On the accuracy of the ground force estimated in vibroseis acquisition

For a linear elastic Earth the time derivative of the ground force is considered proportional to the far-field wavelet. Under the assumption that the baseplate is stiff and the bending forces of the baseplate are negligible, the ground force is also approximated by the sum of the accelerations of the baseplate and the reaction mass weighted by the respective masses. Combining these two assumptions, the time derivative of the weighted sum is considered proportional to the far-field wavelet. This result, often referred to as the far-field wavelet assumption, although convenient and most often employed is not always valid. We explore its validity using the spectral harmonic ratios of recorded data, which are used extensively in data filtering and analysis of vibratory data. We show that the far-field wavelet assumption fails particularly for harmonic components of even order. More compact soil after repeated shots further invalidates this assumption. Non-linear modelling of the ground under the vibrator point may provide a direction towards solving this discrepancy. Finally, we describe a method for the estimation of the harmonic spectral ratios.