1. MAGNETOMETER SURVEY OF THE LA VENTA PYRAMID, 1969

Frank Morrison, C. W. Clewlow, Jr. and Robert F. Heizer

I ntroducti on

The La Venta pyramid, although the largest single structure at the
important Olmec ceremonial center in lowland Tabasco, has until recently

been afforded scant attention by researchers at the site. Early investigations
there by Matthew Stirling and Philip Drucker were concentrated on the unique
art style embodied in the large carved stone monuments and the problems of
ceramic stratigraphy (cf. Stirling, 1943; Drucker, 1952). The large scale
explorations of Drucker and Heizer in 1955 explored the complexities of

Complex A (Drucker, Heizer, and Squier, 1959; Drucker and Heizer, 1965).

Although the northern two-thirds of the site was mapped in 1955, the pyramid
(referred to as Complex C) was covered with a dense growth of jungle cover
and was incorrectly shown by the party surveyor to be a somewhat elongated
rectangle.

It was with understandable surprise, then, that Drucker and Heizer
viewed the pyramid in 1967, stripped of its heavy cover of foliage, and

recognized that it was not rectangular at all, but was actually a fluted
cone or, more technically, a conoidal frustum (Heizer and Drucker, 1968;
Heizer, 1968). Ten alternating valleys and ridges were seen to run up

the sloping surface of the structure's 100 foot elevation, spaced at roughly
equal intervals around its circular basal plan.   In 1968 Heizer returned to

La Venta with a University of California field party and, among other things,
completed a detailed topographic map, shown here in Figure 4, of the entire
pyramid structure which constitutes Complex C (Heizer, Drucker, and Graham,
1968; Heizer, Graham, and Napton, 1968).

This entirely new information, as well as providing fresh insights into
Olmec culture history (cf. Ibid., p. 137; Heizer, 1968, pp. 12-21), has

generated a renewed interest in the unique structure itself (Bernal, 1969,

pp. 35-36). Much of this interest of course revolves around the problems of

the possible function of the mound and the possibilities that it might contain
smaller buried structures.   It was in hopes of providing partial answers to
these questions that the 1969 magnetometer survey was conceived. It was

known that most of the large Olmec carved monuments as well as the natural

basalt columns which were used in the enclosure and the "tomb" in Complex A

were of a highly magnetic basalt from the Tuxtla Mountains, some 70 kilometers
to the west (Williams and Heizer, 1965). Samples of clays from the site
constructions were tested and found to be effectively non-magnetic. Thus
it was felt that should the Olmecs have buried any large stone monuments

or buiIt any structures of basalt within the pyramid they would be detected
by a sensitive magnetometer (cf. Stuart and Stuart, 1969, p. 200).

Most of the groundwork for the survey was done in Berkeley by Heizer,

who was unable to accompany the field party. The National Geographic Society
through its Committee on Research and Exploration granted funds for the

magnetometer survey. The authors wish to thank Dr. Melvin Payne, President

of the NGS and Dr. Leonard Carmichael, Secretary of the Committee on Research
and Exploration and the several members of the Committee for their support.

The field party itself was led by F. Morrison of the Department of Materials
Science and Engineering, University of California, Berkeley. He was aided
by Jack Mego, an electronics technician in the same department, and by

C. W. Clewlow, a graduate student in Anthropology. Invaluable assistance in
Mexico City, in Villahermosa, and at the La Venta site itself was provided

by Arql. Eduardo Contreras, Jr. of INAH, and Arql. Carlos Sebastian Hernandez,
Conservador of the Museo del Estado, Villahermosa, Tabasco. Considerable

enthusiasm and support from the Instituto Nacional de Antropologia e Historia
through the Director, Dr. Ignacio Bernal, contributed immensely to the success
of the survey. The survey itself took place between May 11 and May 29, 1969.

Description of the Magnetometer

Calculations of the magnetic anomalies to be expected from significant
basalt monuments buried within the La Venta pyramid were carried out on the

computer at Berkeley prior to the field work. Samples of sand and clay from
1968 test excavations in the La Venta area were tested for magnetic suscepti-
bility and found to be essentially non-magnetic. Assuming that the pyramid
itself was constructed of similar materials, and consequently possessing no
magnetic anomaly of its own, models consisting of basalt cubes three meters
on a side were run on the computer and values of the anomalous magnetic
field to be expected on the surface of an idealized model of the pyramid

were obtained. These calculations indicated that to detect such a basalt
structure, at the center and base of the pyramid, sensitivities as high

as 0.05 gammas (y) would be required (the Earth's total magnetic field at
La Venta is approximately 43,000 y). These same calculations showed that
a station spacing of three meters would be adequate to detect any major
structures.

Since natural time variations with periods from I second to diurnal are
a characteristic of the Earth's magnetic field and because these time vary-
ing fields can have amplitudes from O.Oly to 100y (respectively) it is

necessary to have a means of correcting for, or eliminating, these variations
in order to conduct such a high sensitivity magnetometer survey. The time
varying magnetic field is uniform over distances measured in kilometers so
that an obvious solution for small area surveys is to use two magnetometers
and measure the difference in the field. In this way, if one magnetometer

is placed in a fixed position the roving magnetometer will map the field due
to subsurface effects independently of the time variations. This configura-
tion was selected for the La Venta survey.

