Statistical Analysis of Magnitude Jumps in Earthquake Catalogs
Code to calculate the value of b and gamma of the p(dm) distribution with incompleteness
This script performs a statistical analysis of magnitude differences between nearby earthquakes in space.
Overview
This repository contains a Python implementation of a maximum likelihood estimation method. It estimates parameters b and gamma of a two-branch model for magnitude differences (dm) between temporally-close earthquakes. The approach is based on:
- Selecting earthquake pairs separated by a small spatial distance (dth) and a magnitude threshold (dmth).
- Computing dm between each valid pair.
- Fitting the log-likelihood.
- Estimating parameter uncertainties via bootstrap.
Files
like_bgamma.py: main Python script (this file)input_catalog.dat: input catalog file with 5 columns:
time,magnitude,latitude,longitude,depthoutput.dat: output file containing the fitted parameters and uncertainties
Usage
Run the main script with:
python main.py
Ensure your input_catalog.dat is in the correct format:
time magnitude latitude longitude depth
12345678 4.5 34.05 -118.25 12.0
...
Each line must have at least 5 floating point values.
Usage
The output is written to output.dat and contains the following columns:
dth b sb a sa
Where:
• dth: distance threshold (fixed to 20.0 km)
• b, a: maximum likelihood estimates
• sb, sa: bootstrap standard deviations
Notes
A small Gaussian noise is added to each magnitude to break ties:
q.append(qi + 0.1 * (np.random.rand() - 0.5))
Requirements
Please install Python packages with:
- pip install numpy scipy
Contact
For questions, suggestions, or contributions, please contact:
Giuseppe Petrillo