source_modelling.moment

 1"""Utility functions for working with moment rate and moment."""
 2
 3import numpy as np
 4import numpy.typing as npt
 5import pandas as pd
 6import scipy as sp
 7from scipy.sparse import csr_array
 8
 9# Shear scaling constant
10MU = 3.3e10
11
12
13def moment_rate_over_time_from_slip(
14    area: npt.ArrayLike, slip: csr_array, dt: float, nt: int
15) -> pd.DataFrame:
16    """Compute a moment rate dataframe from subfaults given with area and slip.
17
18    Parameters
19    ----------
20    area : array like
21        The area of each subfault (in cm^2).
22    slip : csr_array
23        A sparse containing the slip for each subfault and each time
24        window. Has shape (number of points, number of time windows).
25    dt : float
26        Length of each time window (s).
27    nt : int
28        The number of time windows.
29
30    Returns
31    -------
32    pd.DataFrame
33        A dataframe with index in time (s) and column 'moment_rate' (Nm/s).
34    """
35    slip_over_time = (
36        np.asarray(sp.sparse.diags(np.asarray(area)).dot(slip).sum(axis=0))[0] / 1e6
37    )
38    moment_rate = MU * slip_over_time
39    time_values = np.arange(nt) * dt
40
41    moment_rate_df = pd.DataFrame(
42        {"t": time_values, "moment_rate": moment_rate}
43    ).set_index("t")
44    return moment_rate_df
45
46
47def moment_to_magnitude(moment: float) -> float:
48    """Convert moment to magnitude.
49
50    NOTE: the qcore mag_scaling module does not have this expression.
51
52    Parameters
53    ----------
54    moment : float
55        The moment of the rupture.
56
57    Returns
58    -------
59    float
60        Rupture magnitude
61    """
62    return 2 / 3 * np.log10(moment) - 6.03333
63
64
65def moment_over_time_from_moment_rate(moment_rate_df: pd.DataFrame) -> pd.DataFrame:
66    """Integrate a moment rate dataframe into a cumulative moment dataframe.
67
68    Parameters
69    ----------
70    moment_rate_df : pd.DataFrame
71        Dataframe containing time as an index, and 'moment_rate' column.
72
73    Returns
74    -------
75    pd.DataFrame
76        A dataframe the same index and a 'moment' column with cumulative rupture moment.
77    """
78    integrate_f = np.vectorize(
79        lambda i: np.trapz(
80            moment_rate_df["moment_rate"].iloc[: i + 1].to_numpy(),
81            moment_rate_df.index.values[: i + 1],
82        )
83    )
84    return pd.DataFrame(
85        {
86            "t": moment_rate_df.index.values,
87            "moment": integrate_f(np.arange(len(moment_rate_df))),
88        }
89    ).set_index("t")