 are averaged areal density along the muon
paths for Layer 0 and Layer 1, respectively. Equation (6) indicates that the
muon flux ratio only depends on the ratio of the areal density. As a result,
if we know the density of Layer 0 (ρ0), we can uniquely derive the
average density of Layer 1 (ρ1) by dividing
X1 by the average thickness of
Layer 1 (ℓ1), and vice versa. Equations (6)
indicates that we can derive these densities without knowing the active
area (S), detection efficiency (Aeff), and solid angle (Ω)
of the detector. By taking this ratio, the factor (A) in Eq. (1) is also
cancelled, and only the index of the integrated muon flux is required for the
calculation because the index of the muon spectrum power law does not vary in
this energy range. An index of -2.2 is almost constant within the zenith
angular range between 0 and 50∘ (Haino et al., 2004; Achard et al.,
2004). However, if the areal density of the overburden exceeds
103 m w.e., the stochastic process becomes dominant in the muon's
energy loss, and thus the index ε in Eq. (4) varies as a function
of energy, and thus this simple formulation cannot be used.
If the muon counts (N) contain background events (δn),
i.e., N0=n0+δn and
N1=n1+δn, the muon count ratio N0/N1
will not be equal to the actual flux ratio I0/I1, where n0 and
n1 are the number of events without background events, respectively.
However, we can reasonably assume that n≫δn when the rock
overburden above the detector is thicker than 20 m. This thickness is
equivalent to 100 times longer than the electron's radiation length in
matter. Also, the hadron's interaction length is up to 100 g cm-2,
which is 50 times shorter than this thickness. Therefore, we can expect that
electromagnetic and hadronic components would be effectively removed by the
time they reach the detector. This assumption is supported by a result
obtained in the similar experiment in 1955. George (1955) installed a Geiger
counter in the Guthega–Munyang tunnel, where the rock overburden was
previously measured to be an areal density of 175 ± 6 m w.e. with the
drilling and sampling method. He simply compared the counting rate measured
inside and outside the tunnel without any background treatments to obtain an
areal density of 163 ± 8 m w.e. that is in agreement with the
muographically derived areal density. Therefore, it is reasonable for us to
approximate Eq. (6) as
N0N1≈X0X1-2.2,
as long as the overburden thickness exceeds 20 m. Figure 2 shows the scheme
of the muographic observation of the rock overburden that is divided into two
horizontal layers.
Discussion
In this section, we examined our technique by applying it to three different
kinds of targets: the Pyramid of Chephren in Egypt, the limestone cave in
Italy called Grotta Gigante, and the Price 5 deposit at the Myra Falls mine,
Canada. For all of the targets, the muography data were collected in the past
and had already been published. These data were used for testing our
technique.
Scheme of the muographic observation of the rock overburden. A Greek
letter μ denotes the incident muons. The rock
overburden is divided into two horizontal layers with a uniform density
of ρ0 and ρ1, respectively. I0 and I1 are the
expected numbers of muon intensity, respectively, at the bottom of each
layer.
Case study 1: the Pyramid of Chephren
The pyramids of Giza are not geological products. However, their sizes are
remarkably large for man-made architecture, and the observational
configuration of muography performed by Alvarez et al. (1970) was essentially
the same as other types of muography performed inside tunnels to measure the
rock overburdens (Oláh, 2012; Caffau et al., 1997; George,
1955). The Pyramid of Chephren offers us a unique target volume to test our
technique for the following reasons: (A) the geometrical shape of the pyramid
is much simpler than regular geological targets and its topographic features
have been studied with aerial surveys (Alvarez et al., 1970);
(B) Gerald Lynch did a direct measurement of a rock piece exploited from the
surface of the Chephron Pyramid in 1968, and derived a density of
1.8 g cm-3 (Alvarez, 1987); (C) the subsurface structure can be directly
observed in the partial cross section located near the top of the Pyramid of
Chephren; and (D) the Pyramid of Chephren is the only pyramid in which
muography surveys were performed by Alvarez et al. in 1970.
The Pyramid of Chephren is the second largest of the Giza pyramids and the
tomb of the Fourth-Dynasty pharaoh Chephren (2558–2532 BC) It is located
20 km southwest of central Cairo (Fig. 1). After construction, the height
was probably 143.87 m; however, now the base length measures 215.5 m and
the height measures 136.4 m. This reduction in height occurred as a result
of the loss of the capstone originally located at the apex of the pyramid. A
unique feature of the Chephren Pyramid is that the original casing stones
made of Tura limestone remain on the upper region of the pyramid (Fig. 2).