An alternate procedure which is often used in conventional geophysical
prospecting is to use only one sensor and to return periodically to a fixed
point, correcting the intervening readings in proportion to the amount the

3

field at the fixed point has varied. This method is inappropriate if

sensitivities of l.Oy or less are required because it would be necessary
to reoccupy the fixed station every 15 to 20 seconds.

The two-sensor difference magnetometer is useful for high sensitivity
surveys only if each sensor is itself of high sensitivity and consequently
such surveys have been possible only since the development of the alkali

vapour magnetometer. These devices have limiting sensitivities of 0.001y
and operating sensitivities of O.Oly are easy to achieve. The first

two-sensor difference survey, using Varian rubidium vapour magnetometers,
was conducted in 1965 (Breiner, 1965, Rainey and Ralph, 1966), and in the
summer of 1966 two fully developed systems were used with great success
in the search for Sybaris (Ralph, Morrison and O'Brien, 1968).    A more

complete description of the operation of the alkali vapour magnetometers
may be found in the articles referenced above.

To describe the actual electronics associated with the measurement

of the fields, it is only necessary to note that the output from an alkali
vapour magnetometer is a frequency proportional to the magnetic field in
which the sensor is placed. In the case of the rubidium sensor, the

constant of proportionality is 4.667 cycles per second per gamma (Hz/ y).
Thus in a field of 40,000y the frequency output of the magnetometer would
be 186,680 Hz.  For cesium the constant is 3.499 Hz/y.     These output

frequencies are easily measured on standard electronic counters (devices

to measure the number of cycles in a prescribed time). We can now easily

determine the sensitivity of a single magnetometer; for rubidium a      change
of ly in the field changes the frequency by 4.667 Hz. If the counter

displays the integer number of cycles in one second, we have a sensitivity
of +lcycle/second or approximately 1/4.667y.     If we count for 10 seconds,
we Then have a sensitivity of 0.1 cycle/second or approximately 1/46.67y.

Ideally in difference operation we would use a counter that measured

the difference in two output frequencies. The Varian portable magnetometer
readout unit accomplished this, but a simple and less expensive alternate
approach is to use the configuration of Figure 1.    This particular

difference magnetometer used two different Varian sensors, one rubidium and
one cesium. This was dictated solely by availability of sensors and in no
way affects the theory of operation.

The entire magnetometer system was powered by a lightweight 350 watt
gasoline motor-generator. Battery operation is also possible, but the

weight of the batteries required for 8 hours of operation is as great as

the generator plus gasoline. Moreover most electronic counters, especially

those available on a rental basis, are IlOv ac and would require an inverter
for battery operation. This would simply replace the converter used in

this system to supply the dc power to the sensors. The couplers associated
with each sensor in Figure I are mixers that supply the regulated 28v dc

power to the sensor and extract the output signal frequency returned from
the sensor to be fed to the counter. In the Varian readout unit the two

couplers, the power suppiy, and the counter are combined in a single unit
powered by a battery pack.

4

We shall see below that it is not necessary to use a counter that actually
measures the difference of the two sensor outputs. In fact, for "small"

differences in magnetic field between the two sensors the ratio of the two
frequency outputs is linearly proportional to the difference. This allows
us to use any counter which can measure ratios. The Hewlett-Packard Model
5325Awas selected for this survey for its light weight, low power consump-
tion and low monthly rental.

Magnetometer Sensitivity

To show the relationship of ratio to difference for this magnetometer
and to determine the difference mode sensitivity for the La Venta survey,
the following calculations are included in this report.

Let the output frequency of the rubidium magnetometer be A Hz at a

fixed point. At the same point the output of the cesium magnetometer will
be B Hz. If the Earth's field at that point is Ty , then A = 4.667T and

B = 3.499T. The ratio A/B is 1.333809. EA more correct ratio, using more
significant digits is 1.333400. This value thus constitutes the zero
contour in this survey.]

Now, disregarding time variations for the moment, if the cesium

magnetometer is moved to a position where the field has increased a small
amount, 6   , then the frequency output will increase 6 x 3.499 or A . The

ratio is now A/(B+A) or A/B(I A).    Now if A/B <<I, (I + A/B)    may be

22     B

expanded as I - A/B + A /B   - . . . .    If  A/B is less than .001, then
neglecting the terms beyond A/B in the series will affect the value of

- I                     ~~~~~~~~6

(I - A/B)    by less than one part in 106.    In that case the ratio becomes

A       A

BB

or

A   A   .A
B   B2

Thus, the ratio is a linear function of A.

We may now apply numbers from the La Venta survey. The mean value for

A  at La Venta was 202,700 Hz or 43,432.6y.    Thus the value of    B  is 202,700 x
3.499/4.667 or 151,970 so that A/B2 becomes 8.77x 10-6.     If the field at
sensor B now increases by 6y's, then A = 3.4996 and the ratio becomes

A             -6

-6A   8.77 x 10 6x 3.4996
or 1.333808 - 30.686 x 10 6

5

To translate this into limiting sensitivities, if we can measure the

ratio to + I unit in the sixth decimal place then the difference sensitivity
is 1/30.686 or .0325y/ unit. For six decimal ratio accuracy the count time

was I second with the corresponding sensitivity of 0.325y . The entire survey
at La Venta was conducted with a sensitivity of + 0.0325y. In retrospect,
we will see below an order of magnitude less would have been satisfactory.

