Chiguata_magnetic_prospection.pdf

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A magnetic survey carried out in
Chiguata - Arequipa - Peru for
archaeological purposes*
Manuel Ivan Zevallos Abarca1
1
Cusco, Perú
Correspondence
Author: Manuel Z. Abarca, Address Urb. Lucrepata B-12, Cusco, Perú
Email: manuel.z.abarca@outlook.es
Phone: +51 937 708 483
Abstract
The applications of geophysical prospecting techniques on Archaeological-type
targets have little propagation in Peru. In this investigation, the use of the
magnetometric method was proposed, since it is a geophysical technique that
is reliable in its results and that had already demonstrated its usefulness in
archaeological surveys carried out in Europe. The selected place was the
Tambo de Chiguata, in Arequipa-Peru. The processing of the magnetic data
followed the classical methodologies in principle; with excellent results, as with
them a buried lithic structure was found that had not previously been detected
by visual inspection. Then, a post-processing with more advanced geophysical
techniques, such as Laplacian transformation, digital filters, wavelet image
processing, inversion in two and three dimensions, showed evidence of other
buried bodies with archaeological affiliation. It is known from anthropological
studies that the place was occupied by the Churajon and Inca cultures, from
the years 1000 A.D. until the arrival of the Spaniards in Peru. But the 3D
models discovered structures at greater depths, raising the possibility that they
may have had earlier human occupation.
* Submitted to Archaeological Prospection. August 26, 2022.

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Key words: magnetometry; magnetic prospection; geophysical inversion;
potential field transformations; pre-inca cultures;
1 | INTRODUCTION
Archaeological exploration found in geophysical methods a great auxiliary tool
that allowed the analysis of the earth's subsurface without having to invade or
alter the archaeological environment. One of the oldest geophysical methods
that was used for archaeological purposes was magnetic. The most significant
advantage of magnetic prospecting is that it covers large areas of land in a
short time, giving indications of the presence of buried objects on which an
excavation could be focused following classical archaeological methods. Also,
noteworthy is the low cost of executing a magnetic survey.
Nuclear precession magnetometers (protons) were developed in 1958. Aitken
made the first attempt to apply to archaeological studies that year. Other
instruments as fluxgate gradiometer were in use in that epoch (Alldred, I. C.,
1964); but its extensive applications to archaeological exploration were made
only in the 1970s. A comprehensive reference to this method in the
archaeological literature dates back to 1969 (Aitken, 1969); the same author
later published a summary of the method (Aitken, 1974). A milestone in the
development of geophysical methods applied to Archeology was the special
issue of Geophysics journal (1986), highlighting terrestrial magnetometry.
Looking at the geological characteristics of the archaeological zone that was
the object of this study, all the rocks of volcanic origin, and considering the
construction materials that the natives of the area would use at that time,
terrestrial magnetometry was chosen as the geophysical method of exploration
to be applied and the one that could give the best results for the archaeological
study.
2 | LOCATION
The archaeological area under study is located near the town of Chiguata, in
the department of Arequipa-Peru (Fig. 1).

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Figure 2: Topographical map of the
archaeological area of Tambo de Chiguata,
the black dot and circle indicate the place of
the magnetic survey.
Figure 3: Aerial photograph of the
Tambo de Chiguata area, the red
rectangle shows the limits of the
magnetic survey. You can see the
remains of the walls of what was
an old pre-hispanic town.
The current inhabitants of the region know it as Pueblo Viejo (Old Town);
probably because the remains of buildings are still visible and because of its
proximity to the town of Chiguata (Figs. 2 and 3).
3 | TERRESTRIAL MAGNETOMETRY APPLIED TO ARCHEOLOGY
3.1 | DIURNAL VARIATION
Figure 1: The archaeological area under
study is located near the city of Arequipa
in Perú (black circle in the map of South
America).

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The diurnal variation of the natural magnetic field of the earth occurs due to an
external influence. The main source of that external magnetic field is the solar
wind (Yamazaki and Maute, 2017; Sergipe, P., Marangoni, Y., dos Santos, P.,
Moura, D,. Jovane, L., 2021), which increases the intensity of the magnetic
field on the side of the Earth that faces the Sun. The diurnal variation curve
begins to grow at the moment that the Sun appears on the horizon and
reaches its maximum at noon (when the Sun is at its zenith), then gradually
descends in the afternoon until it reaches a minimum during the night. At
epochs where the Sun has a normal activity, we call solar quiet (Sq), then the
curve of diurnal variation is smooth. But, with a period close to eleven years,
the Sun has a year of storms and flares in his corona (Balogh, A., Hudson,
H.S., Petrovay, K., von Steiger, R., 2014), which produces strong variations in
the Earth's magnetic field.
The measurement of the total component of the magnetic field in the terrain
was made along lines covering the area of investigation. Since we had only one
magnetometer in use, we had to apply the reoccupied base station technique
to measure the diurnal variation curve. In this way, the base station was
reoccupied approximately every twenty minutes, resulting in the measurement
points that appear in Fig. 4 (blue marks).
Unfortunately, that day in which the magnetic prospecting was carried out, the
magnetic field was altered, there was a slight solar storm (Rajesh et al.,
2021). To prevent jumps in the diurnal variation curve caused by the solar
storm from affecting creating spurious anomalies, we decided to correct this
Figure 4: Diurnal variation curve of the terrestrial magnetic field; the blue dots are the data
measured in the terrain, the green solid curve is the least squares fit to a polynomial piecewise
function.

