Non-impulsive source waveforms for physical modelling

Kevin W. Hall, Joe Wong, Kevin L. Bertram, Kristopher A. H. Innanen

The physical modelling system is being upgraded with an arbitrary waveform generator (AWG), that will allow us to use non-impulsive source waveforms including sinusoidal frequency sweeps, square-wave frequency sweeps, and m-sequences (pseudorandom binary sequences). Some of these waveforms, such as constant amplitude mono-frequency square waves or mono-frequency spike series can be run without an AWG. Square wave signals and spike series have only two normalized values: +1 and -1. Therefore, they are called binary-valued sequences, and are much more easily generated by electronic circuits for practical usage than are sinusoidal signals. This report examines the theoretical effect of running a variety of source waveforms, including Vibroseis sweeps, through our system, and predicts our future results if we use a pair of millimeter-sized source transducers, which have a characteristic impulse response. We also show actual data resulting from a spike series run through 37 mm buzzers. Of interest for all source waveforms is the expected amplitude at the receiver for 10 kHz (equivalent to 1 Hz after scaling by 10000 to real-world seismic exploration frequencies), which we need if we wish to run full-waveform inversions (FWI) on physically modeled data. Our results show that running a frequency sweep that spends proportionately more time near 1 Hz (scaled) can improve our recorded amplitudes at that frequency, but enhancing this signal will require further processing.