The pyramid of El Osario was initially studied to demonstrate the effectiveness of the proposed ERT-3D method, by employing unconventional and non-invasive geoelectric arrays7,8. As mentioned above, this structure was built on top of a natural cavity, which was discovered in the late 19th century17. The results obtained are highly relevant to investigate the pyramid of El Castillo subsurface, which might present the same characteristics of El Osario18.

El osario pyramid

A series of flat-base cooper electrodes were deployed around the base of the pyramid (Fig. 2A) to test the ERT-3D methodology proposed. A special sequence of resistivity observations was acquired to study the subsoil of the pyramid by employing the ERT-3D method.

Figure 2 To demonstrate the possibilities of the proposed ERT-3D method, 72 electrodes were deployed around the base of the temple of El Osario (A). The inverted model shows a high resistivity anomaly towards the central part of the WRC (B). This anomaly can be isolated and a void structure can be observed, corresponding to the mentioned cavity17 (C). The image of the WRC, seen from above, defines the dimensions of the structure, and the 3 passages that connect it (D, broken arrows). The outline of El Osario was placed on top of the resistivity model for a better visualization, as well as the location of the vertical shaft entrance17,18 (E). Full size image

The inverted resistivity data from the Pyramid of El Osario is displayed in Fig. 2B. The Working Resistivity Cube was obtained after 7 iterations with a RMS = 4%19, where a smooth inverted resistivity distribution at depth was achieved. A lateral view of the Working Resistivity Cube is shown, where several prominent features can be observed. The approximate perimeter of the pyramid has been outlined to facilitate the correlation of the detected anomalies (broken line).

An elongated anomaly (~1000 Ohms-m) can be observed extending approximately towards the central portion of the Working Resistivity Cube. This feature possesses an interesting geometry that stands out above the rest of the geoelectric anomalies. Other high resistivity anomalies could be associated to the pyramid foundations, infill materials employed to level the terrain or voids in the limestone. Resistivity values about the order of 350 Ohm-m could be related to the natural rock in the area, limestone in this case. Lower resistivity values (~70 Ohm-m) may represent water-saturated areas of seeping through the pyramid into the ground due to rainwater.

A range of resistivity values (300 Ohm-m to 500 Ohm-m) were considered and displayed as iso-surfaces to obtain the image in Fig. 2C. The morphology of the already mentioned high resistivity anomaly can be observed more clearly. This feature is defined by a hollow structure, whose wrapping represents the surrounding medium (limestone), and reaches an approximate depth of 14 m from the base of the pyramid to its lowest portion. This natural structure must be the resistivity signature of the cavity already reported E. Thompson17,18.

The pyramid’s outline is shown on top of the Working Resistivity Cube (Fig. 2D). This image shows the resistivity model seen from the top of the pyramid. The inferred cavity possesses an approximate diameter of 15 m. Today’s entrance to the vertical shaft17 is shown in image (2E). Observe that such feature is not precisely centered on the midpoint of the cavity18. On the other hand, 12 different exits were reported inside the cave17, overlooking their course. Our ERT-3D study could only depict three different passages displayed in Fig. 2D (broken arrows). One inferred channel run towards the northwestern direction, where the Pyramid of El Castillo is found. This model leads us to consider a possible underground connection between El Osario and El Castillo pyramids. It will be necessary to perform in the future further ERT-2D lines in between the two pyramids to demonstrate it. Other passage runs in the western direction towards the Cenote Xtoloc, partially explored by E. Thompson17, and the third one to the east.

El castillo pyramid

The famous pyramid of El Castillo subsoil was investigated by deploying around its base 96 flat-base electrodes, separated 3 m (Fig. 3A). 5 iterations were needed with a RMS error of 2.1%19 to obtain the inverted resistivity model displayed in Fig. 2B. Low resistivity values (<80 Ohm-m) revealed evidence of a body saturated with sweet water beneath the Pyramid of El Castillo extending 20 m in the N-S direction and 16 m in the E-W direction, approximately. Intermediate resistivity values (~350 Ohm-m) could be associated with the limestone rocks. High resistivity values (>800 Ohm-m) might correspond to materials employed in the different constructive periods of the pyramid.

Figure 3 The flat-base electrodes were placed in a trench around the base of the Pyramid of El Castillo, separated 3 m (A). The WRC shows a water-saturated zone towards the center of the pyramid (~70 Ohm-m) (B). It is possible to isolate that resistive structure. The geometry of a cavity partially filled with water is observed, where the digital image of the pyramid has been placed on top of the WRC for a better visualization of the structure (C). Full size image

When displaying only low resistive values (~80 Ohm-m) as iso-surfaces, the geometry associated to the highly saturated materials is clearly observed (Fig. 2C). The feature surrounding the low resistivity body might correspond to a drier feature (limestone, ~350 Ohm-m), suggesting the geometry of a buried cavity (or karst) partially filled with water. For best viewing, we have placed the digital image of the pyramid on top of the Working Resistivity Cube. The arrows in the figure attempt to represent the possible direction of the groundwater flow. This interpreted cavity (karst) extends beneath the pyramid from the surface to more than 20 m deep.

Under the present results, several questions arise, which might be answered by the specialists on the Mayan culture:

Did the ancient Mayans know about the existence of this subterranean structure? If so, why did the Mayans built this huge temple on top of this structure?

Further archaeological and geophysical investigations will provide the answers to such questions.

Synthetic modelling

It is important to point out that the inverted resistivity model obtained for the pyramid of El Castillo shows an open cavity towards the surface, as if most of this emblematic edifice was built on that ‘open surface’. Such a result means that the method employed depicts a poor vertical resolution towards the center of the ERT array due to the lack of resistivity observations on this portion, forcing the inversion to pop out the body on to the surface in the inversion process8,20. A similar inaccuracy was observed for the inverted resistivity model of El Osario, where the inferred cavity outcrops on the surface beneath the base of the pyramid. However, E. Thompson17 discovered the entrance to this cavity 3 m below the base of the pyramid. Such lack of vertical resolution is due to the inversion algorithm used, which is part of the commercial software employed to carry out the inversion process. Some authors8,20 have mentioned that such commercial algorithms, often considers grids formed by lines of electrodes to deal with a 3D interpretation. However, the methodology exposed in this investigation only needs electrode lines surrounding the studied targets7,8,20. Then, it is crucial to analyze the effectiveness of the methodology employed in order to understand the results obtained for El Osario and El Castillo pyramids. Therefore, synthetic examples have been designed to examine the behavior of the inverted solutions and to consider the possibilities and limitations of the arrays applied. Two different models have been designed to analyze the inversion results.

Synthetic model 1

Initially, we have considered an array comprised by 40 electrodes separated 1 m, deployed in a square geometry. A grid of 10 × 10 m2 was constructed to model the response of the resistive synthetic model. Such model is represented by a block of 4 × 4 × 2 m3, and positioned towards the central portion of the grid. The resistivity value assigned to the model was 10 Ohm-m embedded in a 100 Ohm-m half-space. The ERT-3D arrays have been included to compute the resistivity response of this block. Two different cases are dealt with, first the model outcrops to the surface (Fig. 4A), and second, the model is buried at a depth of 2 m (Fig. 4B).

Figure 4 A synthetic model cube is computed, located towards the central portion of a 3D grid of 10 × 10 m2. Initially, the block outcrops (A) and then the model is buried 2 m from its top (B). Inverted solutions obtained are quite similar (C,D). The inverted solutions pop up to the surface, indicating a poor vertical resolution of the arrays employed. Full size image

It is important to point out that the inverted models look quite similar (Fig. 4C,D). In both diagrams, the inversion algorithm inserted in the commercial program EarthImager3D19, vertically prolongs the solution towards the surface for the buried block, nevertheless the horizontal resolution is adequate and its original lateral dimensions have been recovered as well as its resistivity value. Unfortunately, the lack of data towards the central portion of the block cannot resolve the actual depth of each block.

Synthetic model 2

Let us now consider a block model located towards the left-upper corner of the Working Resistivity Cube (Fig. 5A). The dimensions of this block are: 5 × 5 × 2.5 m3, with an assigned resistivity of 10 Ohm-m, embedded as the previous example in a 100 Ohm-m half-space. The grid is 10 × 10 m2 as well, with 40 electrodes separated 1 m, forming a square geometry. The three arrays discussed in this investigation have also been applied to calculate the resistivity response. It is important to say that the observed data has been contaminated with noise (5%).

Figure 5 A synthetic cube is shown positioned towards the upper left-hand corner of the 10 × 10 m2 grid (A). The inverted solution also is stretched unto the surface (B). Plotting the interval between 1 Ohm-m to 10 Ohm-m (C), the geometry of the inverted block is depicted distorted and its top outcrops. However, the lateral dimensions and the original resistivity of the block is well recovered. Full size image

The inverted solution (Fig. 5B) depicts a circular low resistivity anomaly on the surface, within the interval of 10 Ohm-m. The green color corresponds to the half-space with a resistivity of 91 Ohm-m. High resistivity values surrounding the main anomaly may correspond to noisy effects. The program allows removing not required data, leaving values within an interval of 1 Ohm-m to 10 Ohm-m. Figure 5C depicts the isolated inverted structure. The correct geometry of the original synthetic model has not been recovered; nevertheless, position, lateral dimensions and its resistivity value are well defined. As in the previous example, the inverted solution depicts an outcropping block and again, a lack of vertical resolution.

It has been shown that the arrays employed present a poor vertical resolution, because the inversion algorithm employed expects to have data on top of the anomalous resistivity structure8,20, which is not the case in the methodology presented. We must say that there is not a physical or theoretical restriction on the way to display the electrodes20, as well as the geometry designed to deploy them8. This means that the ERT-3D arrays treated here, will present such limitations, when applied on real data; nevertheless, lateral dimensions of the synthetic models presented are well achieved. Therefore, we can conclude that the resistivity models obtained for the pyramids of El Osario and El Castillo possess a good estimation on their lateral distribution and do not have an adequate vertical resolution.