Below the lower border of the existing casing stones, all casing stones as
well as several back stones (those stones located behind the casing stones)
have been lost, and as a result the subsurface structure of the pyramid is
exposed. This subsurface exposure allows us to see a partial cross section of
the interior structure and reveals that both casing stones and back stones
are tightly packed without spaces and that one layer of casing stones
originally covered the surface of the entire pyramid (Fig. 2b). The pyramid
was probably intact until at least until 100 BC, since Diodorus Siculus
wrote in that year that “the stones remain to this day still preserving
their original position and the entire structure undecayed” (Siculus and
Oldfather, 1933). Therefore, trusting this description, we can assert that in
the intervening 2100 years, the subsurface materials (casing and back stones)
of the Chephren Pyramid were lost. Croci and Biritognolo (2000) reported,
based on their close observations, their conclusion that the missing
materials had been systematically removed in a manner similar to quarrying
techniques.
Number of muon events collected by Alvarez et al. (1970) in the
direction of west to east. The casing stones remain well within an angle
range between 72 and 87∘. The events are integrated over 24∘
wide bands in the north to south direction.
Two different types of limestone were used to build Chephren's pyramid: Tura
and Mokattam. Tura limestone (high-quality stone similar to marble) was used
for the decorative casing stones. Arnold (1991) reported that the density of
limestone used for the casing stones ranges from 2.65 to 2.85 g cm-3.
Tura limestone is thought to have covered the outside layer of the pyramid
and accounted for about 5 % of its entire volume. In comparison to the Tura
limestone, the Mokattam limestone is more porous and less dense, and was used
for the core of the pyramid. Although the blocks of Mokattam limestone were
exploited near the Chephren Pyramid, some of them were transported from a
quarry located in southeastern Cairo, Egypt. The geology of this quarry is
attributed to the Middle Eocene series. According to Arnold (1991), the
average density of limestone used for building the core of the pyramid ranges
from 1.7 to 2.6 g cm-3. Gerald Lynch did a direct measurement of the
rock piece taken from the surface of the
Chephron Pyramid in 1968, and derived a density of 1.8 g cm-3
(Alvarez, 1987).
Alvarez et al. (1970) collected 650 000 muons during their muography
experiment in 1968; 100 000 of these muons had passed through the upper zone
that consists of casing, back stone, and core layers, as defined in Fig. 2.
However, there is no description of the measurement time t in Alvarez et
al. (1970). This unknown parameter is cancelled if we take the ratio of the
number of muon events accumulated in the different histogram bins. The muon
counts are statistically sufficient to apply Eq. (7) to compare the
subsurface density (the density of the deviation near the apex that consists
of casing and back stones) with the pyramid's core density (the average
density of the pyramid without this deviation part). For the calculation
of ℓ0
and ℓ1, the virtual detector was located
13.5 m east and 4 m north of the center on the ground level as described in
the report written by Alvarez et al. (1970) (Fig. 2).
Location of the Great Pyramid of Giza. The inset shows geometrical
arrangements of the pyramids of Cheops, Chephren, and Mycerinus.
Ratio of the average density of the deviation (the part remaining
near the apex that consists of casing and back stones) to the density of the
pyramid without the deviation part.
In Table 1, we show the number of muon events (N) that Alvarez et
al. (1970) collected inside the Belzoni Chamber together with the number of
events without casing and back stones (N1) and their ratio (N/N1).
For this, we employed the value simulated by Alvarez et al. (1970) for the
numbers of events without casing and back stones. The events are integrated
over 24∘ wide bands centered on the middle of the pyramid in the
north to south direction. In order to reduce uncertainties arising from
irregular casing near the lower border of the upper zone, the analysis was
constrained to an angle range between 72 and 87∘. As a result, a
value of 1.08 ± 0.1 was obtained for the ratio of the subsurface
density (ρ0) to the core density (ρ1). In Table 2 and Fig. 5,
the ratio ρ0/ρ1 is shown as a function of elevation angle. The
ratio does not vary with the muon's arriving angles beyond the error bars
associated with these values. In order to derive ρ0/ρ1 from
X0/X1, I0(θ, φ) and I1 (θ, φ)
were calculated based on the topography of the pyramid and the detector
location, and averaged over the range within an elevation angle range shown
in Table 1.