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through the least squares adjusted curve, which was smooth and without
bumps. The fitted curve appears as a continuous green line in Fig. 4. and takes
the form,
γ (t)=24.24 ln(t−3.9)ln(1+t)+2.91(t−1.03)−1.19(t−2.38)
2
.
The difference between points A and P, on the γ axis, is the correction that had
to be applied to a measurement made at time tP to translate this to the time tA.
We can make the time tA (or any other) our reference time, so,
tA=t0=0
in such a way that the effect of the diurnal variation on the measurements
made in the field would be canceled if we assumed that all these
measurements were made at the same instant t0. We achieve this result by
applying a reduction to the magnetic intensity values measured along the lines
that cover the area under study with the following formulae,
Γ(x, y, 0)=Γ(x, y , t)−(γ (t)−γ (t0))
where,
Γ(x, y,t) ; is the value of magnetic intensity (nT) measured at the
geographical position (x, y) and at the time t;
Γ(x, y, 0) ; is the value of magnetic intensity reduced to the time t0.
3.2 | MAGNETIC ANOMALY
Reducing the magnetic intensity measurements to a time t0 does not yet
produce a map of magnetic anomalies. The concept of anomaly in geophysics
always refers to a value of the field considered normal. This normal value could
be the one measured at a point on the ground, in which the magnetic field is
stable, without spatial variations (Lasfargues, Pierre, 1966). We could have
also taken as a reference value the one given by the algorithm of the
International Geomagnetic Reference Field (IGRF) for the coordinates of the
region. Alternatively, we were lucky to have a geomagnetic observatory (San
Agustín University) very close to the study site (a few km) in which the

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intensity value of the total magnetic field is regularly measured, which has an
average value of 25,000 nT. Then, the calculation of the magnetic anomaly
was calculated by subtracting 24,900 nT from the points measured on the
ground ΔΓ=24900−Γ(x , y ,0) ; in nT. With this data we elaborate a map of
magnetic anomalous field (Fig. 5).
3.2.1 | MAGNETIC ANOMALIES IN SOUTHERN HEMISPHERE
Figure 5: Map of magnetic anomalies; intensity of the total
field. Pueblo Viejo archaeological area. Local coordinates.

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There are two forms of magnetic anomalies of geological interest. The first is
that induced by the geomagnetic field of origin in the core of the Earth (dipolar
field) and the magnetic property associated with this anomaly is the magnetic
susceptibility, magnetite being the main mineral responsible for this property.
The induced magnetization is directly proportional to the strength of the
geomagnetic field, that is, B=κ H where κ is the magnetic susceptibility.
The other form of anomaly, which can overlap to the induced, is due to the
natural remanent magnetism of the rock, which exists even in the absence of
an external geomagnetic field. It is about the magnetization acquired during a
rock formation. The direction of the remanent magnetism does not necessarily
coincide with the local geomagnetic field, in contrast to the induced
magnetization. The existence of remanent magnetism complicates the
interpretation of magnetic anomalies.
Since the induced magnetization vector is much less than the strength of the
magnetic field, generally on the order of 1000 times, the vector resulting from
the sum of the two fields is very close to the direction of the current magnetic
field. The direction of the total magnetic field vector is defined by two
elements, the magnetic declination (D) and the magnetic inclination (I). The
declination is an angle that the magnetic vector forms with respect to the
geographical north. In our region, for that time, it is -6.236 degrees, which
indicates that the magnetic vector points to the west of the geographical north.
The inclination is the angle that the magnetic vector forms with respect to the
horizontal plane. In our region, the inclination is -10.421 degrees. As the
positive inclination is in the downward direction, the magnetic vector in our
region points outward; in other words, the magnetic force line emerges from
the surface of the ground.

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3.3 | RESIDUAL FROM REGIONAL ANOMALIES SEPARATION
Looking at the map of magnetic anomalies (fig. 5) we notice two shapes that
stand out, a high-intensity dipole anomaly in the south central region and a
magnetic gradient that has an NNE-SSW direction. The dipole anomaly seems
to come from some body buried very close to the surface; it will be the main
object of study in this investigation since it is of archaeological interest. While
the magnetic gradient could be considered the regional field created by some
body buried deeper and of larger dimensions than our study area. For the
Figure 6: Typical magnetic
anomalies on the magnetic
Southern Hemisphere. Due
to magnetic inclination (I)
in the region the negative
part of the anomaly is more
intense. Note that in the
magnetic equator the
anomaly would be
monopolar and totally
negative.

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purposes of modeling the dipole anomaly, it will be necessary to eradicate the
magnetic gradient, since in this case, it acts as magnetic noise. This analytical
procedure is known as the separation of the regional anomaly from the
residual anomaly.
We know several ways to separate the regional and residual fields. One is to
take upward continuation of the total field (Henderson, R., Zietz, I., 1949;
Phillips, J., 1996) (Fig. 7), then subtract the continued field from the measured
field (Keating, P., Pinet, N. and Pilkington, M., 2011).
Upward continuation is based on the property of potentials according to which
potentials can be calculated at any point simply from the behavior of the field
at its boundaries.
Figure 7: Map of upward continuation of
magnetic field, virtual height 10.0 m above
ground.

