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, depth
• output.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

giuseppe51289@gmail.com