Weight of the pyramid
As an outlet of deriving the density ratio between the subsurface density and
the core density of the pyramid, we attempted to derive the total weight of
the pyramid. Lehner (2007) measured the thicknesses of the casing stones to
be 82, 67, 45, 66, 44, and 45 cm from the lower edge of the upper zone to
the apex. The size of the stones with the exception of those near the lower
edge has been calculated to be an average of 53 cm. Therefore, we assumed
that a quarter of the volume of the deviation consists of Tura limestone
within a density range of 2.75 ± 0.10 g cm-3. The pyramid
consists of (A) Tura limestone, (B) back stone, and (C) core stone. A density
of (A) is given by Arnold (1991) and a density of (B) (1.8 g cm-3) is
given by Alvarez (1987). Since (A) remains only at the top of the pyramid,
Alvarez's measurement gives the number of muon counts after passing through
all of (A), (B) and (C), and through only (C). Since it is reasonable to
assume that the density of (B) is the same as that of (C), the density of (C)
can be calculated. The back stone density is 1.8 g cm-3; the pyramid's
core density will be 1.89 ± 0.20 g cm-3, which is in agreement
with the back stone density within the statistical error. Since both casing
stones and back stones are tightly packed without spaces (at least near the
surface), this assumption is reasonable. By considering the total volume of
the Chephren Pyramid to be 2 211 096 m3, the total weight of the
pyramid is derived to be 3.98 × 106 t.
A thermal scan technique that provides us with a spatial distribution of
subsurface thermal conductivity complements muography technique that gives us
an areal density distribution along various muon paths and, therefore, a
joint measurement between muography and thermal scans, will provide us with a
more comprehensive picture on structural irregularities inside a pyramid.
Case study 2: Grotta Gigante
The area around the natural limestone cave called Grotta Gigante consists of
400 m thick limestone bedrock including a known aquifer located 250 m below
the ground surface, and a number of branch caves are undiscovered. Karst
topography is a unique geological landscape formed by the natural dissolution
of soluble bedrock, mostly made up of a thick layer of limestone that is
eroded by being dissolved gradually into the underground aquifer. This
dissolution is likely to occur in the crack of the ground, and thus the
specific part of the ground tends to be eroded and forms a doline
(sink hole) on the ground surface and a limestone cave underground. As a
result, a complicated cave system that consists of a number of small caves
will spread around the region where the large main cave is developed. Many of
the caves are not opened to the outside, and therefore it is expected that
the unique ecosystem is developed there without being disturbed by exterior
biological activities (e.g., Rohwerder et al., 2003).
Geometric configuration of muographic measurements performed by
Alvarez et al. (1970) along with a view of the south face of the Chephren
Pyramid. The viewing angle and the position (Mu) of their apparatus are
shown. An elevation angle (θ) is defined as an angle measured from the
west to the east direction. The upper, medium and lower zones were defined
based on the different surface conditions that were characterized by Croci
and Biritognolo (2000). The region called “deviation” was defined by
Alvarez et al. (1970) as distances from the surface of the medium zone.
Casing remained on the surface of the upper zone. The grey arrow shows the
viewing direction in which we can see the cross-sectional subsurface of the
upper zone (a). The illustration of the cross-sectional view
contains casing [A] and back stones [B] (b). The deviated region
consists of a mixture of the remaining casing and back stones.
Density ratio of the deviated region that consists of casing and
back stones (ρ0) to the pyramid's core (ρ1) as a function of
an elevation angle (θ).
Conceptual drawing of the muographic density derivation by using a
borehole. ρ0, ρ1, …, and ρn, respectively,
denote the average density in Layer 0, Layer 1, …, and Layer n with a
thickness of d0, d1, …, and dn.