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By conducting a mathematical analysis of Green's function, we get to know
that the continuation upwards has the form of a convolution integral. So the
operation becomes very simple by applying the Fourier transform; since the
convolution is equivalent to the product of the transforms (Bhattacharyya,
1967),
ℱ Γ(x, y, h)=ℱ Γ(x, y ,0)⋅eh(u2
+v2
)1 /2
Where h is the height until would be continued the potential field.
Figure 8: Residual magnetic anomaly map;
resulting from subtracts the field continued
upwards from the total field at the height of the
sensor.

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A second way to extract the residual anomalies is by fitting the magnetic field
to a low degree 2D polynomial function. In this case we seek a function of the
form,
Γ(x, y)=c1+c2 x+c3 y+c4 xy+c5 x2
+c6 y2
and we carry out the subtraction with respect to the original magnetic field
(Fig. 9).
A third way to isolate residual anomalies is by applying filters to the map grid.
They would be 2D filters in the space domain (wavelength) of the low-pass
type; then this filtered grid would be subtracted from the original field grid.
The procedure is equivalent to applying a high-pass (or band-pass) filter to the
original grid. In our research, we have seen, after some experimentation, that
the best result is obtained by applying the high-pass filter to the residual
Figure 9: Residual anomalies achieved by fitting
the magnetic field to a second order 2D
polynomial function.

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anomaly grid obtained by the polynomial function fitting procedure (Fig. 10).
In this way, the dipole anomaly in the southern sector has been clearly
defined, which is what interests us from the archaeological viewpoint.
3.4 | REDUCTION TO THE EQUATOR
The anomaly produced by a body of ferromagnetic material is dipolar. The
shape of said anomaly will have a different configuration depending on the
magnetic latitude in which the body is buried. For the southern hemisphere,
the orientation of the dipole anomalies will have their negative pole toward the
geographic South and their positive hemicycle toward the geographical North
(Fig. 6). However, it is to be noted that the magnetic anomaly will be centered
exactly at the epicenter of the body only at the magnetic poles and at the
Figure 10: Filtered map, of the field of residual
anomalies. High-pass Butterworth filter with cut-
off wavelength of 16 m.

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magnetic equator. At the equator it will be a negative monopole and in the
poles a positive monopole.
This characteristic of the anomalies caused by a magnetized body, buried
under the surface, is used to find the location of the body through a map of
residual magnetic anomalies. The reduction to the pole (or to the equator) of
the anomaly is carried analytically, where the presence of monopoles on the
map should indicate the position of the magnetized bodies. The operation
becomes simpler if we take the Fourier transform of the magnetic field and
multiply it by a factor of the form,
F(kr )=ℱ [Γ( x, y)]
R(kr )=|kr|
2 F(kr )kr
2
B
2
kr =√k2
2
+ky
2
B=
1
|ikx cos D cos I iky cos D cosI+kr cos I|
Figure 11: Reduction to the equator. As expected,
the negative anomaly is centered over the body.

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The reduction to the equator is a process is applied to magnetic data at low
magnetic latitudes. This is because a reduction to the pole at these latitudes
would create artificial deformations in the anomaly. In the map of reduction to
the equator (Fig. 11) we note that the center of the most conspicuous negative
anomaly is located at coordinates (9, 10.3); It corresponds to a buried lithic
body very close to the surface (5 cm) of which we can attest because we could
observe it directly in the field.
The other notable negative monopole is located at coordinates (15.2, 15.2),
but we have no direct evidence of a subsurface body because we did not
excavate in that area. Actually, our postgeophysical field work was located in
the first anomaly already described.
3.5 | HORIZONTAL DERIVATIVES
In a map of isomagnetic values, the great density of the level curves would
indicate that the slope of the function is high, this is associated with the limits
of the anomaly produced by a buried body. Therefore, an analytical method to
detect these body edges is by taking the horizontal derivatives on the map
reduced to the equator. High values of the derivatives would indicate the edges
of the body (Fig. 12).
Figure 12: The derivatives
of the magnetic field (dx,
dy) have their maxima at the
points of maximum
curvature, that is, these
maxima are interpreted as
the edges of the body
inscribed underground.

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Again, the mathematical operations are simplified working in the domain of the
wave number,
∂Γ( x, y)=F(ω)iω
This is the Fourier transform of the function; multiplied by the imaginary
constant and the wavenumber variable, give us the derivative in the wave
number domain. If we add the vertical derivative to the horizontal derivatives
of the magnetic field, we will have the analytical signal,
|A(X ,Y )|=
⟦(∂Γ
∂x )
2
+
(∂Γ
∂ y )
2
+
(∂Γ
∂ z )
2
⟧
1/2
.
This has the property that it is independent of the direction of magnetization of
the body and allows locating the edges of the body with greater precision, even
though its shape is not totally symmetrical in the case of three-dimensional
magnetization (Keating, Pierre and Sailhac, Pascal, 2004). The horizontal
derivatives have a base from which to extract them in the horizontal gradient
of the field; but for the vertical derivative it would be necessary to have the
vertical gradient of the magnetic field measured. We are not aware of that
vertical gradient, since we do not use a gradiometer. Therefore, we did not use
the analytic signal in our study; although some algorithms allow the calculation
of a pseudoanalytical signal; some tests that we did with these programs gave
results that did not improve what was achieved with the horizontal derivatives.
3.6 | ANOTHER ANALYTICAL TRANSFORMATIONS
The problem of locating the body that originates the magnetic anomaly has
been solved with a certain degree of precision by the transformations that we
have already seen (reduction to the pole and derivatives); however, the
influence of the magnetization direction is still great in these transformations.
Other transformations have been studied (Stavrev, Petar and Gerovska,
Daniela, 2000) that are less sensitive to the direction of magnetization. One of
them that has given good results in our experiments is the squared Laplacian,
∇
2
(Γ
2
)=2(|∇ Γ|
2
+Γ∇
2
Γ)=2(|∇ X|
2
+|∇ Y|
2
+|∇ Z|
2
) .
This function has positive values and can be considered harmonic outside the
body, under the conditions of medium amplitude of the anomalies and that the
local magnetic field has a constant direction. It has the advantage that the
maxima of the function is always above the body and that it removes the
peripheral maxima. From the squared Laplacian function form (Fig. 13) we can
say that it represents a set of alignments that make up a square, perhaps built
with andesitic stones, which abound in the area.

