Wavelets

sim2x has a module for handling wavelet functionality related to the convolutional modelling in sim2x seis. The wavelets module has both methods for manual creation of wavelets and Wavelet derived classes which are used by the modelling package.

A full listing of the available wavelet functionality is available in the api.

Some of the wavelet module functionality is detailed in this example.

Imports¶

The wavelet functionality for sim2x can be imported as a contained module. Here we import as wv to reduce the verbosity in the example.

In [1]:

from sim2x import wavelets as wv
import matplotlib.pyplot as plt
from matplotlib import rc

rc("font", size=15)

from sim2x import wavelets as wv import matplotlib.pyplot as plt from matplotlib import rc rc("font", size=15)

Wavelet Methods and data structures¶

Let's create a standard ricker wavelet using the ricker method.

In [2]:

nsamp = 128 # the number of samples
dt = 0.001 # the sample rate in seconds
f = 25 # the dominant frequency Hz

rwave = wv.ricker(nsamp, dt, f)

nsamp = 128 # the number of samples dt = 0.001 # the sample rate in seconds f = 25 # the dominant frequency Hz rwave = wv.ricker(nsamp, dt, f)

rwave is returned as structured numpy array with labelled axes 'time' and 'amp'.

In [3]:

plt.plot(rwave['time'], rwave['amp'], label="rwave")
plt.legend()

plt.plot(rwave['time'], rwave['amp'], label="rwave") plt.legend()

Out[3]:

<matplotlib.legend.Legend at 0x7fb105d186d0>

Functionality is available to calculate the spectra of the wavelet using wavelet_spectra().

In [4]:

rwave_spec = wv.wavelet_spectra(dt, rwave["amp"], df=1)

rwave_spec = wv.wavelet_spectra(dt, rwave["amp"], df=1)

rwave_spec is also a numpy structured array which has the following dtypes

In [5]:

rwave_spec.dtype

rwave_spec.dtype

Out[5]:

dtype([('freq', '<f8'), ('amp', '<c8'), ('mag', '<f8'), ('phase', '<f8')])

In [6]:

fig, axs = plt.subplots(ncols=3, figsize=(15, 4), sharex=True)
axs[0].plot(rwave_spec['freq'], rwave_spec['amp'].real, label="amp")
axs[0].plot(rwave_spec['freq'], rwave_spec['mag'], label="mag")
axs[0].set_xlabel("Freq (Hz)")
axs[0].set_ylabel("Amplitude")
axs[1].plot(rwave_spec['freq'], rwave_spec['phase'], label="phase")
axs[1].set_xlabel("Freq (Hz)")
axs[1].set_ylabel("Phase (rad)")
axs[0].legend()

axs[2].scatter(rwave_spec["amp"].real, rwave_spec["amp"].imag)
fig.tight_layout()

fig, axs = plt.subplots(ncols=3, figsize=(15, 4), sharex=True) axs[0].plot(rwave_spec['freq'], rwave_spec['amp'].real, label="amp") axs[0].plot(rwave_spec['freq'], rwave_spec['mag'], label="mag") axs[0].set_xlabel("Freq (Hz)") axs[0].set_ylabel("Amplitude") axs[1].plot(rwave_spec['freq'], rwave_spec['phase'], label="phase") axs[1].set_xlabel("Freq (Hz)") axs[1].set_ylabel("Phase (rad)") axs[0].legend() axs[2].scatter(rwave_spec["amp"].real, rwave_spec["amp"].imag) fig.tight_layout()

Wavelet Classes¶

We can perform the same functionality using the built in classes for Wavelets. This example repeats the wavelet method with the RickerWavelet class.

Note: With wavelet classes, the attributes of the wavelet are accessed via the . operator not with keys as for structured numpy arrays.

In [7]:

rwave_class = wv.RickerWavelet(f, nsamp=nsamp, dt=dt, name="ricker", df=1)

rwave_class = wv.RickerWavelet(f, nsamp=nsamp, dt=dt, name="ricker", df=1)

In [8]:

fig, axs = plt.subplots(ncols=2, figsize=(10, 4))
axs[0].plot(rwave_class.time, rwave_class.amp)
axs[0].set_xlabel("Time (s)")
axs[0].set_ylabel("Amplitude")
axs[1].plot(rwave_class.freq, rwave_class.fmag)
axs[1].set_xlabel("Freq (Hz)")
axs[1].set_ylabel("Phase (rad)")

fig, axs = plt.subplots(ncols=2, figsize=(10, 4)) axs[0].plot(rwave_class.time, rwave_class.amp) axs[0].set_xlabel("Time (s)") axs[0].set_ylabel("Amplitude") axs[1].plot(rwave_class.freq, rwave_class.fmag) axs[1].set_xlabel("Freq (Hz)") axs[1].set_ylabel("Phase (rad)")

Out[8]:

Text(0, 0.5, 'Phase (rad)')

You can rotate the wavelet phase if needed.

