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Fast - Wavlet is a deprecated ultrasonic wavelet generator module designed for high-frequency signal simulation in the megahertz (MHz) range. Unlike conventional seismic processing tools that work with frequencies in the Hz range, this module operates on ultrasound data where sample rates, frequencies, and depths are measured at scales appropriate for laboratory or borehole acoustic measurements (centimeter-scale depths, MHz-range frequencies).
The module generates a synthetic waveform by first constructing a wavelet of the chosen type (or a linear frequency sweep), then encoding it as a Pulse Width Modulation (PWM) signal using a sawtooth carrier wave, and finally applying a Butterworth analog bandpass filter to the PWM output. The resulting multi-channel gather contains the original wavelet signal, the sawtooth carrier, the raw PWM signal, the binary PWM signal, and the bandpass-filtered output. All computed timing parameters (sample rate in time, total record length, and number of samples) are derived automatically from the physical parameters you supply.
Note: This module is deprecated and is retained for legacy compatibility. All frequency and depth parameters in this module use MHz and meter (centimeter-scale) units, not the Hz and millisecond units typical of seismic processing modules.
The standard input data connection for the processing pipeline. Connect the upstream data source here so that the module can integrate into the workflow sequence. Because this module generates its output waveform synthetically from the parameters you define rather than modifying the input trace content, the input gather provides context for the pipeline but the output waveform is entirely synthetic.
The input seismic or ultrasonic gather fed into the module. In this module the input gather is used for pipeline connectivity; the actual output is a synthetic waveform constructed from the wavelet parameters, not a transformation of the input trace amplitudes.
The digital sampling frequency of the ultrasonic acquisition system, specified in megahertz (MHz). This value determines the time-domain sample interval of the generated waveform: the sample interval in seconds equals 1 / (SampleRateMHZ × 10<sup>6</sup>). Together with the maximum depth and propagation velocity, it sets the total number of samples in the output gather. Default value: 50 MHz. The minimum allowed value is 0.01 MHz. Use a value appropriate for your transducer's sampling rate; typical ultrasonic transducers operate in the range of 1 to 100 MHz.
The acoustic propagation velocity of the medium being modelled, in metres per second (m/s). This value is used together with the Maximum Depth to compute the two-way travel time of the record: Total Time = (2 × MaxDepth) / Velocity. It should reflect the average sound speed in the material under investigation (for example, approximately 1550 m/s for soft tissue or water, 2500–5000 m/s for rock). Default value: 1550 m/s.
The maximum depth of investigation, in metres (m). Because this module targets ultrasonic frequencies, typical values are on the order of centimetres (for example, 0.10 m = 10 cm). This parameter, combined with the propagation Velocity, determines the total two-way travel time of the generated record. Default value: 0.10 m (10 cm). Increase this value to generate a longer waveform covering a greater depth range.
The time-domain sample interval of the generated gather, in seconds. This field is computed automatically by the module as 1 / (SampleRateMHZ × 10<sup>6</sup>) and is displayed for reference only. You do not need to set this value manually; it updates whenever the Sample Rate MHZ parameter changes. Default displayed value: 0.5 (initial placeholder).
The total number of time samples in the output gather. This value is computed automatically as Total Time / Sample Interval and is displayed for reference only. It reflects the combined effect of your chosen depth, velocity, and sampling rate. You do not set this parameter directly.
The period of the sawtooth carrier wave used for Pulse Width Modulation (PWM) encoding, specified as a number of samples. The sawtooth waveform ramps linearly from -1 to +1 over this number of samples and then resets. The wavelet amplitude is compared to this carrier at each sample to produce the PWM signal: where the wavelet exceeds the sawtooth value, the PWM output is set to 1; elsewhere it is 0. A smaller window produces a higher-frequency carrier and finer PWM resolution; a larger window produces a lower-frequency carrier. Default value: 10 samples. Minimum value: 1 sample.
The total two-way travel time of the generated record, in seconds. This value is computed automatically as (2 × MaxDepth) / Velocity and is displayed for information only. It equals the duration of the output gather and is updated whenever Velocity or MaxDepth are changed.
A scaling multiplier applied to the computed total record duration. A value of 1 uses the natural record length derived from MaxDepth and Velocity. Values greater than 1 extend the record beyond the two-way travel time. Default value: 1. Minimum value: 1.
This parameter group controls the shape, frequency, and length of the synthetic wavelet to be generated. Set Wavelet Type to choose the waveform shape, then configure the associated frequency and length parameters within this group. When the Wavelet Type is set to Sweep, the controls in this group are supplemented by the separate Sweep extraction group.
Selects the mathematical shape of the synthetic wavelet. The available options are:
Ricker1 — Classic Ricker (Mexican hat) wavelet. The amplitude is a function of the squared envelope of a Gaussian modulated by a polynomial, centred at time t0 = 1 / fpeak. This is the most commonly used wavelet for modelling ultrasonic pulses and seismic sources. Default choice.
Ricker2 — Second variant of the Ricker wavelet (after Ricker, 1953), defined as a symmetric function with a specified period. Provides a slightly different shape from Ricker1.
AKB — Alford-Kelly-Boore wavelet, a damped sinusoid of the form -(t-t0) × exp(-2 f<sup>2</sup> (t-t0)<sup>2</sup>). Commonly used in finite-difference acoustic modelling.
Spike — A unit impulse (delta function) at time sample zero. Use this to test the system response or to compute the impulse response of a filter.
Unit — A constant unit waveform (all samples equal to 1). Useful for testing amplitude scaling behaviour.
Berlage — Berlage wavelet, a causal waveform of the form t<sup>n</sup> × exp(-αt) × cos(2πf t + φ). The time exponent, decay rate, and initial phase are set internally. This shape approximates real source pulses that build up and then decay.