Caffau et al. (1997) installed their detector at a location of 115 m below
the ground surface in order to map out the areal density of the rock
overburden of Grotta Gigante in various directions. The detector was located
underneath the region with the presence of the doline on the ground
surface. The void associated with the doline exists in the direction
of 50∘ from the zenith. The typical rock density around the detector
was measured to be 2.7 g cm-3. The angular resolution of the generated
muogram was 10 and 5∘ in the azimuthal and elevation direction,
respectively. The thickness of the rock overburden in the vertical
direction (ℓ0) was 20 m; i.e., the
corresponding areal density (X0) was
54 m w.e., and the number of muon events counted in this
direction (N0) was 200. On the other hand, the rock thickness in the
direction of 50∘ from zenith (ℓ1)
was 70 m after reduction of the cave effect, and the corresponding number of
muon events (N) was 25. The muon flux ratio (N0/N1) can therefore
be calculated to be 8. From Eq. (7), X1/X0 is then calculated to
be 2.6, and here we assumed that the vertical muon flux closely matches with
the flux in the direction of 50∘ from zenith (Haino et al., 2004;
Achard et al., 2004). Consequently, the areal density of the overburden in
the direction of 50∘ is derived to be 140 m w.e. If we assumed the
uniform density of 2.7 g cm-3, the overburden thickness in this
direction will be 52 m, which is slightly shorter than the
expected ℓ1.
Once the muographic anomalies are detected, we can compare them with the
gravimetric data. In the area of the Grotta Gigante, the Osservatorio
Geofisico Sperimentale (OGS) conducted a gravimetric survey using a
LaCoste–Romberg microgravity meter. More than 200 data points were acquired
in an area of ∼ 800 × 650 m2 to map out the gravity
anomaly in this area. The region where the muographic anomaly was observed
showed a gravity deviation of 0.1 mgal from the value expected from the
terrain topography. By combining these data with the gravimetric data, it
was revealed that this anomaly came from a red-soil deposit laying beneath
the doline, and its volume and total weight were estimated to be
5 × 103 m3 and 8.5 × 106 kg, respectively (Caffau et al., 1997).
Case study 3: ore body explorations
This muographic data analysis may also be applied to localization of ore
bodies because typically the ore density is 1.4–1.8 times higher than the
surrounding medium. Liu et al. (2012) conducted muographic observations in
the Price 5 deposit at the Myra Falls mine, Canada, in order to estimate the
total weight of the zinc ore body. This target was suitable for the proof of
concept trial for muographic mineral explorations because the mine gallery
exists at relatively shallow depths from the ground surface and a density map
is available based on the diamond drilling results. The averaged ore and the
surrounding medium density were, respectively, measured to be 3.2 and
2.7 g cm-3 based on the drilling and sampling method prior to their
muographic measurements. A 348 h operation of the detector located
underneath the overburden not containing the ore body (Overburden A)
collected 5.6 .× 105 muons, while a 283 h operation underneath
the overburden that contains the ore body (Overburden B) collected
1.6 × 105 muons. The muon flux ratio (N0/N1) can
therefore be calculated to be 2.8. The geometrical thickness of
Overburden A (ℓ0) and
Overburden B (ℓ1) is, respectively,
∼ 100 and ∼ 140 m. Likewise, from Eq. (7),
(X0/X1)-1 is then calculated to be 1.6. Since the areal density of
Overburden A is calculated to be ∼ 270 m w.e., the areal density of
Overburden B is derived to be ∼ 430 m w.e.; therefore, the average
density is 3.1 g cm-3. By inputting the ore density of
3.2 g cm-3, the thickness of the ore can be calculated to be
∼ 100 m, which is in agreement with the result from the prior drilling
and sampling work. We anticipate that this method will also be applicable to
exploring the pyrite-polymetallic and wolfram deposits of the Greater
Caucasus (Eppelbaum and Khesin, 2012).
This technique is applicable to future underground muography observations by
utilizing, e.g., a borehole (Fig. 6). Once we determine the near-surface
density (ρ0) with drilling and sampling methods, the average density
of the depth region (d1) between the core sampling depth (d0) and
the detector location (d) will be measured without requiring knowledge of
the active area (S), detection efficiency (Aeff), and solid
angle (Ω) of the detector. If the measurement time is fixed for each
measurement, the ratio of the number of muon events (N0/N1) counted
at depths of Depth 0 and Depth 1 will give the density
ratio ρ0/ρ1 by considering the muon's path length in each
layer, which is proportional to the depths, d0 and d1. Therefore,
if we compare the number of muon events measured at different depths, the
average densities above the detector locations are derived one after another,
and thus the vertical density distribution of the soil will be obtained. If
two or more boreholes are available for this kind of measurement,
three-dimensional information on the density distribution will be obtained.