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Figure 14: Compendium of magnetic
maps with a qualitative interpretation.
Two maps are used for archaeological
interpretation: the reduction to the
equator (blue-red) and the squared
Laplacian (gray). The geometrical
figures and dashed lines indicate possible
buried archaeological structures.
3.7 | TREATMENT OF MAGNETIC MAPS AS DIGITAL IMAGES
Sometimes the transformations applied on the magnetic field data are not
enough to eliminate certain types of noise, or to highlight some structures that
the expert eye perceives in the data.
In dealing with lithic structures, we would like the magnetic data to highlight
the presence of such structures. Under the assumption that all these
structures were built with the same type of rock and, therefore, have the same
magnetic signature, it is possible to empirically choose a reference value that
identifies the change between the fill terrain and the building stones. Andesite
rocks abound in our study area; all the old constructions that are visibly were
built with this type of stone, so it is reasonable to think that if there were
buried walls, they would be made with andesite. Andesite is an extrusive and
subvolcanic igneous rock, which, in our area, has a high degree of
magnetization. This tells us that walls built with this rock should appear as
Figure 13: Laplacian squared. In this
analytical transformation, the maxima must
remain in the epicenter of the magnetized
bodies.

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magnetic highs on our residual anomaly map. To identify possible buried walls,
we apply a range compression filter to our data (Scollar, Irwin , Weidner,
Bernd and Segetht, Karel, 1986). This filter has the form,
g(i, j)=arctangent[(Γ(i, j)−B)C ]80.25+127;
where, B is the bright constant and C is the contrast factor.
In our filtered map (Fig. 15) we do not identify any structure that we can call a
wall. But sectors with high magnetization values (white) In contrast, other
sectors with low magnetization (dark gray) are clearly delimited. These sectors
of high magnetic intensity and low magnetic intensity, considering that they
correspond to a soil layer very close to the surface (due to the regional-
Figure 15: One type of map that provides
important information about lithology contrasts
on the ground is the compressed range map.
Here the compression was applied on the
residual anomaly magnetic map.

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residual separation and the applied high-pass filter), could be interpreted as
soils that they had diverse forms of use in their cultural occupation epoch.
The wavelet transform image processing technique (Fig. 16) allows selecting
and filtering elements of the figure of different scales (wavelengths). In this
case we have cleaned the residual anomaly map of those very short wave
elements. In this way we intend to highlight the long wavelength and
superficial elements that could indicate land with different uses.
3.8 | INVERSION OF RESIDUAL MAGNETIC ANOMALY
Until now, the transformations and filters applied to the magnetic data have
provided useful results for making qualitative interpretations of the magnetic
data. A further step in the interpretation of magnetic information is to obtain
quantitative results, such as those that can be obtained from geophysical
inversion. An inversion of the magnetic data offers two useful results for the
interpretation: the geometry of the source body and estimation of the
magnetic susceptibility of the body that originates the anomaly.
Figure 16: On the left side, the residual anomaly was obtained through background removal by
fitting a third-degree polynomial surface; on the right side, the map was processed by the wavelet
transform. The sectors called "dominio 1" and "dominio 2" have different (superficial) magnetic
properties, so it is interpreted that they have had diverse cultural use.

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Having in hand the measurements of the total component of the terrestrial
magnetic field; survey carried out on a mesh on the ground; applying an
analytical procedure to these data such that we can estimate the shape and
physical magnitudes of the subsurface body (or bodies) that generates the
magnetic field, is to find the solution of the inverse problem in Geophysics.
The inverse problem in magnetometry is linear. Its solutions can be found
through the mathematical methods developed to solve systems of linear
equations. However, the Geophysical Inversion suffers from problems that
must be solved in the inversion procedure itself, so that its results are reliable:
a) existence of the solution; sometimes the problem is mathematically ill-
posed and has no solution or has an infinite number of solutions; it must be
turned into a well-posed problem; b) the inversion does not have a unique
solution; this is due to the existence of noise (with different sources) in the
field data, so many physical models can be found that fit the data with the
same margin of error; c) the solution of the inverse problem may be unstable;
that is, a small error in the input data will cause the inverse solution to be very
different (Mendonca, 2020).
The existence of the solution to the inverse problem is ensured by conditioning
the system to reduce the error of an objective function, typically a least
squares function. The nonuniqueness of the solutions is solved by a
regularization procedure. The most used regularization method is the one
proposed by Tijonov: including a priori information in the system of equations.
The stability of the solution is achieved through the regularization procedure,
in which a weighting factor of the regularization, called a stabilizing factor, is
included.
3.8.1 | TWO-DIMENSIONAL INVERSION IN TERRESTRIAL
MAGNETOMETRY
The anomaly that occurs in the southwestern region of our study area differs
from the typical form of a dipole anomaly that produces a single buried body.
It rather has the shape of a positive pole (coordinates: 9.5, 15) surrounded by
a semicircle of negative intensity (Fig. 17), which may be due to a filling of
diamagnetic material with that shape. It is unusual for archaeological
exploration due to its large amplitude, ~1900 nT; therefore, it becomes a good
target for inverse modeling. We will start with an inversion in two dimensions,
on the profile A-A'.

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Figure 18: 2D model resulting from the inversion of the A-A' profile. The
discretization of the magnetic medium is made of squares that have 0.5 m
per side. A compactness regularization acts on the inversion. But the bodies
of high magnetic susceptibility show a bowl distribution, between distances
8-12 m and with a depth of up to 1.5 m.
Figure 17: Residual magnetic anomaly map showing digitization
points of the A-A' profile; with which the 2D modeling will be carried
out, through geophysical inversion techniques.

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Our entire study area is covered by rocks of volcanic origin, mudflows of
pyroclastic rocks dragged by the rains. Next to these are scattered blocks of
andesite. This scenario makes us expect that the magnetic field of the medium
is of high intensity, but dispersed; without consistent guidelines.
The 2D magnetic model (Fig.18) confirms what we expected, regarding the
high values of magnetic susceptibility (k). However, some interesting
regularities appear. As a channel at a 6-m distance with lower values of k. This
coincides with the observation we made in the field, where we found a landfill
with a yellowish color, very different from the environment. In conversations
with some archeologist friends, they suggest that it could be corn offerings,
which have disintegrated over time. Then, between 8 and 12 m, we see rocks
of higher k, it takes the shape of a bowl. It reaches a depth of 1.5 m. No type
of structure was found on the surface that could explain such a high
susceptibility.
3.8.1 | THREE-DIMENSIONAL INVERSION IN TERRESTRIAL
MAGNETOMETRY
The next step in our data interpretation is to perform 3D modeling of the entire
sector. But the computer's operating system could not allocate enough
memory for the arrays that were generated. Therefore, we had to reduce the
study area, and focus on the most conspicuous anomaly. Yet, our arrays had
dimensions of 6561x6400 elements.
We use the solution of the forward 3D problem proposed by Gallardo & Perez &
Gomez (2003) and the solution of the inversion subject to least squares,
G p=do subject on min ‖do−G p‖+α2
‖W‖
(G
T
G+α2
W ) pα=G
T
do
pα =(G
T
G+α2
W )
−1
⋅G
T
do ; where
G=: is the sensitivity matrix, the double bar above the letter is indicative of
bi-dimensional matrix;
p=: is the matrix of unknowns, the single bar above the letter is indicative of
mono-dimensional matrix;
do=: is the observed data matrix, in our survey here are the values of
magnetic intensities measured on the field;

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W =: is the regularization matrix. Since we use compactness regularization,
this matrix takes the form,
wii=
ri
2
|pi|+ϵ
(all other elements of the matrix are equal to zero); here ri is the
distance from any element of discretization to one point or a straight line
selected as inertial center and ε is a very small constant (Barbosa, Valéria C. F.
and Silva, João B. C, 2006). Finally,
α=: is the stabilization factor.
Due to the size of our matrices, the solution of the linear system was
performed using an iterative method, successive over relaxation (SOR).
Figure 19: The 3D model of the residual magnetic field. Each
body of the discretization has 0.5 m extension, but the reference
point is the centroid of each one. Due to the regularization
constraint, the bodies of high magnetic susceptibility appear
concentrated in a stratum that goes from 1 m to 1.5 m deep.

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The inverse modeling presents the results that appear in Fig. 19. In which the
first thing we must consider is that there is not a single body that concentrates
all the rocks of high magnetic susceptibility, as could be expected from the
shape and amplitude of the magnetic anomaly and from the compactness
constraint used in the regularization.
We set a point of center of inertia at the coordinates (9.2 east, 10.3 north, 1
depth) to calculate the radius ri in our regularization matrix, based on two
criteria: the first, that a stone structure was found in that place during our field
work, although of small diameter (~0.5 m) we had the hope that it would
appear in the models, second, that this is the center of the most intense dipole
magnetic anomaly that is shown in the map; data that is confirmed by the
reduction to the equator (Figs.11 and 14) and that was the reason why we did
a shallow exploratory excavation at that point. However, the 3D model
resolves the anomaly with a combination of low magnetic susceptibility bodies
at the surface and other high susceptibility bodies at greater depth.
Another noteworthy aspect of the 3D model is that some magnetic lineaments
are perceived that cannot be inferred from a qualitative evaluation of the
residual anomaly map. These lineaments are better appreciated if we perform
some deep horizontal tomography (Fig. 20).
Figure 20: The layers of the modeled bodies pass through their centroids. The upper layer ranges
from z=0 to z=0.5 m. In the figure it is seen that the ground at these depths has intermediate
magnetic susceptibilities. The high susceptibilities appear from 0.75 m and downward. However,
they do not make up a body with regular shapes. On the other hand, the deepest modeled stratum
(1.5 - 2 m) reveals a structure with very regular geometric shapes (rectangular), which would
indicate the foundations of the walls, which would correspond to cultural periods prior to those
found on the surface.

