Numerical Study on Earthquake Energy Partitioning: Relationships Among Radiated Energy, Seismic Moment, and Stress Drop. Issue 1 (10th January 2020) - Khademian, Z.; Nakagawa, M.; Ozbay, U.
Abstract: This paper aims at mechanistically studying some aspects of earthquake energy partitioning with a focus on the radiated energy ( E s ) and seismic moment ( M o ) relationships for investigating differences between estimates of average dynamic stress drop ( ∆ σ ¯ d ) and static stress drop ( ∆ σ ¯ s ). We evaluate to what extent a relatively simple but analytically verified faulting simulation can explain such differences. We adopt a numerical methodology developed in the 2‐D Universal Distinct Element Code to simulate fault slip with slip‐weakening responses. A method is introduced for recording the ground reaction to slip and from which we discuss the energy partitioning in ideal cases of rupture. We examine a shallow strike‐slip fault model where a locally peaked stress is gradually developed on the fault by applying tectonic stresses away from the fault surface until a rupture is initiated locally and propagated outward. The rupture is terminated when the available energy is exhausted by the fracture energy and friction work especially as the rupture is followed by a creep. With investigating roles of the available energy for rupture and the fracture energy, we display limited cases where M o does not, at least proportionately, scale with E s . Results show this is because M o, compared to E s, does not fully represent the energy available for initiating a rupture and the fracture energy consumed during its propagation. That is why 2 μE s / M o and 2 μE s / η R M o estimates, with the radiation ratio η R and rigidity μ, may significantly differ from ∆ σ ¯ d and ∆ σ ¯ s . Plain Language Summary: Numerical techniques are a practical way of understanding earthquake energy budget components that cannot be directly measured. The potential energy stored in rocks partially transforms into kinetic energy that generates earthquakes. This simple concept is translated into a modeling methodology that calculates energy terms contributing to the occurrence and intensity of an earthquake. In order to verify the modeling approach, the results are compared to existing analytical solutions and globally recorded seismic data. Given the consistency between numerical results, analytical solutions, and field measurements, we study a controversy in this field regarding the scaling of the radiated energy with the seismic moment, two commonly used measures of earthquake size. We also evaluate to what extent a simple model can explain the dependence of the stress changes on the earthquake size. This can help us understand what parameters really determine the occurrence and size of earthquakes. Key Points: The seismic moment does not necessarily scale with the radiated energy so there may not be a unique moment for a given radiated energy The radiated energy dependence on the fracture energy and available energy causes the lack of scaling between the radiated energy and seismic moment Differences between different estimates of stress drop can be partially explained by the relationship between radiated energy and seismic moment