Source code for openquake.hmtk.seismicity.smoothing.kernels.isotropic_gaussian

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"""
Module :mod:`openquake.hmtk.seismicity.smoothing.kernels.isotropic_gaussian`
imports :class:`openquake.hmtk.seismicity.smoothing.kernels.isotropic_gaussian.IsotropicGaussian`
the simple isotropic Gaussian smoothing kernel as described by Frankel (1995)

Frankel, A. (1995) Mapping Seismic Hazard in the Central and Eastern United
States. Seismological Research Letters. 66(4) 8 - 21
"""

import numpy as np
from openquake.hmtk.seismicity.utils import haversine
from openquake.hmtk.seismicity.smoothing.kernels.base import (
    BaseSmoothingKernel,
)


[docs]class IsotropicGaussian(BaseSmoothingKernel):
    """
    Applies a simple isotropic Gaussian smoothing using an Isotropic Gaussian
    Kernel - taken from Frankel (1995) approach
    """

[docs]    def smooth_data(self, data, config, is_3d=False):
        """
        Applies the smoothing kernel to the data

        :param np.ndarray data:
            Raw earthquake count in the form [Longitude, Latitude, Depth,
                Count]
        :param dict config:
            Configuration parameters must contain:
            * BandWidth: The bandwidth of the kernel (in km) (float)
            * Length_Limit: Maximum number of standard deviations

        :returns:
            * smoothed_value: np.ndarray vector of smoothed values
            * Total (summed) rate of the original values
            * Total (summed) rate of the smoothed values
        """
        max_dist = config["Length_Limit"] * config["BandWidth"]
        smoothed_value = np.zeros(len(data), dtype=float)
        for iloc in range(0, len(data)):
            dist_val = haversine(
                data[:, 0], data[:, 1], data[iloc, 0], data[iloc, 1]
            )

            if is_3d:
                dist_val = np.sqrt(
                    dist_val.flatten() ** 2.0
                    + (data[:, 2] - data[iloc, 2]) ** 2.0
                )
            id0 = np.where(dist_val <= max_dist)[0]
            w_val = (
                np.exp(-(dist_val[id0] ** 2.0) / (config["BandWidth"] ** 2.0))
            ).flatten()
            smoothed_value[iloc] = np.sum(w_val * data[id0, 3]) / np.sum(w_val)
        return smoothed_value, np.sum(data[:, -1]), np.sum(smoothed_value)