For this linear relationship between ratio and difference to hold it is
only required that A/B be less than .001, ie., 3.4996/151,970 be less than
.001 or that 6 be less than 43y approximately. Rarely do anomalies in

excess of IOy occur in archaeological prospecting so it is seen that the
magnetometer used here is, to a very high order, a true difference

magnetometer. Practically speaking, if the anomaly is greater than 43y

a sensitivity of + I in the sixth decimal place of the ratio is unnecessary.
With a relaxing of the sensitivity to + I in the fifth place, the linear
approximation is again valid for anomalies up to several hundred gammas.

There remains the proof that the time variations are in fact cancelled
in such a configuration. We will consider the two outputs as before except
-that now the field increases by 6 y's at each of them.     The ratio then
becomes

A +4.6676                            A CA
B + 3.4996   or for convenience   B + C 6

Note that C B/C = r a fixed constant. We may now write the ratio as

BA~~~~~A

A6

A E I +A I

B6
BE I +    B

Again, if CB6/B is <<I, we may write this ratio as

0 c6           0 6
(I +  A    (I    B

AB6   CA6    CACB62
B        B     A     AB
Now

B _ AA I T 50 the two middle terms cancel leaving

B  ~  2A

2-

A (I-      )
B      T2

6

Here again we find that the restriction required to keep the ratio constant
to I part in 106 is that 62/T2 must be less than 10-6 approximately. At
La Venta T is 43,000y so 6 must be less than 43y .

Thus we find that for time variations to have no effect on the sixth
decimal place of the ratio, the magnitude of the variation must be less
than 43 y. Since the normal short period variations that we are trying
to eliminate are rarely greater than 10, we see that for all practical

purposes the time variations will have no effect on the ratio. If varia-
tions greater than 43y do occur, they may be corrected for by monitoring
the total field of the fixed sensor. Readings of total field frequency
were recorded at half hour intervals during the survey to ensure that

the amplitude did not change greatly. Maximum changes of less than 20y
were common to all the data recording periods.

As indicated in Figure 1, the rubidium sensor was used as the fixed

sensor and the cesium as the roving or mobile sensor. The technical reason
for this choice is that the cesium sensor is less subject to orientation

error and consequently easier to use as a hand carried device.      It should
be noted that the output frequency is independent of the orientation of
the cell but that the signal-to-noise ratio is highest when the sensor

axis is at 450 to the total-field direction and decreases away from this
position--the decrease being less for cesium than for rubidium.

A final point is that this magnetometer provides an absolute zero

for a particular area which is of some help in the interpretation of the
data.

Field Operation at La Venta

The equipment involved in the La Venta survey, schematically

described in Figure I, is shown packaged in Plate I.     In operation the

fixed sensor was placed well away from the readout area and both it and
the roving sensor were connected by coaxial cable to the readout unit.
The fixed sensor and the roving sensor are shown together in Plate 2.

The readout unit consisting of the two couplers, the power supply, and
the counter is shown in Plates 3 and 4.

To facilitate carrying the roving sensor dragging its cable along
with it, it was necessary to clear the pyramid of the dense underbrush

(see Plate 5). Survey lines were then laid out radially using ordinary

cord marked off in 3 meter intervals.    Readings were taken each 3 meters
out one line (Plate 7), the line was then swung approximately 6 meters

in chord distance at the 60 meter radius and surveyed again.     Intermediate
values, between lines, at large radii were filled in by estimating
position.

Azimuth readings were taken periodically and topographic features
were noted on the survey lines so that the data could later be fitted
accurately to the plan map of the pyramid. This surveying technique

7

was rather crude but relative positioning error is less than one meter and

the maximum absolute error is less than 2 meters in the azimuthal direction
and less than I meter in the radial direction.    More accurate surveying
procedures would have increased the survey time unreasonably without
significant improvement in the overall data.

The ratio values at each station were recorded directly on radially
scaled graph paper, an example of which is shown in Figure 2.     This
allowed preliminary contouring of data in the field as the example

indicates. Note that the ratio values are inverted with respect to the

true magnetic anomalies; that is, ratio lows correspond to magnetic highs
and vice versa.

To facilitate steady positioning of the roving sensor on the often uneven
surface of the pyramid the operator was "lowered" down the pyramid by a

rope as shown in Plate 6.   The process was found to be considerably easier
on the sensor operator, inasmuch as scrambling up and down a 30 slope in

high temperature and humidity can be rather wearying.     The sensor was carried
at a mean height of .8 meters above the ground.

