B Value Analysis

B-value Analysis

Description

Calculate the b-value from the Gutenberg-Richter relationship using earthquake catalogs, estimate the magnitude of completeness (Mc), and plot frequency-magnitude distribution.

Main Functions

load_catalog_file(path)

Auto-detect format and load earthquake catalog.

Parameters:

• path : str — Path to catalog file, supports .csv / .json / .txt (phase pick format)

Returns: CatalogData object with attributes .magnitudes, .depths, .lats, .lons, .times, etc.

from seismo_stats.catalog_loader import load_catalog_file
catalog = load_catalog_file("/data/catalog.csv")
print(catalog.summary())
# Output: CatalogData: 1523 events, mag range [0.2, 5.1], ...

calc_mc_maxcurvature(magnitudes, mag_bin=0.1, correction=0.2)

Estimate minimum magnitude of completeness (Mc) using maximum curvature method.

Parameters:

• magnitudes : array-like — List of magnitudes
• mag_bin : float — Magnitude bin width, default 0.1
• correction : float — Bias correction added to raw maximum-curvature Mc, default 0.2

Returns: float — Estimated Mc value

from seismo_stats.bvalue import calc_mc_maxcurvature
import numpy as np
mags = catalog.magnitudes
Mc = calc_mc_maxcurvature(mags, mag_bin=0.1)
print(f"Maximum curvature Mc = {Mc:.1f}")

calc_mc_gof(magnitudes, mag_bin=0.1, r_threshold=95.0)

Estimate Mc using goodness-of-fit method, more robust than maximum curvature.

Parameters:

• magnitudes : array-like
• mag_bin : float — Magnitude bin width, default 0.1
• r_threshold : float — Required percentage of data fit, default 95.0

Returns: float — Estimated Mc value

from seismo_stats.bvalue import calc_mc_gof
Mc = calc_mc_gof(mags, mag_bin=0.1, r_threshold=95.0)
print(f"Goodness-of-fit Mc = {Mc:.1f}")

calc_bvalue_mle(magnitudes, mc=None, mag_bin=0.1, mc_method="maxcurvature")

Calculate b-value using maximum likelihood estimation (MLE / Aki 1965), highest precision.

Parameters:

• magnitudes : array-like
• mc : float or None — Magnitude of completeness; estimated automatically when None
• mag_bin : float — Magnitude bin width, default 0.1
• mc_method : "maxcurvature" or "gof" — Method used when mc is None

Returns: BvalueResult object

BvalueResult attributes:

• .b_value — b-value
• .b_uncertainty — Standard error of b (Shi & Bolt 1982)
• .a_value — a-value (G-R relationship intercept)
• .n_events — Number of events used for calculation
• .mc — Mc value used
• .mean_magnitude — Mean magnitude of complete events
• .method — "mle" or "lsq"
• .mc_method — Mc source/method

from seismo_stats.bvalue import calc_bvalue_mle
result = calc_bvalue_mle(mags, mc=Mc, mag_bin=0.1)
print(f"b = {result.b_value:.3f} ± {result.b_uncertainty:.3f}")
print(f"a = {result.a_value:.3f}")
print(f"Events used: {result.n_events}")

calc_bvalue_lsq(magnitudes, mc=None, mag_bin=0.1, mc_method="maxcurvature")

Calculate b-value using least-squares fitting of G-R relationship, suitable for method comparison.

Parameters: Same as calc_bvalue_mle

Returns: BvalueResult

from seismo_stats.bvalue import calc_bvalue_lsq
result_lsq = calc_bvalue_lsq(mags, mc=Mc, mag_bin=0.1)
print(f"LSQ b = {result_lsq.b_value:.3f}")

plot_gr(result, output_path, title=None)

Plot frequency-magnitude distribution (G-R plot) from a BvalueResult with b-value annotation.

Parameters:

• result : BvalueResult returned by calc_bvalue_mle or calc_bvalue_lsq
• output_path : str — Save path
• title : str or None — Optional plot title

from seismo_stats.plotting import plot_gr
plot_gr(result, "fmd.png")
print("F-M distribution plot saved: fmd.png")

Complete Example

from seismo_stats.catalog_loader import load_catalog_file
from seismo_stats.bvalue import calc_mc_maxcurvature, calc_mc_gof, calc_bvalue_mle
from seismo_stats.plotting import plot_gr, plot_temporal, plot_all

# 1. Load catalog
catalog = load_catalog_file("/data/catalog.csv")
print(catalog.summary())
mags = catalog.magnitudes

# 2. Estimate Mc (compare two methods)
Mc_mc = calc_mc_maxcurvature(mags, mag_bin=0.1)
Mc_gof = calc_mc_gof(mags, mag_bin=0.1, r_threshold=95.0)
print(f"Maximum curvature Mc = {Mc_mc:.1f}")
print(f"Goodness-of-fit Mc = {Mc_gof:.1f}")
Mc = Mc_gof  # Use goodness-of-fit result

# 3. Calculate b-value
result = calc_bvalue_mle(mags, mc=Mc, mag_bin=0.1)
print(f"\nb-value (MLE) = {result.b_value:.3f} ± {result.b_uncertainty:.3f}")
print(f"a-value       = {result.a_value:.3f}")
print(f"N (M>=Mc)   = {result.n_events}")

# 4. Plot
plot_gr(result, "fmd.png")
plot_temporal(catalog, "temporal.png")
plot_all(result, catalog, "catalog_summary")

print("\nAnalysis complete, plots saved.")

Notes

• MLE method (Aki 1965) is statistically superior to LSQ; recommended as primary method
• When event count < 50, b-value is unstable; results for reference only
• When using mag_bin=0.1, ensure catalog magnitude precision is 0.1
• The MLE uncertainty follows Shi & Bolt (1982)