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Introduction
At Cotopaxi volcano, Ecuador, the periodic alternation of basic andesitic (56-62% ) and evolved rhyolitic (70-75% ) magmatism from the same volcanic center is an engaging and complex problem. The complexity of the issue is exacerbated by a lack of working models to explain the absence of an intermediate constituent, dacite. Traditional explanations for bimodal magmatism do not agree with geochemical data sets for this Andean arc volcano. Geochemical studies suggest there has been limited mixing between andesites and rhyolites (1). The few mingled samples that do exist consist of andesite endmembers (2). The Instituto Geofísico of the Escuela Politécnica Nacional (IG-EPN) has been monitoring Cotopaxi with more than 50 active monitoring systems, including 15 seismic instruments since 1979 (3). Increased magma supply to a reservoir 3km at depth is thought to have caused fluids to migrate and cause earthquakes on the NE edifice of the volcano (4). Cotopaxi erupted again from 2015 to 2016 (5). Seismic imaging revealed a very low velocity ratio (Vp/Vs) beneath the SW flank of the edifice (6). This observation is consistent with either a zone of partial melt accumulation or concentrated hydrothermal fluid migration (7). Gravimetric data agrees that there is a shallow aquifer or magma reservoir on the SW flank(8).
Figure 1: Google Earth satellite image of the Cotopaxi volcano and the location of the magma body on the southwest flank and a map of Ecuador that highlights Cotopaxi’s proximity to two largely populated cities, Quito and Latacunga.
Methodology
Magnetotellurics (MT) is a natural-source electromagnetic geophysical technique that images electrical conductivity. Subsurface electrical conductivity models have been invaluable in exploring the complexity of volcanic systems (9,10). Measuring strong contrasts in electrical conductivity in volcanic materials allows for the interpretation and examination of the subsurface geologic structure and geochemistry of the internal system. Used in conjunction, seismic and MT are useful for providing constraints on the chemical composition of fluids as well as inferring the melt fraction of magmas.
Equation Set 1: A list of the foundational equations used for the MT method. Maxwell’s equations provided the mathematical foundation for Tikhonov and Cagniard to develop the MT method and the functionality of impedance tensors.
Figure 2: A typical layout for an MT Recording station. Measurements are taken of the orthogonal components of magnetic and induced electric field variations
Using Finite Difference Forward Modeling
Here, forward modeling was used to create a sensitivity analysis for the Cotopaxi volcano. Starting model conductor geometry is based on geophysical results from a 2015 Gravity survey (4, 6). The smallest scenario is a 6 cubic km conductor approximately 3 km beneath the subsurface. In order to determine the sensitivity of a magma body to an MT survey with 81 grid stations separated by 10 km and centered over the conductor. Nine random periods were chosen and impedance tensors as well as apparent phase and resistivity were calculated. In total, 7 starting models were made to consider changes in shape along the x,y plane as well as along the z axis. These three models were chosen to share because as the surface area of the conductor increases the dimensionality of the target in the data increases from 1-D to 2-D to 3-D. Finite difference forward modeling in ModEM was used to calculate the forward response (11).
Figure 3 : 2D slices of 3D infinite half space models. The top layer of each model is a resistive 200 Ohm*m layer of 36 km depth. Beneath the 200 Ohm*m layer is a highly conductive 10 Ohm*m layer. In model 1, a 6 cubic km 80 Ohm* m conductor ,3 km beneath the subsurface and centered in the model, is intended to represent Cotopaxi’s magma reservoir. The surface area of the conductor is increased in the x and y dimensions 3 times and again by 6 times with no changes along the z axis.
Forward Response
Figure 4 : Apparent resistivity and phase plots. Station 1 is away from the conductor and Station 41 is directly over the conductor. Here are side by side comparisons to see if changing the size of the conductor along x and y changes the forward response after calculating the apparent resistivity and phase for each site.
Impedance Tensors and Dimensionality
It is more apparent in the impedance tensors that model 1 is exhibiting 1-dimensional structure due to the target being too small. In the diagonal (Zxx and Zyy) a fractal pattern emerges, and the off diagonals exhibit near linear symmetry. As the period increases (f decreases) for a 1-D model the diagonals tend towards 0 which can be seen in Model 1. As the x,y surface area of the conductor increases, the impedance tensors exhibit a 2-D structure (Zxx= -Zyy) in the subsurface as can be seen on Model 2. As the surface area increases to fit well between the stations the impedance tensors lose the trend that can be seen in 1-D and 2-D structure and exhibit a strong 3-D structure.