All the equipment performed excellently. In the peak of the mid-day

heat, the heater control unit in the rubidium sensor failed but this problem
was easily eliminated by removing the unit. Apparently the high ambient
temperature was sufficient to keep the cesium cell vaporized. The survey
was completed in 8 days, and the equipment was actually on for a total of

41 hours. The progress of the survey was impeded in the early days by the
fact that the pyramid could not be cleared fast enough by a work crew of

eight men. The number was eventually increased to 24 and the survey progressed
more rapidly. Further, due to encroaching houses with their associated debris,
garden plots, etc., it was not possible to extend the survey radially as far
as had been planned. This was extremely unfortunate because on most lines

it was not possible to survey far enough away from the pyramid to get a zero
or background reading, nor was it possible to search for any monuments,

structures, etc., that might be near the base.    Approximately 2500 data points
were obtained.

Data Processing

The field data were transferred to a large scale plan map of the pyramid
and replotted.  The ratio 1.334000 was chosen as the base for this plot and

subtracted from all the readings. The readings were then contoured in levels
of 100 units or 3.25y. An ink tracing of the resulting contour map was then

made with the contours now marked in (3.00y was assumed instead of the correct
3.25) and with the correct sign. This map was then photo-reduced to the
same scale as the topographic map of the pyramid. This final contoured

magnetic map is shown in Figure 3. The topographic map is shown in Figure 4.
Finally, since shading or coloring of contour intervals emphasizes patterns
not immediately evident from the contours, the map was then color shaded as
shown in Figure 6.

8

The data were also converted to digital form for a later, more extended
analysis by digital computer. A preliminary step in this analysis is the

presentation of the magnetic data in a perspective view drawing.    Like the
color shading mentioned above these perspective drawings are helpful in

discerning anomaly patterns that are difficult to recognize in the contour
maps themselves. In Figure 3a a perspective view of the magnetic data,
taken from the South East, is shown to illustrate this effect.

All the maps presented in this report are oriented with respect to
magnetic north, since this is the important direction used in the inter-
pretation.

Interpretation

The color shaded map, Figure 6, shows the important magnetic patterns
more clearly than the simple contoured map, Figure 3. The general pattern
is one of strong radial anomalies on the southern half of the pyramid's
surface, turning into gentle broad circumferencial anomalies on the

northern half. Near the top and to the south is a striking magnetic high
falling off sharply to the north into a tight arc-shaped low area. These
anomalies show up clearly in the perspective view, Figure 3a. The major
anomaly near the top is very evident in this persepctive view and stands

out as the most important feature in the data. The color shading is likely
to place undesirable emphasis on minor features if they happen to be

colored overly brightly. Unfortunately this is the case for the blue areas
of Figure 6. The eye is drawn to the blue as an area of maximum anomaly,

whereas in fact it is only the small area of dark blue-violet near the top
which is indicative of a truly anomalous region. The red area is clearly
anomalous, sitting two full color intervals (orangie and yellow) above the

general "background".   In interpreting the field map, it is also important
to realize that the zero level contour is somewhat arbitrary. For the

detailed analysis to follow, we have used the ratio value 1.334400, the

approximate value of the rubidium/cesium constant, as the zero level but
since this ratio will go up or down with respect to the fixed station it
is obvious, for example, that if the fixed station were placed on the

highest magnetic anomaly then the whole map would come out with negative
contours. A better approach would be to take the mean of all the data

points as a zero but this is a rather tedious process without having the
data in digital form.

In the present case the choice of the zero level was somewhat sub-
jective, having been arrived at after considerable experimentation with
various models. We will see in the discussion to follow that it is the
pattern of the interpretational model that is Important rather than the

exact numerical fit. The area at the top of the pyramid was not surveyed
due to the presence of several concrete blocks with Imbedded iron bolts.

Some readings taken within 6. meters of the center showed steep gradients with
anomalies as high as lOOy's.   It is unlikely, however, that the Iron bolts

are responsible for the extreme values of the magnetic low encountered about
6 meters due south of the center (the deep blue-violet on the color map)

9

and it is evident that the accentuation of the low at this point is due
to very shallow magnetic objects, perhaps buried iron pipe.

The large magnetic low in the north west is caused by roofing metal,
and probably a host of other iron objects associated with the closest of
all the encroaching houses mentioned earlier.

The radial pattern is produced by the radial ridge and gully topo-

graphy of the pyramid (see Figure 4).   The Earth's magnetic field in the

La Venta area has an inclination of approximately 45? so that on the north
side of the pyramid the field is parallel to and inclined at only 15? to

the ridge and gully pattern.   At such low inclination very little secondary
field is to be expected.   On the eastern and western flanks, however, we
might assume that the ridges were represented by long cylinders with a

component of the field perpendicular to them, giving rise to typical high
on the south low on the north anomalies.    While the actual combination

of multiple ridge effects will not yield a simple pattern the radial nature
of the anomalies should be most pronounced on these flanks.     On the

southern surface the field is of high inclination to the ridges and of

zero strike with respect to them, so that the pattern of the anomalies will
be broad highscoinciding with the ridges.    This general pattern is so well
demonstrated in the magnetic map that there is little doubt that these
features are in fact due to the topography.

