Module: tide.wavelets

Wavelet generators used for source design in FDTD propagation.

Functions

• ricker
• gaussian
• gaussian_derivative
• morlet
• sine_burst

ricker

Signature:

ricker(freq, length, dt, peak_time=None, dtype=None, device=None)

Parameters:

• freq: dominant frequency in Hz, must be > 0
• length: number of samples, must be > 0
• dt: time sample interval in seconds, must be non-zero
• peak_time: optional peak time, default is 1/freq
• dtype/device: optional torch dtype and device

Returns:

• torch.Tensor with shape [length]

Typical usage:

src = tide.ricker(8e8, length=1000, dt=4e-11).view(1, 1, -1)

Definition and timing

The returned source is

$$w(t)=\left(1-2\pi^2f^2(t-t_0)^2\right) \exp\left(-\pi^2f^2(t-t_0)^2\right).$$

freq is the dominant frequency and peak_time is $t_0$. The default peak_time=1/freq leaves a causal-looking lead-in, but it does not guarantee that the finite trace contains negligible endpoint energy. Choose length and timing from the full source spectrum required by the experiment.

Other pulse shapes

All generators use the same freq, length, dt, peak_time, dtype, and device arguments as ricker. When omitted, peak_time defaults to 1/freq.

gaussian(freq, length, dt, peak_time=None, dtype=None, device=None)
gaussian_derivative(freq, length, dt, peak_time=None, dtype=None, device=None)
morlet(freq, length, dt, peak_time=None, cycles=3.0, dtype=None, device=None)
sine_burst(freq, length, dt, peak_time=None, cycles=3.0, dtype=None, device=None)

gaussian returns a unit Gaussian pulse. gaussian_derivative returns its first derivative normalized to unit magnitude. morlet returns a real, Gaussian-windowed cosine. sine_burst returns a cosine limited to cycles periods by a Hann envelope.

Expanding to shots

wavelet = tide.ricker(
    freq=8.0e8,
    length=600,
    dt=4.0e-11,
    dtype=epsilon.dtype,
    device=epsilon.device,
)
source_amplitude = tide.workflow.expand_source_amplitude(
    wavelet,
    n_shots=16,
    n_sources=1,
)

The generator returns one dimension. Maxwell experiments require [shots, sources, nt], so reshape or use expand_source_amplitude.

Validation

Frequency, sample interval, length, and cycle count must be positive. Match dtype and device to the material tensors to avoid an implicit copy during setup.