Visualizing the Reality of Earthquakes
A decade of theoretical development opening new horizons in seismology
Beyond the "Limitations" of Seismology
What exactly happens deep underground the moment an earthquake occurs? We estimate the answer from vibrations (seismic waves) observed at the surface. However, for a long time, seismic analysis methods have relied on a somewhat "unrealistic premise": the assumption that we already know the underground structure perfectly.
The interior of the Earth cannot be seen directly. Even slight variations in subsurface structure can significantly distort the calculated image of an earthquake. Yet, in conventional analysis, these uncertainties were largely ignored.
Acknowledging the Unknown
In 2011, we shifted our paradigm.
If the subsurface structure is unknown, we should incorporate that "uncertainty" directly into our calculations from the start.
This approach (Yagi and Fukahata, 2011) enabled stable estimation of fault slip without being misled by modeling errors. Even for a giant event like the 2011 Tohoku-oki earthquake, we were able to visualize the subsurface phenomena with greater reliability.
DOI: 10.1111/j.1365-246X.2011.05043.x (Yagi and Fukahata, 2011)
Evolution of Theory: 2011 Tohoku-oki Earthquake Comparison
Structural uncertainty appears as "unnatural normal-fault slip (artifacts)," obscuring the true nature of the event.
By incorporating uncertainty, noise is removed, and the main rupture area of the giant earthquake clearly emerges.
Noise or Reality? The complex patterns and back slip (normal-fault slip) seen in the left figure are actually artifacts—modeling errors due to unknown subsurface structures being misinterpreted as slip. Traditional methods often forcibly restricted the slip direction to stabilize the solution. In contrast, our approach treats this "error" statistically correctly, successfully recovering a highly reliable image of the source process (Yagi and Fukahata, 2011).
After countless trials and errors, I will never forget the moment I arrived at this idea and saw this clear image emerge from the noise. This research paved the way for flexible source models. By "redefining the question," the view of the world changes dramatically. That excitement remains the core driving force of my research.
Yuji Yagi
Finding Meaning in "Errors"
The next challenge was the shape of the fault itself. Real faults are not smooth, perfectly flat planes; they are bent and irregular. Previously, these complexities were treated as "errors." However, we thought differently:
These are not errors—they are signals that can reveal the true geometry of the fault.
This idea led to the methodology presented in Shimizu, Yagi et al. (2020).
DOI: 10.1093/gji/ggz496 (Shimizu, Yagi et al., 2020)
Releasing the Fault from the "Plane" —— PDTI
Today, we have arrived at PDTI (Potency Density Tensor Inversion). PDTI abandons the concept of "slipping on a pre-defined fault plane" and instead captures the deformation of the Earth's interior in a much more flexible form.
As a result, we can now visualize phenomena with startling clarity, such as:
- The realistic geometry of complex, bent faults.
- Unique "boomerang" earthquakes where the rupture front reverses direction.
- Source images that once seemed "strange" or "anomalous" under old models.
3D Visualization of Fault Geometry and Slip Distribution via PDTI
Liberation from the "Plane" Constraint. PDTI does not fix the fault geometry in advance. By allowing the data to dictate the deformation, we can now simultaneously map the true form of complex, curved faults and the slip distribution across them (Sato, Yagi et al., 2026, Fig. 13).
The "Personality" of Earthquakes: Boomerang Rupture
Rupture that "returns," defying common sense. This animation shows a rupture front propagating outward and then reversing direction toward the hypocenter. These findings (Inoue et al., 2025) were made possible by PDTI's ability to provide stable analysis of complex strike-slip events.
No two earthquakes are the same. PDTI is a new lens that allows us to understand the individual "personality" of each seismic event.
Technical Deep Dive: How PDTI Works
Potency Density Tensor Inversion (PDTI) does not geometrically fix the fault plane. Instead, it directly estimates the potency density tensor components at each grid point. This allows the data itself to reveal changes in fault strike and dip during the rupture process, removing human bias from the initial model setup.
Message from Yagi Lab
Our challenge over the past decade has been a journey to increase the "resolution" of our understanding of earthquakes. Knowing the precise source process is an indispensable step toward predicting future damage and deepening our understanding of our planet.