The magnetic low area just off the centerline at the extreme south
of the area surveyed coincides with a bulldozed excavation and probably

results from the removal of this magnetic soil layer.    A "hole" in magnetic
material produces a reversed anomaly, i.e., a low over the hole surrounded
by smaller highs.  The pits on the north slope of the pyramid will have

much smaller anomalies due to the low inclination of the field.     The small
anomaly almost on the center line at the southern margin of the map is a

clear exampie of the inverse anomaly havi ng been observed over a wel I def ined
pit about 1.5 m in diameter and 1.0 m deep.    The small isolated 6-y low about
15 m farther west is associated with a smaI I basalt block of .5 m maximum
dimension.  The maximum anomaly expected from such a small block of basalt

(susceptibi I ity 1o-3 e.m.u.) is on the order of 10y. The interesting feature
is, however, that the anomaly is negative rather than positive indicating a
high magnetic remanence for the block.    This fact wi I I be considered
further in the final summary.

The apparent high susceptibility of the soils was unanticipated, since
soil samples from the La Venta site, taken in 1968, were tested for their
magnetic susceptibil ity prior to the survey and found to be essential ly

non-magnetic.  A crude test of soil susceptibility on the pyramid was made
by placing small cups of soil of known volume four inches frQm the sensor.

The highest anomaly produced in this test was .26y, yielding a susceptibility
of 7 x 10-5 e.m.u.   The uncertainty in this crude test is on the order of

5 x 10-5 e.m.u. so it may only be concluded that the soil susceptibility is

between 10-5 and 10-4 e.m.u.   A too hasty calculation in the field led the senior
author to bel ieve the susceptibility was less than lO-9 and to conclude that
the topograph ic effect was cau sed by a magneti c sub-lIayer.

10

Soil susceptibilities of this order are not uncommon. Le Borgne (1955),
Aitken (1961), and Cook and Carts (1962) have shown that many highly organic
soils have volume susceptibilities of 5 x 10-    e.m.u. due to the in-situ

formation of the mineral. maghemite.   However, as Le Borgne has pointed out,
*in areas of high humidity where the drainage is sufficient, the iron is

usually leached out. Why the soil of.the La Venta pyramid should remain
so magnetic is not known.

The contradiction between this survey's results and the tests made prior
to.. the survey may be due to the following two factors.   The "soil" samples

tested may have been taken below the actual soil line or the pyramid may be
made of quite different clays and sands than the surrounding features.

It should be noted for future work of this sort that the optimum survey
should be preceded by some carefully controlled soil sampling and magnetic
susceptibi.l.ity measurements with a standard susceptibility bridge or with
an in-situ susceptibility meter.

The effect of this surface layer of magnetic material is to mask

anomalies from subsurface bodies with a "noise" level of 5 - IOy.      This

could be removed by digital processing of the data, namely by assuming a

surface layer of variable thickness and magnetic susceptibility and calculat-
ing, by surface integration for each data point, a new map of topographic
anomalies alone. The best fit to the observed topographic effects would
then be subtracted from the actual data leaving a map of anomalies from

subsurface bod.ies. Fortunately. in our case the main anomaly, just south

of center, is sufficiently above the topographic noise level so that this
costly.correction is not necessary.    In our discussion of this anomaly we

will have occas.ion to discuss the effect of the topography on the interpreta-
tion, but it will not be necessary to make calculations for it.

Finally the presence of the pronounced topographic effect decreases the
sensitivity requirement so that a sensitivity of 0.3y would have been

sufficient for this survey.   This, however, could not have been foretold
and the survey was actually run at a .0325y sensitivity.

The large magnetic anomaly to the south of the center of the pyramid

has been replotted in greater detail in the detail map, Figure 5.      For this
plot the ratio 1.334400 was chosen as the zero level, the ratios were

converted accurately to gammas, and the final map was contoured with an
interval of 2y.

The pattern of this anomaly is complex, although it may conveniently
be bro.ken down into two parts.  The first is the broad high contained

within the l.Oy contour, with an associated belt of lows roughly outlined

by the zero contour, which runs from the southeast, across the top of the
pyramid and off to the northwest.    Superimposed on this general high-low

pattern is a -further region of high values confined within the 26y contour.
The very high gradient along the northern and eastern margin of the broad

high suggests an origin near.surface whIle the extent and slope to the west

I I

and south suggest that the high is caused by a relatively large body at
greater depth.

To effect a quantitative interpretation of this anomaly, we have
designed a program to compute the anomaly due to any three-dimensional

rectangular block as measured on the surface of an approximately equivalent
cone.  This program could equally well compute the anomaly on the actual

surface, but this would require digitization of the topographic map, a step
considered unnecessary for the present interpretation. The method of
computation is that outlined by Bhattacharyya (1964).

An important assumption involved in all the discussion to follow is

that the anomalies observed are the result of induced magnetization and that
remanent magnetization is negligible. The separation of the two effects

is a major problem when dealing with high iron minerals such as are anticipated
here in the basalt.   Probably the only satisfying comment that can be made
about this situation is that if the remanent magnetization is strong, i.e.

as strong as the induced, there will still result a strong anomaly that will
certainly be interpreted as a magnetic body, but the interpreted body may
be in error. Only rarely will the magnetic bodies be placed in such a

fashion that the two fields cancel. That remanence is a problem in this
survey is undoubted, since the only known piece of basalt detected (the
small isolated 6 low mentioned earlier) had a remanent inverted anomaly.

