Numerical models of Cascadia earthquake scenarios constrained by energy budget analyses

1 Numerical models of Cascadia earthquake scenarios constrained by energy budget analyses LINDSAY GROSS, San Jose State University Twin Mentor 1: Elizabeth Madden, San Jose State University Twin Mentor 2: Amanda Thomas, University of California Davis ABSTRACT Megathrust subduction zone earthquakes are a deadly hazard that many areas, including the North American Pacific Coast, face. Understanding the mechanics behind these events is pertinent for assessing the possible impact on local communities. Megathrust earthquake energy budgets, which are a sum of the energy components of frictional, rupture, and radiated energy, are not perfectly understood. High-performance computational models, using software, such as SeisSol, are one way to visualize the ruptures and understand the dissipation of energy during them. We re-run a suite of models from Madden et. al (2022) of the SumatraAndaman earthquake of 2004 to estimate the energy budget for that event. We compare the model findings to observations from the 2004 earthquake to see how well the model fits the energy observations. We will construct a model of a potential megathrust event at the Cascadia subduction zone in the Pacific Northwest and compare its energy budget to that for the 2004 Sumatra earthquake. Our findings will allow us to better understand megathrust earthquake energy budgets, improve our models to accurately represent them, and better understand the nature of the seismic hazard millions of people face living on the Pacific Northwest coast, where a megathrust earthquake will inevitably strike. INTRODUCTION Earthquakes are one of the greatest natural dangers to mankind (Kammer et al., 2024), especially in countries that have not established building regulations to combat death and injury from megathrust earthquakes. Megathrust faults are subduction zone faults that cause some of the most destructive earthquakes and can create damaging tsunamis. Take Indonesia, for example: in 2004, a Mw 9.1 earthquake struck the coast, where the Indo-Australian plate subducts under the Eurasian plate, in a megathrust event. There were over $13 billion in damages, and hundreds of thousands of civilians were killed. The United States Geological Survey (2019) roughly estimates the energy produced from this event at 2.00 x 1018 Joules, which is comparable to the strength of 23,000 Hiroshima bombs. This earthquake had a rupture length of roughly 800 miles, comparable to the length of California, and lasted for 8-10 minutes. North America has its own megathrust seismic hazard: the Cascadia Subduction Zone (CSZ). Our project aims to analyze the rupture and energy budget of the 2004 Sumatra event, as well as compare it to that of a likely megathrust event on the CSZ. The only major subduction zone in the United States is located on the West Coast and runs from Canada to Northern California. Here, the Juan de Fuca and Explorer plates subduct under the North American plate. Oregon’s Department of Emergency Management tells us there have been no major earthquakes here since 1700. Understanding potential earthquakes using modeling is important when it comes to hazard mitigation for Short Contributions CRESCENT Volume 1 October 2025 Doi: 10.5281/zenodo.17280397 Twinning Program 2 CRESCENT Twinning Contributions, v. 1, 2025 areas where the residents do not experience major earthquakes often, and studying the energy budget can improve these models. We will model the Cascadia subduction zone and run different scenarios with varying pore-fluid pressures, with respect to the 2004 Sumatra-Andaman earthquake, and compare our results to that of the Sumatra models from Madden et. al (2022) and observations from that 2004 event. With these models, we are going to get results of radiated energy, seismic moment, static and total frictional work. With these results, we will be able to deduce how the energy is distributed amongst the energy budget components in a Cascadia event, similar to Sumatra. Figure 1. Image of 2004 Sumatra-Andaman earthquake rupture from Shearer, P., & Bürgmann, R. (2010). BACKGROUND Subduction zones are a type of convergent plate boundary that occurs when one tectonic plate subducts, or slides under, another plate. Megathrust earthquakes and tsunamis present significant hazards at subduction zones. The subduction zone in the United States is Cascadia, where the Juan de Fuca and Explorer plates subduct beneath the North American plate, creating a dangerous zone that stretches from Canada to Northern California. Many major North American cities lie along the Cascadia Subduction Zone, including Seattle, Portland, Eugene, Eureka, and Vancouver. Since there is no large earthquake recorded here since 1700, the chances of the fault slipping soon are