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We will go directly to the tomographic section that presents the most
interesting lineaments. At a depth of 1.75 m, a quadrilateral made up of high-k
bodies can be seen, and further east, a straight line of high-k bodies with a
south-north direction (dotted lines in Fig. 20). We interpret these guidelines as
the foundations of ancient walls and that, due to their depth and the absence
of surface evidence, could be attributed to a culture before that which later
occupied the same place and raised its buildings on the surface.
The wall foundations described above are also clearly seen in the iso-surface
figure (Fig. 21). Here it appears as a relief step between 1.5 and 2.0 m deep,
although it could probably continue downwards.
4 | ARCHAEOLOGICAL CHARACTERIZATION OF THE RESEARCH AREA
Figure 21: The isosurface mapping of
the deepest two layers shows relief in
the eastern sector (viewpoint is
approximately the same of Fig. 19).
Aligned almost perfectly South-North,
we interpret it as the foundation of an
old construction, before the buildings
that were later built on the surface.

25
In the northern direction of our study area, there are semi-destroyed
residential buildings and irrigation canals. Around, platforms that are evidence
of the presence of an agricultural society. The dwellings have various forms,
built with uncut stones and joined with clay mortar. All these constructions
show that there was a pre-Hispanic Tambo here. The Tambo, is a set of
buildings that had the purpose of storing food, supplies, weapons and animals;
as well as serving as a resting place for travelers.
It is possible to ensure that this is the Tambo de Chiguata, the name by which
it was known in colonial times. Along the slopes of the hill, Inca road crosses
from south to north, with a maximum width of 4.5 m. To the south of the
Tambo is the population's cemetery, with an area of 1350 m2
, it is the location
where we did our magnetic survey. Here you can see several desecrated
tombs, also along the Huasamayo river ravine. The general model of these
tombs is circular, built of rough stones joined with clay, having a maximum
diameter of 0.8 m and the same depth.
The Tambo de Chiguata had two well-defined human occupations: the
Churajón (Puquina) culture and the Inca culture. It is estimated that the
Churajón culture occupied the South of Peru during the years 1000–1200 of
this era. The Inca occupation has been verified through typological analysis of
the pottery found at the site (Gomez Rodriguez, Juan, 1966).
4.1 | ARCHAEOLOGICAL INTERPRETATION OF THE MAGNETIC SURVEY
The Tambo de Chiguata, although known since colonial times, had had very
few archaeological studies and none using the exploration tools offered by
Geophysics. The excavations in the area were limited in number; perhaps the
looters (huaqueros) had better knowledge of the tombs and other structures
that project in depth. This is how we emphasize the study of all bodies and
objects that are not visible on the surface, of which we have reference only
through this geophysical study.
The first archaeological-type object that we could locate using the indications
offered by the map of residual anomalies and the reduction to the pole, was
the well (let's call it that, for lack of a better description) located at the
coordinates (9.2 east, 10.3 north). This body had the shape of a vertical

26
cylinder built with more or less finely carved stones, the external diameter
would be about 0.5–0.6 m, as a cylinder lid there was a very fine stone slab,
covered only by a few centimeters of ground. Immediately below the lid, we
found two fired ceramic objects, they did not have any content; the shape and
color of ceramics indicate Inca origin. Although they show the influence of the
Churajón culture since the ocher and black colors are also typical of this
culture. The stone cylinder could not be the entrance to a tomb, because the
internal diameter was too small to allow the passage of a body. Although it
could also have been built after depositing the corpse at a lower level. But no
human corpse could be found; filling the cylinder there was yellowish earth
(possibly offerings of corn and other organic elements) which was extracted as
far as an arm could reach, the narrowness of the cylinder only allowed the
passage of an arm and it was impossible to advance beyond the length of the
arm.
On the outside of the stone well and surrounding it in the shape of a crescent,
there were fillings of yellowish earth. These were discovered after removing a
thin grayish soil cover, but we did not have time to further explore its extent,
depth, or whether it had retaining walls. We could see that this yellowish earth
fills coincide on the magnetic map with the area of low magnetic intensity that
surrounds the highest positive pole. In the 2D inversion model (Fig. 18) it
coincides with the intermediate k values at 6 m distance.
As we had already mentioned above, these yellow-colored lands would be
deposits of corn and other organic elements (degraded by the passage of
time). One could doubt that it is a matter of organic origin due to the large
volume it occupies; but, let us remember that this place was a Tambo, where
large amounts of food reserves were deposited.
The other buried bodies, detected through geophysical maps and inversion
models, were not explored, due to lack of time and because in that short time
in which the field work was carried out, only one map of residual anomaly
could be counted on. Then, we will only indicate the location of bodies of
possible archaeological interest. As the one shown by the Laplacian
transformation map (Fig. 13) that has the shape of a quadrilateral with
vertices at 8–10 east and 12–15 north. Another buried body, possibly
cylindrical in shape, has its center at the coordinates (15, 15) (Fig. 14). The 2D