In large structures, platforms, walls, etc., the remanent field of

each piece of basalt used in the construction will cancel leaving the induced
anomaly. It will be safe to proceed with the induced-only interpretation

if the anomaly is large and "complicated" in this sense. The interpretational
blocks are thus assumed to have no remanence.

The use of such blocks represents the practical limit of complexity in
,Interpretational models. Since, by its very nature, the potential field is

non-unique, there is nothing to be gained using models with greater shape
variability.  As with all indirect techniques, it is necessary to choose
a model which is geologically realistic and which provides a good general

fit to the data. This process, while not presenting a "true" picture of the
causative body does allow estimation of the extent of the body and its

depth limits.  Presumably in archaeological studies even more restraints
may be placed on the model to improve reliability.     In the present case,

for example, it is expected that any significant structures will be basalt
so that a susceptibility value may be assigned to the model. Further,

sharp discontinuities are expected between any structure and the surrounding
clay or sand, whereas in the normal mineral exploration survey the magnetic
rock unit may have a very poorly defined or irregular contact causing the
anomaly to spread misleadingly.

-3

In this interpretation a value of 10     e.m.u. has been assigned for

the susceptibility of the model material in order to represent an average

basalt.  In their study of the rock types used in Olmec monuments, Williams
and Heizer (1965) describe most of the rocks used at the La Venta site as
olivine basalt with scattered magnetic grains which would certainly not

12

classify them as iron deficient. Assuming a normal basalt, and since roughly
50 percent of the basalts tested by Slichter (1942) had susceptibilities

between 10-3 and 4 x 10-3 e.m.u., it is evident that the choice of 10-3 is
in fact conservative.

The values have been calculated for points on the surface of an equivalent
cone; these project in plan to an equidimensional grid. These points are
then contoured within the computer program and the resulting anomaly is

plotted by a CALCOMP plotter. The computer drawn maps for the detail map
area are on the same scale as the data plot, Figure 5. All data has been

plotted with the vertical margin of the plot corresponding to magnetic north.
For all the calculations in this study, the Earth's field is assumed to be
44,000y with an inclination of 450 and a declination of 8030? west of

geographic north. The equivalent cone is 30 m high and 80 m in radius.

The horizontal location of a block will be given in a plan drawing, with
the vertical coordinate (Z) and the half height (Az) written on the drawing.
The x coordinate is positive north, y positive east, and z positive up,
all with respect to the base and center of the pyramid.

From a preliminary inspection of the anomaly, it may be suspected that
the anomaly could be the result of a discontinuity in the susceptibility of
the surface soil layer. Since the block models have sides that parallel

the coordinate axis, models representing layers parallel to the pyramid slope
must be approximated by horizontal slabs with an appropriately corrected

inclination. A second program was written to calculate the field observed
on a horizontal grid above a horizontal slab thus approximating the pyramid

surface over a limited area by a flat plane. These anomalies were calculated
and plotted for the detail area as in the block model and are also presented
in the same scale as the detail map, Figure 5.

Values of soil susceptibility are usually less than 10      e.m.u. and
certainly the susceptibility contrast will be even less for natural soil

gradations. Further, natural soils will not possess abrupt discontinuities
so maximum effects may be calculated using thin slab models with vertical
boundaries.

A large slab 10.5 meters on a side and of varying thickness has been

chosen as a representative model for the anomaly in Figure 5. The resulting
contour maps for slab thicknesses (h) of 0.5, 1.0, 2.0, and 4.0 meters are

shown in Figures 8 to 11. The outline of the slab is shown in heavy dotted

lines in Figure 8. To assist in the study of these models and their relation-
ship to the field data, the N-S profiles, B-B', through each contour map are
presented in Figure 22 and these may be compared to profile B-B' of Figure 5.

In all models the anomalies were obtained for a sensor height above the
slab of 0.5 meters.

It is obvious from these plots that a thin discontinuous soil layer
(0.5m) cannot produce the observed anomaly either in character or in

13

amplitude. The extremes of the anomaly occur close to the nothern and
southern margins of the body and the maximum value is less than 6y.

Increasing the susceptibility from 10-4 to 5 x 10-4 would amplify the

anomaly magnitudes appropriately but would preserve the isolation of the
high and the low.

As the thickness of this slab increases, however, the anomaly, at least
in the profile shown, becomes remarkably similar to the observed data. The
slab 4 meters thick has roughly the same "width" (indicated by Ax     on the

I

profile, Figure 22) on the south as the field data, but is not nearly as

wide (A ) on the north as the field data. While this thick slab represents

X2

the central N-S profile quite well it fails in other respects. The field

data is quite asymmetric in an East-West profile as section A-A' of Figure
19 shows, and the low area bounding the eastern and northern edges of the
anomaly, trends off to the north west rather than wrapping around on the
west as the slab model does. The model could probably be converted to a
wedge, thickening to the East but this shape would be too costly to model
with the existing techniques.

The result of this interpretation using the slab model is that the

anomaly could be produced by some slab-like body at least 4 meters thick
with a susceptibility of 10-4 approximately. Possibilities are: (1) a
pit filled with highly organic soil, (2) a pit filled with stone other
than basalt. It is difficult to imagine a pit of this composition and

dimension showing no erosional expression or no surface gological express-
ion. In fact, comparing the magnetic data (Figure 5) and the topographic

map for the same area (Figure 7), it can be seen that there is no apparent
correlation between the proposed pit and the topography. Should the pit

have been filled with a less susceptible stone than basalt (e.g. serpentine)
then a significant archaeological structure is still indicated.

The above interpretation is restricted by the susceptibility assumed
for the slab material. To expand the interpretation to include the

typical basalts that have been assumed for monument material requires the
model structures to be at greater depth. For example, if the preceding

slab models were of basalt the anomalies would be increased tenfold. The

0.5 widths,Ax  and A    , would be too small to approximate the field profile.

Xl~x2

12

(Increasing the susceptibility simply multipliesthe anomaly but does not
change the position of the peaks, troughs, zero crossings, etc. in the

horizontal dimension). To increase these model widths it would be necessary
either to deepen the slab or increase its thickness, and the latter process
would of course make the amplitude of the anomaly too high. After a number
of such models (i.e. slabs of basalt at varying depths) were processed, it

was found that deepening the model destroyed the essential character of the
field profile and worsened the fit around the margins.

Turning to the "standard" buried block models now becomes a matter of
trial and error fitting procedures. This process is5 extremely tedious and

14

also quite costly in computer time so that in the present analysis

it has not been continued beyond a model that provides a basic fit. From
this basic fit and from a knowledge of the behaviour of the anomalies

from bodies of varying parameters, it is possible to postulate a number of
likely configurations for the actual causative body.

Single block models proved early in the interpretation to be inadequate.
This combination of the steep gradients around the margin and broad high

to the south necessitated multiple bodies. Wall-like structures were then
placed close to the surface to provide the steep gradients and the final

configuration achieved is shown in the plan diagram, Figure 12, as Model 5.

These plan diagrams have the elevation of the top of each block written
on the block. The surface elevation of the pyramid at a point directly

above that corner of the block which comes closest to the surface is noted
in the plan view just off the block. It is assumed that the sensor is

positioned on the equivalent surface. Thus in speaking of depth of a body
below the surface the depth is actually that below the sensor.

The east-west wall of Model 5 is higher than the north-south wall, but
the north-south wall comes within 1.0 meters of the surface, accounting for
the 18y peak to the south in Figure 15. The A-A' and C-C' profiles of

Figures 19 and 21 show a fairly good fit in general shape for the two walls
alone, but it is evident that the whole anomaly must be "pushed up" and
that the north wall should be brought closer to the surface.

To effect the general uplift and broadening of the model anomaly large
blocks of basalt at depth were added to the model. Model 5b is a combina-
tion of the two walls mentioned previously and a large block (4 x 4 x 6
meters, off center, and with its center 10 m above the base as shown in
Figure 12). The A-A' and C-C' profiles for Model 5b show the result of
this combination. The amplitude is in fact raised but the plan view of
the anomaly shows the inadequacy of the result. No single large block
(which would play the role of a major structure, such as a stone sub-

pyramid within the pyramid) could be found to raise the central area of the
anomaly (say the area within the 16y contour of Figure 5). This area

appears to be a magnetic platform upon which are superimposed wall-like
anomalies. A wide flat slab, subparallel to the pyramid surface could
result in this effect.

There is also the problem of the 30+y high just off the N-S center
line, below center, in Figure 5. This might be the effect of another

block, but a single block here would have a marked low to the north rather
than the gentle dip seen in Profile B-B', Figure 20.

The 30+y high and the general area of values greater than 20y were

finally well approximated with the wall-plus-horizontal slab model (Model
6a) of Figures 13 and 16. In this model a thin (0.5m) horizontal slab

forms a base for the two walls. The slab itself comes within 1.0 meter
of the surface, the east-west wall within 1.0 meter, and the north-south

wall within 1.5 meters. The resulting fit as seen in the contour maps is

1 5

good, except for the fact that, again, the whole model anomaly needs to
be pushed up and that the west side of the anomaly has to be stretched

out considerably. Profile B-B' of Model 6a has a slightly smaller width
on the north than the field data, indicating that the actual body is

slightly deeper than the model. Profiles C-C' and A-A' of the field data
are both taken over sections of maximum gradient, and the model profiles

for 6a have approximately the same widths. These results indicate that the
body is within 0.5 meter of the surface.    It is more realistic however to
consider the contour map itself and realize that the average width of the

anomaly along the northern and eastern margins is greater than in the cross
sections illustrated. The extreme low to the north is, as mentioned

previously, almost certainly the result of another body farther north and
the low (less than -lOy) on the east is due to accentuation by topography.
This topographic effect is brought about by the gully coinciding with the
low area thus bringing the sensor closer to the body in this area and

increasing the magnitude of the anomaly.   The position of the minimum in
profile A-A' is thus shifted inward giving a false indication of depth.