In [9]:

rwave_class.shift_phase(90)

rwave_class.shift_phase(90)

In [10]:

fig, axs = plt.subplots(ncols=3, figsize=(15, 4))
axs[0].plot(rwave_class.time, rwave_class.amp)
axs[0].set_xlabel("Time (s)")
axs[0].set_ylabel("Amplitude")
axs[1].plot(rwave_class.freq, rwave_class.fmag)
axs[1].set_xlabel("Freq (Hz)")
axs[1].set_ylabel("Phase (rad)")

sct = axs[2].scatter(rwave_class.famp.real, rwave_class.famp.imag, c=rwave_class.freq)
axs[2].set_xlabel("Freq Amp Real")
axs[2].set_ylabel("Freq Amp Imag")
plt.colorbar(sct, ax=axs[2], label="Freq (Hz)")
fig.tight_layout()

fig, axs = plt.subplots(ncols=3, figsize=(15, 4)) axs[0].plot(rwave_class.time, rwave_class.amp) axs[0].set_xlabel("Time (s)") axs[0].set_ylabel("Amplitude") axs[1].plot(rwave_class.freq, rwave_class.fmag) axs[1].set_xlabel("Freq (Hz)") axs[1].set_ylabel("Phase (rad)") sct = axs[2].scatter(rwave_class.famp.real, rwave_class.famp.imag, c=rwave_class.freq) axs[2].set_xlabel("Freq Amp Real") axs[2].set_ylabel("Freq Amp Imag") plt.colorbar(sct, ax=axs[2], label="Freq (Hz)") fig.tight_layout()

Or convert the time axis to milliseconds

In [11]:

rwave_class.as_milliseconds()

fig, axs = plt.subplots(ncols=2, figsize=(10, 4))
axs[0].plot(rwave_class.time, rwave_class.amp)
axs[0].set_xlabel("Time (s)")
axs[0].set_ylabel("Amplitude")
axs[1].plot(rwave_class.freq, rwave_class.fmag)
axs[1].set_xlabel("Freq (Hz)")
axs[1].set_ylabel("Phase (rad)")
fig.tight_layout()

rwave_class.as_milliseconds() fig, axs = plt.subplots(ncols=2, figsize=(10, 4)) axs[0].plot(rwave_class.time, rwave_class.amp) axs[0].set_xlabel("Time (s)") axs[0].set_ylabel("Amplitude") axs[1].plot(rwave_class.freq, rwave_class.fmag) axs[1].set_xlabel("Freq (Hz)") axs[1].set_ylabel("Phase (rad)") fig.tight_layout()

The wavelet can also be resampled to a different sample rate dt.

In [12]:

print("Current sample rate:", rwave_class.dt)
print("Current number of samples:", rwave_class.nsamp)
rwave_class.resample(0.5)
print("New sample rate:", rwave_class.dt)
print("New number of samples:", rwave_class.nsamp)

print("Current sample rate:", rwave_class.dt) print("Current number of samples:", rwave_class.nsamp) rwave_class.resample(0.5) print("New sample rate:", rwave_class.dt) print("New number of samples:", rwave_class.nsamp)

Current sample rate: 1.0
Current number of samples: 129
New sample rate: 0.5
New number of samples: 256

But the overall dimensions stay the same. The spectrum looks different because with a higher number of samples are FFT transforms up to higher frequencies.

In [13]:

fig, axs = plt.subplots(ncols=2, figsize=(10, 4))
axs[0].plot(rwave_class.time, rwave_class.amp)
axs[0].set_xlabel("Time (s)")
axs[0].set_ylabel("Amplitude")
axs[1].plot(rwave_class.freq, rwave_class.fmag)
axs[1].set_xlabel("Freq (Hz)")
axs[1].set_ylabel("Phase (rad)")
fig.tight_layout()

fig, axs = plt.subplots(ncols=2, figsize=(10, 4)) axs[0].plot(rwave_class.time, rwave_class.amp) axs[0].set_xlabel("Time (s)") axs[0].set_ylabel("Amplitude") axs[1].plot(rwave_class.freq, rwave_class.fmag) axs[1].set_xlabel("Freq (Hz)") axs[1].set_ylabel("Phase (rad)") fig.tight_layout()

In [ ]: