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We are happy to share our newly developed methods for estimating complete dimensions of dykes from their partial exposures, even when the tips are not visible, using mathematical approaches based on the elliptical shape for opening-mode fractures. This could be incredibly useful for understanding magma pressure and estimating the depth of origin, particularly in field settings where complete exposures of dykes are rare.
Stress estimates have been made using length/width ratio of fractures by Gudmundsson (1983). Application of this method to dykes requires knowledge of full dyke dimensions to accurately estimate the range of magma overpressure. However, most, if not all, outcrops of dykes in the field are partially exposed owing to erosion, fault related obliteration or due to the nature of the outcrop in itself.
Kusumoto et al. (2013) and Biswas et al. (2023) developed two different methods to estimate complete dyke dimensions from their partial exposures. However, these methods work only when at least one of the dyke tips is visible in the field. But, in nature, finding a dyke with even one visible tip is a matter of pure chance. To solve this issue, Biswas et al. (2025) introduced a mathematical method to estimate full dimensions of a dyke even when no tips are visible in the outcrop.
The present method can be a potent game-changer in volcanology, where measuring the full extent of a dyke is often challenging. By leveraging the elliptical shape of dyke opening as formulated by the canonical model and applying discrete derivatives derived from limited ground measurements of dykes in the differential equations of an ellipse, we infer crucial parameters like the total length, maximum width, and aspect ratio of a dyke. These, in turn, help estimate magma overpressure, depth of origin and provide valuable insights into other factors associated with the mechanics of dyke formation.
We have developed two different codes to estimate complete dyke dimensions from:
1. Partial dyke exposures with one visible tip.
2. Partial dyke exposures with no visible tips.
A web page link is provided below where you can access an interface to calculate complete dyke dimensions from limited ground measurements made on such partial dyke exposures and thereby estimate their magma overpressure. The codes are freely available, and we encourage you to use them as needed.
References:
Biswas, S.K., Mondal, T. K., Saha, A., Mukhopadhyay A.K., and Mukherjee A. (2025). Estimating Complete Dyke Dimensions from Partial Exposures. Journal of Structural Geology, 192, 105350. https://doi.org/10.1016/j.jsg.2025.105350
Biswas, S.K., Saha, K., Das, G., Mondal, T.K. (2023). Estimation of magma overpressure from partially exposed dykes-A new approach. Journal of Structural Geology, 168, 104822.
https://doi.org/10.1016/j.jsg.2023.104822
Kusumoto, S., Geshi, N., Gudmundsson, A. (2013). Aspect ratios and magma overpressures of non-feeder dikes observed in the Miyake-jima volcano (Japan), and fracture toughness of its upper part. Geophysical Research Letters, 40 (6), 1065–1068. https://doi.org/10.1002/grl.50284
Gudmundsson, A. (1983). Stress estimates from the length/width ratios of fractures. Journal of Structural Geology, 5 (6), 623–626. https://doi.org/10.1016/0191-8141(83)90075-5
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