Research Methodology

Earthquake Potential Score (EPS)

The Earthquake Potential Score is a numerical index ranging from 0 to 100 that reflects how close a specific location is to experiencing its next significant earthquake.

• Calculated using natural time intervals between earthquakes
• Higher scores indicate increased likelihood of seismic activity
• Updated continuously as new seismic data arrives
• Provides quantifiable risk assessment for each forecast region

Natural Time

Natural time is a fundamental concept introduced by Varotsos et al. where event counting serves as a unit of "time" instead of clock time. This approach offers two key advantages for earthquake nowcasting:

• Event-based progression: The number of small earthquakes measures stress and strain accumulation between large earthquakes in a defined geographic area
• No decluttering required: Natural time is uniformly valid whether aftershocks dominate, background seismicity dominates, or both contribute
• Earthquake cycle definition: Instead of focusing on recurrent events on particular faults, the method defines an "earthquake cycle" as recurring large earthquakes in a vast seismically active region composed of numerous active faults
• Entropy dynamics: Natural time reveals the dynamical evolution of the seismic system and identifies when it reaches a critical stage

LSTM Neural Networks

Long Short-Term Memory (LSTM) networks are recurrent neural networks specifically designed to learn temporal-spatial dependencies in seismic signals. The architecture addresses the challenge of learning from past events that occurred hundreds or millions of discrete time steps ago.

• Spatio-temporal learning: LSTM networks record correlations among earthquakes across different locations and times
• Long-term dependencies: Performance is not affected by long time intervals between important seismic events
• Signal processing: Handles signals combining low-frequency and high-frequency seismic components
• Input features: Sliding window outputs including natural time statistics, seismic energy release, magnitude distributions, and spatial parameters (°N, °E, km)
• Output predictions: 4-tuple forecast of latitude, longitude, focal depth, and magnitude for future significant events
• Training methodology: Connectionist Temporal Classification (CTC) to maximize likelihood of seismic event sequences

Sliding Window (SW) Technique

A customized dynamic sliding window technique acts as a stochastic filter to fine-tune geoseismic occurrence analysis:

• Temporal segmentation: Seismic catalogs are divided into overlapping time-scaled windows
• Feature extraction: Each window contains statistical properties including earthquake count, mean/maximum magnitude, seismic energy release, and spatial clustering metrics
• Progressive analysis: Windows slide forward in natural time, creating continuous pattern recognition
• Multi-scale patterns: Different window sizes capture both short-term precursory signals and longer-term seismic trends
• Machine learning integration: SW outputs serve as input features for supervised and unsupervised learning algorithms

Validation & Performance

Our model has been rigorously tested against historical California seismic data to ensure accuracy and reliability.

Performance metrics based on retrospective analysis of California earthquake sequences. The methodology is adaptable to other regions with appropriate training data.

Data Flow