elevated, and could create costly consequences. An ocean away is a similar subduction zone, Sumatra, where the Indo-Australian plate subducts under the Eurasian plate. In 2004, a devastating Mw 9.1 megathrust earthquake, with a rupture length of 800 miles, occurred off the coast of Indonesia, killing a quarter of a million people, displacing almost 2 million others, costing a total of $13 billion, and creating a tsunami so powerful it reached Eastern Africa and was observed at Atlantic and Pacific water stations, the National Oceanic and Atmospheric Administration (2023) reports. This earthquake, called the Sumatra-Andaman earthquake, has been studied by many seismologists and geologists including Dr. Hiroo Kanamori and Dr. Elizabeth Madden. Both Kanamori (2006) and Madden et al. (2022) created models to analyze the rupture and respective energy from this event. Kanamori aimed to estimate the radiated energy using a finite source model with varying frequency bands and arrived at an estimate of 3.0E+17 J radiated. He also found that the radiation efficiency (0.16) and energy moment ratio (0.46 x 10-5) estimated from his radiated energy, are smaller than those of similar magnitude earthquakes (Kanamori, 2006). Madden et al. (2022) used supercomputers to model the Sumatra-Andaman earthquake, with varying fluid pressures in each of the six scenarios. In these scenarios, the values of average slip, peak slip rate, static shear stress, and magnitude were reported from the output of the models (Madden et al., 2022). New models for Cascadia will reveal the similarities and differences in these reported values and allow us to better understand earthquake behavior. 3 CRESCENT Twinning Contributions, v. 1, 2025 Earthquake energy budgets are not perfectly understood, and are one of the main focuses for our project. Total energy is the sum of frictional energy, fracture energy, and radiated energy. Frictional energy is the energy released and converted to heat from the faults’ friction from sliding. Fracture energy is the total energy required to propagate rupture along a fault, and radiated energy is energy released in the form of seismic waves. Figure 2 shows the components of the energy budget equation in terms of stress and displacement. Using energy budget equations from Ma and Archuleta (2006) and Coffey et al. (2023), we compare our model results with observations of the event to test our model’s validity, and better understand earthquake behavior. METHODS To run the models, we use the San Diego’s Super Computing Center’s (SDSC) platform Expanse. On Expanse, we use SeisSol, a high-performance computational tool optimized for earthquake dynamics. To understand the Sumatra energy output, we re-run the model from Madden et al. (2022), specifically focusing on scenarios 3 through 6, which have high (93%) to very high (97%) pore-fluid pressures (Pf). These models are structurally the same as the 2004 event, but vary in Pf, scenarios 3 and 5 both have high Pf, while 4 and 6 have very high Pf. Scenario 6 is the preferred model since it is the most similar to the 2004 event, and is the basis for the comparisons with observations. We use the energy output that SeisSol produces and calculate other energy budget components, such as radiated energy, and also the energy moment ratio. We use equations for frictional and fracture energy from Coffey et al. (2023), for back of the envelope calculations. Total energy is comprised of many different components that make up the energy budget. Specifically, total energy is equaled to the sum of fracture energy, radiated energy, and frictional energy. SeisSol calculates total and static work using equations from Ma & Archuleta (2006), finding radiated energy to be equal to total work minus static work. Frictional energy is represented by initial shear stress times average displacement. Fracture energy is found to be half of shear stress drop times the critical displacement, which is the threshold for fault failure. For the Cascadia models, we will use parameters similar to the Sumatra models, but with certain conditions tailored to the Cascadia fault, especially when it comes to the geology, and fault shape which will be reflected in the model’s mesh. We want to examine how a megathrust earthquake at the Cascadia subduction zone is similar to and differs from that of the 2004 Sumatra-Andaman earthquake, by examining the output of energy components from the two models. Figure 2. Components of the energy budget equation: frictional energy, fracture energy, and rupture energy. Stress is represented on the y-axis and displacement on the x-axis, from Coffey et al. (2023) (not to scale). 