This same topographic effect is responsible for the 30+y peak's being
isolated in the field data and an elongate ridge in the model. The high

occurs in a gully where the observations were closer to the slab and thus
higher in amplitude.

Model 6b is a variation of Model 6a wherein the platform has been

dropped 0.5 m, the east wall brought within 0.5 m of the surface, and the

north wall lowered 0.5 m.   Model 6b provides a better fit to the field data
in profile B-B' and to the east in profile A-A'.

To generalize these results, considering the topographic effects and
the average width of the anomaly, it may be concluded that the walI s

assumed for the interpretation come within I - 2 meters of the surface of
the pyramid.

None of the models presented accounts for the general magnetic high

in the anomalous area nor for the gradual slope of the anomaly to the west.
Nor do these models account for the fact that the magnetic low with the
associated steep gradient runs off to the northwest instead of wrapping

around to the southwest. This latter anomaly could be explained by placing
another wall, starting at the western edge of the existing wall (block
3 of Figure 13) and running approximately NW for 10 to 15 meters.

In conclusion, the interpretation that emerges from these models may
best be summarized in the following point form:

(a) The general magnetic high within the 16y contour of Figure 5, or
alternately the yellow area and higher of Figure 6 may be explained
by a substructure within the pyramid. The center of mass of this
body is displaced due south of the pyramid center by as much as

30 meters. None of the simple models that were used in the inter-

pretation were successful in representing this feature. A slab-like
body, possibly parallel to the pyramid surface, at a depth of 3 - 6
meters could be one explanation. It will be noticed in comparing

16

the magnetic map (Figure 5) and the topographic map (Figure 7) that the
two limbs of the magnetic high that develop to the south correspond
almost exactly with two ridges that develop in about the center of

the map area. The magnetization of the ridge and gully topography,
high on the ridge and low in the gully is responsible for the split

pendant shape of the general magnetic high. This effect is even more
evident in the color shaded map.

(b) The detailed structure at the top is well represented by a thin
slab platform with superimposed walls on the eastern and northern
edges. "Walls" might well be basalt columns and the platform a

pavement surface of small blocks. In order that the reader not be

carried away with this interpretation, we add that the anomaly could
also be caused by a rubble level of basalt blocks that simply come
closer to the surface along the northern and eastern margin.

The major fact that emerges from the model interpretation is that the
source of these anomalies near the top of the pyramid is almost certainly
basalt and that it comes within I - 2 meters of the surface.

The precise location of the buried structure could possibly be out-

lined by probing the ground with steel rods. Alternatively the anomalies
could be drilled at relatively low cost with a gasoline-powered auger or

corer. These probings should be carried out in the vicinity of the magnetic
highs. To dig the pyramid, the best technique would probably be to dig a
trench running south from a point 4 meters east and 5 meters south of the

center to a point 4 meters east and 13 meters south. From the southern end
of this trench another trench should be run east into the gully for

approximately 6 meters. These trenches should be at least 3 meters deep.

17
F I GURES

Figure I   Schematic diagram of difference magnetometer
Figure 2   Example of field recorded data

Figure 3   Magnetic contour map of the La Venta pyramid
Figure 3a Perspective view of magnetic map

Figure 4   Topographic map of the La Venta pyramid
Figure 5   Detail magnetic contour map

Figure 6   Color shaded magnetic map of the La Venta pyramid
Figure 7   Detail topographic map

Figure 8   Slab, Model I;   slab thickness 0.5 m
Figure 9   Slab, Model 2;   slab thickness 1.0 m
Figure 10  Slab, Model 3;   slab thickness 2.0 m
Figure 11  Slab, Model 4;   slab thickness 4.0 m

Figure 12 Plan map showing location of model blocks; Model 5

Figure 13 Plan map showing location of model blocks; Model 6a
Figure 14 Blocks, Model 5a; wall configuration
Figure 15 Blocks, Model 5b; wall configuration
Figure 16 Blocks, Model 6a; wall configuration
Figure 17 Blocks, Model 6b; wall configuration
Figure 18 Block, Model 7; large block at depth
Figure 19 Magnetic Profiles A-A'
Figure 20  Magnetic Profiles B-B'
Figure 21 Magnetic Profiles C-C'

Figure 22 Magnetic Profiles B-B' (slab models)

18

PLATES

Plate I    Total packaged equipment for the magnetometer survey

a)  Portable 350 watt generator (40 lbs.)

b) Case containing counter, couplers, fixed sensor, power

supply, and power cable (50 lbs.)
c) Roving sensor (7 lbs.)

d)  Coaxial cable reel for connecting fixed and roving sensors

to the power supply and counter (25 lbs.)
Plate 2    Roving sensor and fixed sensor in operation
Plate 3    The read out unit
Plate 4    The read out unit

Plate 5    Clearing the underbrush from the pyramid
Plate 6    Roving sensor operator steadied by rope

Plate 7    Roving sensor positioned at 3 m mark on white cord

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Magnetometer Survey

Figure 6

106

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PLATE 7

ROVING SENSOR POSITIONED AT 3 M MARK ON WHITE CORD

19
BIBLIOGRAPHY

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Bernal, Ignacio

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20

Le Borgne, E.

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