An engineering professor at the University of California, San Diego solves a deep earthquake mystery

IMAGE: Xanthippi Markenscoff is a Distinguished Professor in the Department of Mechanical and Aerospace Engineering at the University of California San Diego Jacobs School of Engineering. Show more

Credit: Xanthippi Markenscoff

These mysterious earthquakes originated between 400 and 700 kilometers below the Earth’s surface and were recorded at magnitudes of up to 8.3 on the Richter scale.

Xanthippi Markenscoff, Distinguished Professor in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego College of Engineering, is the one who solved this puzzle. Her article titled “Fracture Magnitude Instability in Deep Earthquakes: The Source of Spermic Shear and Pressure Driven” appears in the Journal of Solids Mechanics and Physics.

The term highly concentrated earthquake refers to the fact that this type of earthquake originates deep in the Earth’s mantle where the compressive forces are very high. Since intense focus earthquakes were first recognized in 1929, researchers have been trying to understand the processes that cause them. Researchers thought that high pressures would produce an implosion that intuitively creates pressure waves. However, they were unable to connect the points between high pressure and a particular type of seismic wave – called shear (or distorted) seismic waves – produced by deep-focused earthquakes. (You can feel the distorted energy if you grab your forearm and turn it.)

In her new paper, Markenscoff continues her explanation of this puzzle that is occurring under very high stress. The mystery was exposed in a series of research papers that began in 2019. In addition, its solution provides insight into many other phenomena such as planetary influences and planetary formation that share similar geophysical processes.

“This is an excellent example of how mathematical modeling deeply rooted rigidly in mechanics and physics can help us solve mysteries in nature. Professor Markinskopf’s work can have a profound effect not only on how we understand deeply focused earthquakes, but also on how earthquakes are controlled,” he said. Huajian Zhao, Distinguished University Professor at Nanyang Technological University in Singapore and editor of the Journal of Solids Mechanics and Physics, Markenskov’s paper shows: “Use dynamic phase transformations in engineering materials to our advantage.”

From turning rock to earthquake

It is well known that high pressures between 400 and 700 km below the earth’s surface can cause the olivine rocks to turn into a denser type of rock called spinel. This is similar to how coal turns into diamond, which also occurs deep in the mantle of the Earth.

The transition from olivine to denser spinel causes the rock to decrease in size as the atoms close together under great pressure. This may be called the “breakdown magnitude”. This volume collapse and the associated “transform error” is the main cause of deep focus earthquakes. However, to date, there has been no model based on volume collapse that predicts stern (distorted) seismic waves that actually reach the Earth’s surface during deep-focus earthquakes. That is why other models have also been considered, and the situation has remained stagnant.

Markenscoff has now solved this puzzle using basic mathematical physics and mechanics by discovering instabilities that occur at very high pressures. One of the instabilities relates to the shape of the expanding region of rock transformation and the other to the instability relates to its growth.

In order for the expansion regions to grow at this stage from olivine to spinel, these metamorphic regions of large density will take on a flat, pie-like shape, reducing the energy required for the condensed region to propagate in the unconverted medium as it grows large. This is the symmetry fracture mode that can occur under the very high pressures present where deep focus earthquakes arise, and it is this symmetry fracture that creates the shear deformation responsible for the shear waves that reach the Earth’s surface. Previously, researchers hypothesized a spherical expansion that maintains symmetry, which would not produce seismic shear waves. They didn’t know that he would let the symmetry be broken.

“Breaking the spherical symmetry of the shape of the transformed rock reduces the energy required for the diffusion region for the phase shift to grow substantially,” Markenskov said. “You don’t spend energy to move the surface of a large ball, just the ocean.”

In addition, Markenskov explained that within the expanding region of phase shift of rocks, there is neither particle motion nor kinetic energy (it is a “gap”), and thus, the energy that is radiated out is maximized. This explains why seismic waves reach the surface, rather than scattering so much energy into Earth’s interior.

Markenskov’s analytical model of deformation fields for an expanding seismic source is based on the dynamic generalization of the inclusion of Eshelby (1957) that satisfies the gap theory (Attia et al., 1970). The energy in the expanding region of the phase shift is governed by Noether’s (1918) theoretical physics by which it obtained the instability that led to a growing and fast-moving avalanche from a collapse of volume under pressure. This is the second instability discovered (regarding growth): once a small, dense flat area is arbitrarily turned on, it will continue to grow under critical pressure without requiring more energy. (It keeps crashing “like a house of cards”). Thus, the puzzle is solved: although it is the source of the shear, what drives the spread of deep focus earthquakes is the pressure that affects the change in size.

When asked to think about her discovery that deep-focused earthquakes can be described as theories that are the bedrock of mathematical physics, she said, “I feel connected to nature. I have discovered the beauty of how nature works. It is the first time in my life. Before I take a small step in a person’s footsteps. Else. I felt this great joy. “

Related discoveries

Focused earthquakes are just one of the phenomena in which instability manifests itself. It also occurs in other phenomena of dynamic phase transitions under high pressures, such as planetary impacts and shapelessness. Today, there are new facilities like the National Ignition Facility (NIF) run by Lawrence Liver National Laboratory where researchers can study materials under extremely high pressures that were impossible to test before.

Markenscoff’s new work provides an important presentation and reminder that gaining a deeper understanding of nature’s secrets often requires insights that can be gained by harnessing the fundamentals of mathematical physics alongside research conducted in extreme conditions.

Indeed, Markenscoff co-organized two National Science Foundation (NSF) funded workshops at UC San Diego in 2016 and 2019 that brought together geophysicists, seismologists, and mechanics to ensure that these research communities remain aware of methodologies and techniques developed in mechanics.

“Our education systems must continue to invest in teaching the fundamentals of science as pillars of the advancement of knowledge, which can be achieved through the interdisciplinary convergence of theory, experiment and data science,” Markenskov said.

She also noted the importance of the research support she has received over the years from the US National Science Foundation (NSF).

Markinskov said, “Knowing that my NSF program director believed that this ‘mystery’ and Molney could be solved, it boosted both my confidence and my resolve to persevere.” “I refer to this as a reminder to all of us. It is also important that we provide thoughtful and thoughtful encouragement to our students and colleagues. Knowing that the people you respect believe in you and your work they can be very powerful.”

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