Conclusion
In this work, we evaluated the relationship between the transmitted muon
flux and the areal density along the muon path, and found that it has a
simple relationship as long as the overburden thickness is thinner than a
few hundred meters. Based on this finding, we proposed a simple analysis
method to cancel the contributions from the active area (S),
detection efficiency (Aeff), and solid angle (Ω)
of the detector in the generated muogram by combining the independently
measured density information for the partial volume of the target.
We showed two examples as possible applications of this analysis method. By
re-analyzing the muographic data collected by Alvarez et al. (1970) and
combining the surface sampling results with them, we derived the bulk density
of the core of the Pyramid of Chephren, Egypt; hence its total weight. By
combining the drilling and sampling results taken at the region near Grotta
Gigante, Italy, with the muographic data collected by Caffau et al. (1997),
we calculated the size of the void associated with the doline caused
by karst process. The derived size with our method was consistent with the
result obtained with the conventional method, which utilized the absolute
value of the transmitted muon flux.
Combining non-muographic densimetric techniques with muography has been shown
to be useful for improving the spatial resolution of the density image. We
showed in the case study of Groitta Gigante that this simple analysis method
could be even more powerful by combining gravimetric measurements to provide
useful geological information. Recently, Jourde et al. (2015) showed that
gravimetric and muographic joint measurements enhance the resolving power of
the technique, in particular, when the muographic measurement is
unidirectional. Furthermore, since muographic and gravimetric measurements,
respectively, derive horizontally and vertically integrated density, a
resolution of the deeper region where muography is not applicable becomes
greatly improved by this kind of joint measurement.
The near-surface density is relatively easier to measure, e.g., with a
drilling sampling method, in comparison to deeper region densities.
Therefore, we anticipate that this technique is useful for future muographic
measurements of the rock overburden for the purpose of exploring geological
structures that require an accurate density value, for example, surveys of
natural resources and mechanical fracture regions of the fault zones.
Data availability
The data we used have been already published and accessible through Alvarez
et al. (1970), Caffau et al. (1997), and Liu et al. (2012). Edited by: L. Eppelbaum
Reviewed by: two
anonymous referees
ReferencesAchard, P., Adriani, O., Aguilar-Benitez, M., Van den Akker, M., Alcaraz, J.,
et al.: Studies of hadronic event structure in e + e-annihilation
from 30 to 209 GeV with the L3 detector, Physics Reports, 399, 71–174, 2004.
Allkofer, O. C., Bella, G., Dau, W. D., Jokisch, H., Klemke, G., Oren, Y.,
and Uhr, R.: Cosmic ray muon spectra at sea-level up to 10 TeV, Nucl. Phys. B,
259, 1–18, 1985.
Alvarez, L. W.: Discovering Alvarez: Selected Works of Luis W. Alvarez with
Commentary by His Students and Colleagues, University of Chicago Press, Chicago, 1–282, 1987.Alvarez, L. W., Anderson, J. A., El Bedwei, F., Burkhard, J., Fakhry, A., Girgis,
A., Goneid, A., Hassan, F., Iverson, D., Lynch, G., Miligy, Z., Moussa, A. H.,
Sharkawi, A., and Yazolino, L.: Search for hidden chambers in the pyramid,
Science, 167, 832–739, 10.1126/science.167.3919.832, 1970.
Ambrosino, F., Bonechi, L., Cimmino, L., D'Alessandro, R., Ireland, D. G., Kaiser,
R. B., Mahon, D. F., Mori, N., Noli, P., Saracino, G., Shearer, C., Viliani, L.,
and Yang, G.: Assessing the feasibility of interrogating nuclear waste storage
silos using cosmic-ray muons, J. Instrument., 10, 1–13, 2015.
Arnold, D.: Building in Egypt; Pharaonic Stone Masonry, Oxford University Press,
Oxford, 1–316, 1991.
Barnaföldi, G. G., Hamar, G., Melegh, H. G., Oláh, L., Surányi, G.,
and Varga, D.: Portable Cosmic Muon Telescope for Environmental Applications,
Nucl. Instrum. Meth. A, 689, 60–69, 2012.Bugaev, E. V., Misaki, A., Naumov, V. A., Sinegovskaya, T. S., Sinegovsky, S. I.,
and Takahash, N.: Atmospheric muon flux at sea level, underground, and underwater,
Phys. Rev. D, 58, 054001, 10.1103/PhysRevD.58.054001, 1998.
