gprMax/gprMax/waveforms.py

# Copyright (C) 2015-2019: The University of Edinburgh
#                 Authors: Craig Warren and Antonis Giannopoulos
#
# This file is part of gprMax.
#
# gprMax is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# gprMax is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with gprMax.  If not, see <http://www.gnu.org/licenses/>.

import numpy as np

from gprMax.utilities import round_value


class Waveform(object):
    """Definitions of waveform shapes that can be used with sources."""

    types = ['gaussian', 'gaussiandot', 'gaussiandotnorm', 'gaussiandotdot', 'gaussiandotdotnorm', 'gaussianprime', 'gaussiandoubleprime', 'ricker', 'sine', 'contsine', 'impulse', 'user']

    # Information about specific waveforms:
    #
    # gaussianprime and gaussiandoubleprime waveforms are the first derivative and second derivative of the 'base' gaussian
    # waveform, i.e. the centre frequencies of the waveforms will rise for the first and second derivatives.
    #
    # gaussiandot, gaussiandotnorm, gaussiandotdot, gaussiandotdotnorm, ricker waveforms have their centre frequencies
    # specified by the user, i.e. they are not derived from the 'base' gaussian

    def __init__(self):
        self.ID = None
        self.type = None
        self.amp = 1
        self.freq = None
        self.userfunc = None
        self.chi = 0
        self.zeta = 0
        self.delay = 0

    def calculate_coefficients(self):
        """Calculates coefficients (used to calculate values) for specific waveforms."""

        if self.type == 'gaussian' or self.type == 'gaussiandot' or self.type == 'gaussiandotnorm' or self.type == 'gaussianprime' or self.type == 'gaussiandoubleprime':
            self.chi = 1 / self.freq
            self.zeta = 2 * np.pi**2 * self.freq**2
        elif self.type == 'gaussiandotdot' or self.type == 'gaussiandotdotnorm' or self.type == 'ricker':
            self.chi = np.sqrt(2) / self.freq
            self.zeta = np.pi**2 * self.freq**2

    def calculate_value(self, time, dt):
        """Calculates value of the waveform at a specific time.

        Args:
            time (float): Absolute time.
            dt (float): Absolute time discretisation.

        Returns:
            ampvalue (float): Calculated value for waveform.
        """

        self.calculate_coefficients()

        # Waveforms
        if self.type == 'gaussian':
            delay = time - self.chi
            ampvalue = np.exp(-self.zeta * delay**2)

        elif self.type == 'gaussiandot' or self.type == 'gaussianprime':
            delay = time - self.chi
            ampvalue = -2 * self.zeta * delay * np.exp(-self.zeta * delay**2)

        elif self.type == 'gaussiandotnorm':
            delay = time - self.chi
            normalise = np.sqrt(np.exp(1) / (2 * self.zeta))
            ampvalue = -2 * self.zeta * delay * np.exp(-self.zeta * delay**2) * normalise

        elif self.type == 'gaussiandotdot' or self.type == 'gaussiandoubleprime':
            delay = time - self.chi
            ampvalue = 2 * self.zeta * (2 * self.zeta * delay**2 - 1) * np.exp(-self.zeta * delay**2)

        elif self.type == 'gaussiandotdotnorm':
            delay = time - self.chi
            normalise = 1 / (2 * self.zeta)
            ampvalue = 2 * self.zeta * (2 * self.zeta * delay**2 - 1) * np.exp(-self.zeta * delay**2) * normalise

        elif self.type == 'ricker':
            delay = time - self.chi
            normalise = 1 / (2 * self.zeta)
            ampvalue = - (2 * self.zeta * (2 * self.zeta * delay**2 - 1) * np.exp(-self.zeta * delay**2)) * normalise

        elif self.type == 'sine':
            ampvalue = np.sin(2 * np.pi * self.freq * time)
            if time * self.freq > 1:
                ampvalue = 0

        elif self.type == 'contsine':
            rampamp = 0.25
            ramp = rampamp * time * self.freq
            if ramp > 1:
                ramp = 1
            ampvalue = ramp * np.sin(2 * np.pi * self.freq * time)

        elif self.type == 'impulse':
            # time < dt condition required to do impulsive magnetic dipole
            if time == 0 or time < dt:
                ampvalue = 1
            elif time >= dt:
                ampvalue = 0

        elif self.type == 'user':
            ampvalue = self.userfunc(time)

        ampvalue *= self.amp

        return ampvalue