Added gaussianprime and gaussiandoubleprime waveforms which are direct 1st and 2nd derivatives of the gaussian waveform, i.e. they don't share the same centre frequency.

docs/source/input.rst

@@ -661,6 +661,8 @@ Allows you to specify waveforms to use with sources in the model. The syntax of
     * ``gaussiandotdot`` which is the second derivative of a Gaussian waveform.
     * ``gaussiandotdotnorm`` which is the normalised second derivative of a Gaussian waveform.
     * ``ricker`` which is a Ricker (or Mexican hat) waveform, i.e. the negative, normalised second derivative of a Gaussian waveform.
+    * ``gaussianprime`` which is the first derivative of a Gaussian waveform, directly derived from the aforementioned ``gaussian`` (see notes below).
+    * ``gaussiandoubleprime`` which is the second derivative of a Gaussian waveform, directly derived from the aforementioned ``gaussian`` (see notes below).
     * ``sine`` which is a single cycle of a sine waveform.
     * ``contsine`` which is a continuous sine waveform. In order to avoid introducing noise into the calculation the amplitude of the waveform is modulated for the first cycle of the sine wave (ramp excitation).
 * ``f1`` is the scaling of the maximum amplitude of the waveform (for a ``#hertzian_dipole`` the units will be Amps, for a ``#voltage_source`` or ``#transmission_line`` the units will be Volts).
@@ -672,6 +674,9 @@ For example, to specify the normalised first derivate of a Gaussian waveform wit
 .. note::
 
     * The functions used to create the waveforms can be found in the :ref:`tools section <waveforms>`.
+    * ``gaussiandot``, ``gaussiandotnorm``, ``gaussiandotdot``, ``gaussiandotdotnorm``, ``ricker`` waveforms have their centre frequencies specified by the user, i.e. they are not derived to the 'base' ``gaussian``
+    * ``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.
+
 
 #excitation_file:
 -----------------

gprMax/waveforms.py

@@ -24,7 +24,15 @@ 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', 'ricker', 'sine', 'contsine', 'impulse', 'user']
+    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
@@ -44,8 +52,8 @@ class Waveform(object):
             ampvalue (float): Calculated value for waveform.
         """
 
-        # Coefficients for certain waveforms
+        # Coefficients for specific waveforms
-        if self.type == 'gaussian' or self.type == 'gaussiandot' or self.type == 'gaussiandotnorm':
+        if self.type == 'gaussian' or self.type == 'gaussiandot' or self.type == 'gaussiandotnorm' or self.type == 'gaussianprime' or self.type == 'gaussiandoubleprime':
             chi = 1 / self.freq
             zeta = 2 * np.pi**2 * self.freq**2
             delay = time - chi
@@ -58,14 +66,14 @@ class Waveform(object):
         if self.type == 'gaussian':
             ampvalue = np.exp(-zeta * delay**2)
 
-        elif self.type == 'gaussiandot':
+        elif self.type == 'gaussiandot' or self.type == 'gaussianprime':
             ampvalue = -2 * zeta * delay * np.exp(-zeta * delay**2)
 
         elif self.type == 'gaussiandotnorm':
             normalise = np.sqrt(np.exp(1) / (2 * zeta))
             ampvalue = -2 * zeta * delay * np.exp(-zeta * delay**2) * normalise
 
-        elif self.type == 'gaussiandotdot':
+        elif self.type == 'gaussiandotdot' or self.type == 'gaussiandoubleprime':
             ampvalue = 2 * zeta * (2 * zeta * delay**2 - 1) * np.exp(-zeta * delay**2)
 
         elif self.type == 'gaussiandotdotnorm':

tests/analytical_solutions.py

@@ -19,7 +19,7 @@ def hertzian_dipole_fs(iterations, dt, dxdydz, rx):
 
     # Waveform
     w = Waveform()
-    w.type = 'gaussiandot'
+    w.type = 'gaussianprime'
     w.amp = 1
     w.freq = 1e9
 
@@ -31,7 +31,7 @@ def hertzian_dipole_fs(iterations, dt, dxdydz, rx):
 
     # Waveform first derivative
     wdot = Waveform()
-    wdot.type = 'gaussiandotdot'
+    wdot.type = 'gaussiandoubleprime'
     wdot.amp = w.amp
     wdot.freq = w.freq
 

tools/plot_source_wave.py

@@ -95,7 +95,7 @@ def mpl_plot(w, timewindow, dt, iterations, fft=False):
     if w.freq and not w.type == 'gaussian':
         print('Centre frequency: {:g} Hz'.format(w.freq))
 
-    if w.type == 'gaussian' or w.type == 'gaussiandot' or w.type == 'gaussiandotnorm':
+    if w.type == 'gaussian' or w.type == 'gaussiandot' or w.type == 'gaussiandotnorm' or w.type == 'gaussianprime' or w.type == 'gaussiandoubleprime':
         delay = 1 / w.freq
         print('Time to centre of pulse: {:g} s'.format(delay))
     elif w.type == 'gaussiandotdot' or w.type == 'gaussiandotdotnorm' or w.type == 'ricker':