WSGF — Time for a change part 1: Damped Harmonic Oscillators and the Vibrator/Ground model

Abstract

In land seismic exploration a vibrator is used to generate a controlled wave-train of seismic energy into the earth by the forced oscillations of the ground surface over several seconds in what is known as a vibroseis sweep. Usually, these oscillations are sinusoidal in character and are generated by a hydraulic force acting on two masses, a baseplate (BP) that is in firm contact with the ground and a reaction mass (RM) positioned above the baseplate via a hydraulic actuator connecting both masses. The oscillations generated by the vibrator mechanism propagate away from the vibrator location through the subsurface in the form of seismic waves and are reflected/refracted back to the surface and recorded electronically by multiple sensors laid out on the surface or in a borehole. The energy received at each sensor is the result of the seismic signal generated by the vibrator (its signature) modified by the earth’s geology and the travel paths taken by the propagating wave. In mathematical terms, the signal received at the sensor is the seismic signal convolved by the earth. Unlike impulsive seismic sources, such as dynamite, the raw vibroseis field records are generally uninterpretable because of the relatively low energy output of the source and the multiple overlapping seismic signals that are reflected and refracted during the transmission of the sweep. In addition, the vibroseis signal is contaminated with undesirable environmental and source-generated noise and must be ‘deconvolved’ with the sweep signal to produce an interpretable record that resembles the wavelet generated by an impulsive source. Obviously, the more accurate the deconvolution operator is in replicating the source signature, the greater the resolution obtained in the processing of the seismic data.