4 CRESCENT Twinning Contributions, v. 1, 2025 RESULTS SeisSol provides us with values of static work being 3.67E+18 J, total work 4.23E+18 J, and radiated energy to equal 5.60E+17. Our model also provides us with a seismic moment of 4.93E+22 J. As we do not have any observations of fracture energy or frictional energy. We compare the sum of fracture and frictional energy to static work to test the validity of these findings. Using the equations of frictional energy and fracture energy from Coffey et al. (2023) to calculate static work, we get that the sum is 2.12E+07 J/m2, and static work per square meter, is found to be 5.83E+07 J/m2. Table 1 Energy Component Observed (Kanamori 2006) Model Radiated Energy 1.38E+17 J 5.60E+17 J Seismic Moment 6.68E+22 J 4.93E+22 J Comparison of energy budget components from Madden et al. (2022) model to Kanamori (2006) observations. Table 2 Static Work per Square Meter EF + EG 5.83E+07 J/m^2 2.12E+07 J/m^2 Comparison of static work per square meter, calculated from Madden et al. (2022) model output, with the sum of frictional and fracture energy (static work). DISCUSSION Kanamori (2006) is the main source of our observed values that we compare our model findings to. He found radiated energy to be 1.38E+17 J. Our model findings of 5.60E+17 for radiated energy are larger than Kanamori (2006) findings of 3.0E+17 J radiated. Seismic moment, on the other hand, is observed to be 6.68E+22 J, which is larger than our model’s finding of 4.93E+22 J, as shown in Table 1. With static work per square meter and the sum of fracture and frictional energy, we see in Table 2, that the two values are in the right order of magnitude, but the sum is half of the static work. One explanation for this is that the back of the envelope calculations we do are too simplified. We use averages to calculate these values, while the equations SeisSol uses from Ma & Archuleta (2003) integrate over the entire fault, which may lead to the differences in values. CONCLUSION This project is only scraping the surface of the analyses into subduction zone earthquake energy budgets. Through the CRESCENT Seed Grant and the San Jose State University’s RSCA fellowship, we plan to continue this work and run simulations of megathrust earthquake scenarios in the Cascadia region. We will compare the Cascadia model output with that from Sumatra, allowing us to highlight potential earthquake scenarios and better constrain our models to highlight potential hazard. ACKNOWLEDGEMENT This material is based upon work supported by CRESCENT and the National Science Foundation Co-operative agreement #2225286. I would like to thank my mentor Dr. Elizabeth Madden for all her support, guidance, and feedback over the past year, as well as being the one to introduce me to scientific research. I would also like to 5 CRESCENT Twinning Contributions, v. 1, 2025 thank Dr. Amanda Thomas and her group of researchers for their guidance during the summer, and the opportunity to do field work at Mt. Rainier. Thank you to my CRESCENT twinning cohort, and project director Shannon Fasola for the support through the road bumps I experienced. A special thank you to Ritwik Patil for helping with the energy plots on Expanse. And finally, I would like to thank my family and friends for their continued support through the duration of this project. REFERENCES Coffey, G., Savage, H., & Polissar, P. (2023). Estimates of earthquake temperature rise and frictional energy. Seismica, 2(1). Kammer, D. S., McLaskey, G. C., Abercrombie, R. E., Ampuero, J. P., Cattania, C., Cocco, M., ... & Tinti, E. (2024). Earthquake energy dissipation in a fracture mechanics framework. Nature communications, 15(1), 4736. Kanamori, H. (2006). The radiated energy of the 2004 Sumatra-Andaman earthquake. In: Abercrombie, R., McGarr, A., Kanamori, H. (eds). Earthquakes: Radiated energy and the physics of earthquake faulting. AGU Geophysical Monograph Series, 170. 59–68.!DOI:!10.1029/170GM07. Ma, S., & Archuleta, R. J. (2006). Radiated seismic energy based on dynamic rupture models of faulting. Journal of Geophysical Research: Solid Earth, 111(B5). Madden, E. H., Ulrich, T., & Gabriel, A. A. (2022). The state of pore fluid pressure and 3‐D megathrust earthquake dynamics. Journal of Geophysical Research: Solid Earth, 127(4), e2021JB023382. National Oceanic and Atmospheric Administration. (2023, June 12). JetStream Max: 2004 Indian Ocean Tsunami. https://www.noaa.gov/jetstream/2004tsu_max Oregon Department of Emergency Management. (n.d.). Cascadia Subduction Zone. https://www.oregon.gov/oem/hazardsprep/pages/cascadia-subduction-zone.aspx Shearer, P., & Bürgmann, R. (2010). Lessons learned from the 2004 Sumatra-Andaman megathrust rupture. Annual Review of Earth and Planetary Sciences, 38(1), 103-131. DOI: 10.1146/annurev-earth-040809152537 United States Geological Survey - Earthquake Hazards Program. (2019). M9.0 December 26, 2004 Northern Sumatra. https://www.usgs.gov/programs/earthquake-hazards/science/m90-december-26-2004-northernsumatra