Culpable

Python module containing functionality for performing quantitative analysis of faulting. Current applications are in slip rate/history estimation and paleoseismology.

Installation

1. Download the package, and enter the outer culpable directory

2. create a new Python environment if desired

3. Install with:

   python setup.py install

   or

   pip install -e .

Earthquake magnitude estimation

import numpy as np

from culpable.magnitudes import (M_from_D, D_from_M, p_M_D, M_from_L, p_M_L, 
                                 p_M_DL, make_p_M)
from culpable.offset_marker import OffsetMarker
from culpable.stats import Pdf

np.random.seed(69)

Deterministic estimates

Basic estimation of magnitude from rupture length

length_1 = 50.
M_from_L_est = M_from_L(length_1)

Now let's change the scaling relationship

M_from_L_reverse = M_from_L(length_1, ref='WC_1994_R')

# basic estimation of magnitude from displacement
```python
disp_1 = 2.3
M_from_D_est = M_from_D(disp_1)

basic estimation of displacement from magnitude

mag_1 = 6.7
D_from_M_est = D_from_M(mag_1)

Now let's use our own scaling coefficients

D_from_M_new_scaling = D_from_M(mag_1, ref=None, a=5., b=1., base='10')

Bayesian estimates

Note that these are all probabilistic, and the priors and posteriors are culpable.stats._Pdf classes made through the Pdf function. This class has several useful (necessary, even) attributes and methods. The class is instantiated by passing x and p(x) values. The p(x) values are relative probabilities, i.e. probability mass values. The resulting Pdf class will have been converted to a probability distribution by normalizing by the integral of the PMF.

disp_pdf = Pdf([1., 1.1, 1.3, 1.7, 2.1, 2.2], [0., 0.1, 0.5, 0.7, 0.3, 0.])

First, we need to make a prior for M, p(M)

M_prior = make_p_M(p_M_type='uniform', p_M_min=6.0, p_M_max=7.7,
                   M_step=0.05)

Calculate p(M|D), the posterior probability of the magnitude given the displacement

p_M_D_est_1 = p_M_D(disp_1, p_M=M_prior)

Now the same but with a correction for paleoseismic sampling bias, i.e. that a paleoseismic measurement is proportionally more likely to be taken from a high displacement site vs. a low or average displacement site

p_M_D_est_2 = p_M_D(disp_1, p_M=M_prior, sample_bias_corr=True)

Now let's work with some uncertainty in the amount of displacement

disp_samples = np.random.uniform(1.7, 2.4, size=1000)
p_M_D_est_3 = p_M_D(disp_samples, p_M=M_prior, sample_bias_corr=True)

Here we do a Bayesian inversion for M given L with uncertainty

length_samples = np.random.normal(156, 15, size=1000)
p_M_L_est_1 = p_M_L(length_samples, p_M=M_prior)

Now we do an inversion considering both D and L

p_M_DL_est_1 = p_M_DL(disp_samples, length_samples, p_M=M_prior, 
                      sample_bias_corr=True)