Bull, R., Nash, W. F., and Rustin, B. C.: The Momentum Spectrum and Charge Ratio
of I – Mesons at Sea-Level – II, Nuovo Cimento, XLA, 2, 365–384, 1965.Caffau, E., Coren, F., and Giannini, G.: Underground cosmic-ray measurement
for morphological reconstruction of the Grotta Gigante natural cave, Nucl.
Instrum. Meth. A, 385, 480–488, 10.1016/S0168-9002(96)01041-8, 1997.
Carbone, D., Gibert, D., Marteau, J., Diament, M., Zuccarello, L., and Galichet,
E.: An experiment of muon radiography at Mt. Etna (Italy), Geophys. J. Int.,
196, 633–643, 2013.Cârloganu, C., Niess, V., Béné, S., Busato, E., Dupieux, P., Fehr,
F., Gay, P., Miallier, D., Vulpescu, B., Boivin, P., Combaret, C., Labazuy, P.,
Laktineh, I., Lénat, J.-F., Mirabito, L., and Portal, A.: Towards a muon
radiography of the Puy de Dôme, Geosci. Instrum. Method. Data Syst., 2,
55–60, 10.5194/gi-2-55-2013, 2013.
Croci, G. and Biritognolo, M.: The structural behaviour of the Pyramid of
Chephren, Arch 2000, 1, 1–6, 2000.
Eppelbaum, L. V. and Khesin, B. E.: Geophysical Studies in the Caucasus, Springer,
Berlin, p. 411, 2012.
Gaisser, T. and Stanev, T.: Cosmic Rays, Phys. Lett. B, 667, 254–260, 2008.
George, E. P.: Cosmic rays measure overburden of tunnel, Commonw. Eng., 1955, 455–457, 1955.
Groom, D. E., Mokhov, N. V., and Striganov, S. I.: Muon stopping-power and range
tables: 10 MeV–100 TeV, At. Data Nucl. Data Tabl., 78, 183–356, 2001.
Haeshim, L. and Bludman, S. A.: Calculation of low-energy atmospheric muon flux,
Phys. Rev. D, 38, 2906–2907, 1988.Haino, S., Sanuki, T., Abe, K., Anraku, K., Asaoka, Y., Fuke, H., Imori, M.,
Itasaki, A., Maeno, T., Makida, Y., Matsuda, S., Matsui, N., Matsumoto, H.,
Mitchell, J. W., Moiseev, A. A., Nishimura, J., Nozaki, M., Orito, S., Ormes,
J. F., Sasaki, M., Seo, E. S., Shikaze, Y., Streitmatter, R. E., Suzuki, J.,
Takasugi, Y., Tanaka, K., Tanizaki, K., Yamagami, T., Yamamoto, A., Yamamoto, Y.,
Yamato, K., Yoshida, T., and Yoshimura, K.: Measurements of primary and
atmospheric cosmic-ray spectra with the ESS-TeV spectrometer, Phys. Lett. B,
594, 35–46, 10.1016/j.physletb.2004.05.019, 2004.Hansen, P., Gaisser, T. K., Stanev, T., and Sciutto, S. J.: Influence of the
geomagnetic field and of the uncertainties in the primary spectrum on the
development of the muon flux in the atmosphere, Phys. Rev. D, 71, 083012,
10.1103/PhysRevD.71.083012, 2005.Jokisch, H., Carstensen, K., Dau, W., Meyer, H., and Allkofer, O.: Cosmic-ray
muon spectrum up to 1 TeV at 75∘ zenith angle, Phys. Rev. D, 19, 1368–1372, 1979.Jourde, K., Gibert, D., and Marteau, J.: Improvement of density models of
geological structures by fusion of gravity data and cosmic muon radiographies,
Geosci. Instrum. Method. Data Syst., 4, 177–188, 10.5194/gi-4-177-2015, 2015.
Kamiya, Y., Iida, S., and Shibata, S.: Proceedings of the Asian Cosmic Ray
Conference, Hongkong, p. 133, 1976.