Gaussian — A Gaussian bell-curve centred at t0 = 1 / fpeak with standard deviation σ = 1 / (√2 π fpeak). Produces a smooth, zero-phase pulse with no side lobes.
GaussianDeriv — First derivative of the Gaussian wavelet. Produces an antisymmetric pulse with a zero crossing at the peak time t0. Useful for modelling derivative-type transducer responses.
Klauder — Klauder wavelet, the autocorrelation of a linear frequency sweep. It has a symmetric, band-limited shape with a sinc-like envelope. Use this to model the correlated output of a swept-frequency source.
Sweep — A linear frequency sweep (chirp). Instead of using the wavelet shape defined in this group, the module generates a swept-frequency cosine tone using the parameters defined in the Sweep extraction group. Use this when you want to simulate the raw (uncorrelated) output of a swept-frequency ultrasonic source.
Controls the length of the generated wavelet window as a multiple of the dominant period. The wavelet is computed over a time window of (WaveletLength / fpeak) seconds, which translates to a number of samples equal to that time divided by the sample interval. Larger values include more cycles of the wavelet; a value of 1 generates a wavelet spanning one dominant period. For most wavelet types a value of 1 to 3 is sufficient to capture the full waveform without unnecessary trailing zeros. Default value: 1. Minimum value: 1.
The dominant (peak) frequency of the synthetic wavelet, specified in megahertz (MHz). This parameter sets the characteristic frequency of all wavelet types except Sweep (which uses the Sweep extraction group instead). For example, a Ricker1 wavelet at 5 MHz will have its spectral peak at 5 MHz. Set this value to match the centre frequency of your ultrasonic transducer or the signal frequency you wish to model. Default value: 5 MHz.
When enabled, converts the generated wavelet to its minimum-phase equivalent using spectral factorisation before passing it to the PWM encoder. A minimum-phase wavelet concentrates its energy at the earliest possible time, making it causal (no energy before time zero). This can be useful when the generated wavelet will be used as a source signature in forward modelling or deconvolution contexts. Default value: disabled (false). Note: in the current version of the module this option is internally disabled regardless of its GUI state.
This parameter group is active when the Wavelet Type is set to Sweep. It defines the frequency range, taper shape, timing, and duration of the linear frequency sweep (chirp) waveform. The sweep is a cosine tone whose instantaneous frequency increases linearly from Start Frequency to End Frequency over the sweep duration. Taper windows are applied at the beginning and end of the sweep to avoid abrupt amplitude transitions.
The starting (lowest) frequency of the linear sweep, in MHz. The sweep begins at this frequency at the start of the taper-in period and increases linearly to the End Frequency. Set this to the lower corner frequency of your transducer or the lowest frequency component you wish to include. Default value: 0.001 MHz.
The ending (highest) frequency of the linear sweep, in MHz. The sweep ramps from Start Frequency to this value over the active sweep duration. This should not exceed half the sample rate (Nyquist frequency). Default value: 5 MHz.
The shape of the amplitude taper applied at the start and end of the sweep to avoid abrupt discontinuities. Two options are available:
Cos2 — Cosine-squared taper. Provides a smooth, gradual onset and decay of amplitude, minimising spectral leakage. Recommended for most applications. Default choice.
Linear — Linear ramp taper. The amplitude ramps up linearly during the taper-in window and ramps down linearly during the taper-out window.
The time step of the sweep signal in seconds, displayed in the Sweep extraction group. This value is computed automatically from the Sample Rate MHZ parameter and is shown for reference only. It is updated whenever the main sample rate changes and does not need to be set manually. Default displayed value: 0.002 (initial placeholder).
The fraction of the base sweep duration allocated to the taper-in (onset) window, expressed as a proportion (0 to 1). For example, 0.3 means that 30% of the total record time is used for the amplitude ramp-up at the start of the sweep before the sweep reaches full amplitude. Default value: 0.3 (30%).
The fraction of the base sweep duration allocated to the taper-out (decay) window at the end of the sweep, expressed as a proportion (0 to 1). The amplitude ramps down over this period before the sweep ends. Default value: 0.3 (30%).
A multiplier applied to the base record duration to extend the sweep length. The active sweep portion occupies the time window from 0 to (base duration × (SweepFactor - 1)), and the total output gather is extended to (base duration × SweepFactor). A value of 5 means the sweep occupies four times the base travel-time window, and the full output gather is five times as long. Use this to generate longer sweeps without changing the depth or velocity parameters. Default value: 5.
This parameter group defines a four-corner Butterworth bandpass filter applied to the PWM-encoded signal after PWM generation. The filter is defined by four frequency corners (F1, F2, F3, F4 in MHz) forming a trapezoidal pass-band, with stop-band attenuation levels fixed at 5% amplitude for the outer corners and 95% for the inner corners. Set the four corners to match the target frequency band of your ultrasonic measurement system.
The lower stop-band edge frequency of the analog Butterworth bandpass filter, in MHz. Frequencies below this value are attenuated to the stop-band level (5% amplitude). Default value: 1 MHz.
The lower pass-band edge frequency of the analog Butterworth bandpass filter, in MHz. Frequencies above F2 and below F3 pass through at full amplitude. Between F1 and F2 the filter transitions from the stop-band to the pass-band. Default value: 2 MHz.
The upper pass-band edge frequency of the analog Butterworth bandpass filter, in MHz. The filter passes frequencies between F2 and F3 at full amplitude. Above F3 the filter begins to attenuate toward the stop-band. Default value: 8 MHz.
The upper stop-band edge frequency of the analog Butterworth bandpass filter, in MHz. Frequencies above this value are attenuated to the stop-band level (5% amplitude). Ensure F4 does not exceed half the sample rate (Nyquist frequency). Default value: 12 MHz.