27
model (Fig. 18) indicates a body of high k at a distance of 9.25 m and 1 m
deep. The 3D model (Fig. 20) shows signs of a quadrangular structure at the
1.75 m depth, with extensions ranging from 3–12 east to 6–14 north. This
would be the vestiges of foundations of buildings belonging to older human
occupations (pre-Churajon?).
5 | ACKNOWLEDGMENTS.
First, I must express my gratitude to the people who pointed me to the
appropriate archaeological site to conduct this geophysical survey, Patricia
Cáceres and Robert Loayza. Collaborating in the magnetic data acquisition
work in the field were Julio Cuenca, Prof. Hector Palza Arias-Barahona, Prof.
Alvaro Carpio Begazo, Andres Antallaca, Ramiro Cáceres Tejeda, Ricardo
Pelaez McEvoy. Subsequently, Ruth Caceres Tejeda, Martha Zevallos and Luz
Zevallos participated in the post-geophysical archaeological reconnaissance
work.
This research received a small grant from the National Council for Science and
Technology of Peru (CONCYTEC). The Universidad Nacional San Agustin-
Instituto Geofisico de Characato provided the magnetometer and some
hardware facilities to process the data.
The maps and figures were tailored using Generic Mapping Tools (GMT),
DISLIN, GeoGebra, MeshLab and QGis software. The programs for geophysical
inversion are from the author.
6 | CONCLUSIONS
The terrestrial magnetometry method is used as an indirect exploration tool
over archaeological targets.
The effectiveness of detecting buried bodies of archaeological affiliation was
verified since through the qualitative analysis of the map of residual anomalies
and the reduction to the equator, we could find a lithic structure from the Inca
period.

28
Other more refined processing of magnetic data, such as the Laplacian
transformation and inverse modeling in two and three dimensions, show the
existence of several buried bodies with characteristics of archaeological
interest.
From a purely archaeological viewpoint, the results of the 3D inversion are
interesting, in which lithic structures appear at greater depths than those
expected for the Inca and Churajon cultures, so possibly these are from a
previous era.
7 | REFERENCES
Aitken, M.J., 1969. Archaeometry 11, 109—114.
Aitken, M.J., 1974. Physics and archaeology, 2nd ed., Clarendon Press, Oxford.
Alldred, I. C., 1964. A fluxgate gradiometer for archaeological surveying:
Archaeometry, 7, 14-20.
Balogh, A., Hudson, H.S., Petrovay, K., von Steiger, R., 2014. Introduction to
the Solar Activity Cycle: Overview of Causes and Consequences, Space Science
Reviews.
DOI 10.1007/s11214-014-0125-8
Barbosa, Valéria C. F. and Silva, João B. C, 2006. Interactive 2D magnetic
inversion: A tool for aiding forward modeling and testing geologic hypotheses,
GEOPHYSICS, VOL. 71, NO. 5.
Gallardo-Delgado, Luis A., Pérez-Flores , Marco Antonio and Gómez-Treviño,
Enrique Gómez-Treviño.

29
Gomez Rodriguez, Juan, 1966. Antropologia aplicada a Chihuata, Thesis of
graduation (in spanish), Saint Augustin University, Arequipa – Peru.
Henderson, R., Zietz, I., 1949. the upward total continuation of anomalies in
magnetic intensity fields, geophysics, v. 14(4), pp. 517-534
DOI: 10.1190/1.1437560
Keating, Pierre and Sailhac, Pascal, 2004. Use of the analytic signal to identify
magnetic anomalies due to kimberlite pipes, GEOPHYSICS, VOL. 69, NO. 1, pp.
180–190.
DOI 10.1190/1.1649386
Keating, P., Pinet, N. and Pilkington, M., 2011. Comparison of some commonly
used regional residual separation techniques, GEM Beijing 2011: International
Workshop on Gravity, Electrical & Magnetic Methods and Their Applications
Beijing, China. October 10-13, 2011.
Lasfargues, Pierre, 1966. Magnetisme en Geologie et Prospection Magnetique
au sol, Masson et Cie., Paris.
Mendonca, Carlos A., 2020. Inversao Geofisica – notas de aula (in
Portuguese), Sao Paulo University, Sao Paulo – Brazil.
Phillips, J., 1996, Potential-field continuation: past practice vs. modern
methods, SEG Technical Program Expanded Abstracts.
DOI 10.1190/1.1826376
Rajesh, P. K., Lin, C. H., Lin, C. Y., Chen, C. H., Liu, J. Y., Matsuo, T., et al.,
2021. Extreme positive ionosphere storm triggered by a minor magnetic storm
in deep solar minimum revealed by FORMOSAT-7/COSMIC-2 and GNSS
observations. Journal of Geophysical Research: Space Physics, 126,
e2020JA028261.
DOI 10.1029/2020JA028261

30
Scollar, Irwin , Weidner, Bernd and Segetht, Karel, 1986. Display of
archaeological magnetic data, GEOPHYSICS, VOL. 51, NO.3, Pp. 623-633.
Sergipe, P., Marangoni, Y., dos Santos, P., Moura, D,. Jovane, L., 2021.
Diurnal variation effect in marine magnetometric surveys: clues from surveys
in southeast Brazil, Marine Geophysical Research, 42:28.
DOI 10.1007/s11001-021-09449-7
Stavrev, Petar and Gerovska, Daniela, 2000. Magnetic field transforms with
low sensitivity to the direction of source magnetization and high centricity,
Geophysical Prospecting, v. 48, 317-340.
Wynn, Jeffrey C, 1986. Special Issue Geophysics in Archaeology, GEOPHYSICS,
VOL. 51, No 3, 533-537.
Yamazaki, Y., Maute, A., 2017. Sq and EEJ—A Review on the Daily Variation of
the Geomagnetic Field Caused by Ionospheric Dynamo Currents, Space Sci
Rev, V. 206, pp. 299–405.
DOI 10.1007/s11214-016-0282-z
8 | SOME PERSONAL WORDS ABOUT THIS RESEARCH
This was my graduation thesis as a Geophysicist. The survey of data in the
field was carried out on October 31 and November 1, 1987. For this reason, it
constitutes the first geophysical study applied to Archeology, carried out in
Peru; by Peruvian researchers. Even though the printed volume of the thesis is
in the university library, the results of this research have never been published
internationally. The need to revisit the data with more advanced processing
methodologies is evident from the limitations that I had at that time, both in
theoretical knowledge and in the availability of computing resources. It is
enough to know that I was the first user of the first computer that arrived at
the university. I remember, it was an Epson Equity I, with no hard drive, no
math coprocessor, no graphics card, no printer, no plotter. However, the
quality of the data is good and with the capabilities that I have today, I have
managed to extract a lot of valuable information from the data.