Kusagaya, T. and Tanaka, H. K. M.: Muographic imaging with a multi-layered
telescope and its application to the study of the subsurface structure of a
volcano, Proc. Jpn. Acad. Ser. B, 91, 501–510, 2015a.Kusagaya, T. and Tanaka, H. K. M.: Development of the very long-range cosmic-ray
muon radiographic imaging technique to explore the internal structure of an
erupting volcano, Shinmoe-dake, Japan, Geosci. Instrum. Method. Data Syst.,
4, 215–226, 10.5194/gi-4-215-2015, 2015b.
Lehner, M.: Pyramids: Treasures Mysteries and New Discoveries in Egypt, White
Star Publisher, 46–59, 2007.Lesparre, N., Gibert, D., Marteau, J., Komorowski, J.-C., Nicollin, F., and
Coutant, O.: Density muon radiography of La Soufriere of Guadeloupe volcano:
comparison with geological, electrical resistivity and gravity data, Geophys.
J. Int., 190, 1008–1019, 2012.
Liu, Z., Bryman, D., and Bueno, J.: Application of Muon Geotomography to Mineral
Exploration, International Workshop on “Muon and Neutrino Radiography 2012”,
17–20 April 2012, Clermont-Ferrand, France, 2012.Matsuno, S., Kajino, F., Kawashima, Y., Kitamura, T., Mitsui, K., Muraki, Y.,
Ohashi, Y., Okada, A., and Suda, T.: Cosmic-ray muon spectrum up to 20 TeV at
89∘ zenith angle, Phys. Rev. D, 29, 1–23, 1984.
Neddermeyer, S. and Anderson, C.: Note on the nature of cosmic-ray particles,
Phys. Rev., 51, 884–886, 1936.Oláh, L., Barnaföldi, G. G., Hamar, G., Melegh, H. G., Surányi, G.,
and Varga, D.: CCC-based muon telescope for examination of natural caves, Geosci.
Instrum. Method. Data Syst., 1, 229–234, 10.5194/gi-1-229-2012, 2012.Olive, K. A., Agashe, K., Amsler, C., et al.: Review of particle physics,
Chin. Phys. C, 38, 090001, 10.1088/1674-1137/38/9/090001, 2014.
Rohwerder, T., Sand, W., and Lascu, C.: Preliminary Evidence for a Sulphur Cycle
in Movile Cave, Romania, Acta Biotechnol., 23, 101–107, 2003.
Siculus, D. and Oldfather, C. H.: Diodorus Siculus: Library of History, Books 1-2.34,
Loeb Classical Library, 279, 1–498, 1933.Tanaka, H. K. M.: Development of stroboscopic muography, Geosci. Instrum. Method.
Data Syst., 2, 41–45, 10.5194/gi-2-41-2013, 2013.
Tanaka, H. K. M.: Muographic mapping of the subsurface density structures in
Miura, Boso and Izu peninsulas, Japan, Sci. Rep., 5, 1–10, 2015.
Tanaka, H. K. M., Nakano, T., Takahashi, S., Yoshida, J., Takeo, M., Oikawa, J.,
Ohminato, T., Aoki, Y., Koyama, E., Tsuji, H., and Niwa, K.: High resolution
imaging in the inhomogeneous crust with cosmic-ray muon radiography: The density
structure below the volcanic crater floor of Mt. Asama, Japan, Earth Planet.
Sc. Lett., 263, 104–113, 2007.
Tanaka, H. K. M., Nakano, T., Takahashi, S., Yoshida, J., Takeo, M., Oikawa, J.,
Ohminato, T., Aoki, Y., Koyama, E., Tsuji, H., Ohshima, H., Maekawa, T., Watanabe,
H., and Niwa, K.: Radiographic imaging below a volcanic crater floor with
cosmic-ray muons, Am. J. Sci., 308, 843-850, 2008.Tanaka, H. K. M., Uchida, T., Tanaka, M., Shinohara, H., and Taira, H.: Cosmic-ray
muon imaging of magma in a conduit: degassing process of Satsuma-Iwojima Volcano,
Japan, Geophys. Res. Lett., 36, L01304, 10.1029/2008GL036451, 2009.
Tanaka, H. K. M., Miyajima, H., Kusagaya, T., Taketa, A., Uchida, T., and
Tanaka, M.: Cosmic muon imaging of hidden seismic fault zones: Raineater
permeation into the mechanical fracture zone in Itoigawa-Shizuoka Tectonic Line,
Japan, Earth Planet. Sc. Lett., 306, 156–162, 2011.