T1= 0.4941s T2= 1.9762s T3 = 4.4465s T4= 7.9049s T5= 12.3513s T6= 17.859s T7= 24.2086s T8= 31.6194s T9= 40.0s
Figure 5 : Impedance tensor plots for each station at each period. Using 1-D and 2-D structure equations in Equation Set 1 the impedance tensors were analyzed to determine dimensionality and how much of the conductor was being picked up by the station array. Model 1 exhibits 1-D structure and Model 2 exhibits 2-D. Model 3 does not meet the criteria to be 1-D or 2-D and is considered 3-D.
Future Works
This sensitivity analysis is in development to inform an MT survey in collaboration with IG-EPN in Ecuador. The goal of the survey is to target the magma reservoir as well as fluids associated with earthquakes flowing from the SW to NE. Below is an example of a similar survey where Archie's Law was used to calculate partial melt of the magma reservoir and conductivity further constrain the geochemistry of the system.
Figure 6 : Figure from (9). An example of a large-scale MT survey at the Newberry Volcano in the Cascade arc. The red represents highly conductive materials such as water or magma and the blue represents resistive volcanic rock.
Broader Impacts
Cotopaxi is one of the most dangerous volcanoes in Ecuador. Latacunga , the nearest city, has a population of ~ 200,000 people. Lahars have destroyed Latacunga twice in its history by Lahars from Cotopaxi eruptions. Quito is 50 km from Cotopaxi and has a population of over 2 million.
Figure 7 : Figure from (12). Understanding the potential VEI of Cotopaxi can help prepare for geohazards.
Figure 8 : Students at IG-EPN will assist with the project and use data for their research. Photos taken by Kaitlan Angel.
Summary
In conclusion, The Cotopaxi volcano is a petrologically unique volcano and also one of the most well monitored and dangerous volcanoes in the Ecuadorian Andean arc. MT is a particularly powerful method for constraining temperature, geochemistry, and the geometry and magma reservoirs and associate fluids. Electromagnetic geophysics is not often accessible in Ecuador, and this creates an opportunity to collaborate the IG-EPN to conduct an EM survey of the Cotopaxi magma body for both scientific and educational purposes. A sensitivity analysis of the Cotopaxi volcano is in development to understand the ideal station array and periods to use in order to target 3-D structures in the volcanic subsurface. Future works include collecting MT data at the Cotopaxi volcano and using Archie's Law to calculate partial melt fraction and constrain the temperature and geochemistry of the system. All of this will be done in collaboration with the IG-EPN and their university collaborator The National Polytechnic School.
References and Acknowledgements
1.Hall, M, Mothes, P, Bulletin of Volcanology 70, 675-702 (2008).
2.Martel, C, Andújar, J, Mothes, P, Journal of Volcanology and Geothermal 354, 74-86 (2018).
3.Saalfeld, M, Kelley, D, Journal of South American Earth Sciences 93, 85-101 (2019).
4.Hickey, J, Gottsmann, J, Mothes, P, Solid Earth 120, 1473-1486 (2015).
5.Hidalgo, S, Battaglia, J, Geochemistry, Geophysics, Geosystems 7, 2087-2108. (2018).
6.Araujo, S, U. Grenoble Alpes Sciences of the Universe Geophysics, Thesis, 131-138 (2016).
7.Condie, K, Earth as an Evolving Planetary System, 3rd ed., 144 (2005).
8.Calahorrano, A, Williams-Jones G., Volcanology and Geothermal Research 387, 8-11 (2019).
9.Bowles‐Martinez, E, Schultz, A, Geochemistry, Geophysics, Geosystems 21, 1-18 (2020).
10.Ingham, M, Bibby, H, Geophysical Journal International 179, 887-904 (2009).
11. Kelbert, A, Meqbel, N, Eggbert, G, Computers and Geosciences 66, 40-53 (2014).
12. Gomez-Zapata, J.C, Parrado, C., et al. et al. Sustainability 13, 1714 (2021).
We would like to acknowledge the The Instituto Geofísico of the Escuela Politécnica Nacional (IG-EPN) in Ecuador for sharing student thesis’ and providing intellectual support on this project. We would also like to thank Oregon State University for supporting this graduate student.
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