31
Over time some things have been lost. For example, the photographs of the
work and the pottery found. These elements could be missed by the editors.
But, I think that the geophysical part of the study is valuable enough to
warrant publication.

32
Figure 1: The archaeological area under study is located near the city of
Arequipa in Perú (black circle in the map of South America).
Figure 2: Topographical map of the archaeological area of Tambo de Chiguata,
the black dot and circle indicate the place of the magnetic survey.
Figure 3: Aerial photograph of the Tambo de Chiguata area, the red rectangle
shows the limits of the magnetic survey. You can see the remains of the walls
of what was an old pre-hispanic town.
Figure 4: Diurnal variation curve of the terrestrial magnetic field; the blue dots
are the data measured in the terrain, the green solid curve is the least squares
fit to a polynomial piecewise function.
Figure 5: Map of magnetic anomalies; intensity total field. Pueblo Viejo
archaeological area. Local coordinates.
Figure 6: Typical magnetic anomalies on the magnetic Southern Hemisphere.
Due to magnetic inclination (I) in the region the negative part of the anomaly
is more intense. Note that in the magnetic equator the anomaly would be
monopolar and totally negative, this datum is important for the reduction to
the equator conversion.
Figure 7: Map of upward continuation of magnetic field, virtual height 8.0 m
above ground.
Figure 8: Residual magnetic anomaly map; resulting from subtracts the field
continued upwards from the total field at the height of the sensor.

33
Figure 9: Residual anomalies achieved by fitting the magnetic field to a second
order 2D polynomial function.
Figure 10: Filtered map, of the field of residual anomalies. High-pass
Butterworth filter with cut-off wavelength of 16 m.
Figure 11: Reduction to the equator. As expected the negative anomaly is
centered over the body. A little north of the more conspicuous negative
anomaly we find a positive anomaly; probably the algorithm interprets it as a
monopole and therefore does not make it negative.
Figure 12: The derivatives of the magnetic field (dx, dy) have their maxima at
the points of maximum curvature, that is, these maxima are interpreted as the
edges of the body inscribed underground.
Figure 13: Laplacian squared. In this analytical transformation, the maxima
must remain in the epicenter of the magnetized bodies.
Figure 14: Compendium of magnetic maps with a qualitative interpretation.
Two maps are used for archaeological interpretation: the reduction to the
equator (blue-red) and the squared Laplacian (gray). The geometrical figures
and dashed lines indicate possible buried archaeological structures.
Figure 15: One type of map that provides important information about
lithology contrasts on the ground is the compressed range map. Here the
compression was applied on the residual anomaly magnetic map.
Figure 16: On the left side, the residual anomaly was obtained through
background removal by fitting a third-degree polynomial surface; on the right
side, the map was processed by the wavelet transform. The sectors called
"dominio 1" and "dominio 2" have different (superficial) magnetic properties,
so it is interpreted that they have had diverse cultural use.

34
Figure 17: Residual magnetic anomaly map showing digitization points of the
A-A' profile; with which the 2D modeling will be carried out, through
geophysical inversion techniques.
Figure 18: 2D model resulting from the inversion of the A-A' profile. The
discretization of the magnetic medium is made of squares that have 0.5 m per
side. A compactness regularization acts on the inversion. But the bodies of
high magnetic susceptibility show a bowl distribution, between distances 8-12
m and with a depth of up to 1.5 m.
Figure 19: 3D model of the residual magnetic field. Each body of the
discretization has 0.5 m extension, but the reference point is the centroid of
each one. Thus the mesh reaches up to 2 m depth but the reference points are
up to the 1.75 m layer. Due to the regularization of compactness, the bodies of
high magnetic susceptibility appear concentrated in a stratum that goes from 1
m to 1.5 m deep.
Figure 20: The layers of the modeled bodies pass through their centroids. The
upper layer ranges from z=0 to z=0.5 m. In the figure it is seen that the
ground at these depths has intermediate magnetic susceptibilities. The high
susceptibilities appear from 0.75 m and downward. However, they do not
make up a body with regular shapes. On the other hand, the deepest modeled
stratum (1.5-2 m) reveals a structure with very regular geometric shapes
(rectangular), which would indicate the foundations of the walls, which would
correspond to cultural periods prior to those found on the surface.
Figure 21: The isosurface mapping of the deepest two layers shows relief in
the eastern sector (viewpoint is approximately the same of Fig. 19). Aligned
almost perfectly South-North, we interpret it as the foundation of an old
construction, before the buildings that were later built on the surface.

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