Decomposition of Harmonically Distorted Chirps into their Harmonic Components

Saragiotis, Christos; Scholtz, P.

doi:10.1109/dsp.2009.4785913

Cited by 1 publication

(2 citation statements)

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“…The quantities C k S k , k ≥ 1 are not known in advance, however they can be satisfactorily estimated, if some other initial estimates of C k S k are employed, provided that they correlate well with C k S k . Such initial estimates may be the k th theoretical harmonics of the pilot sweep or the harmonic components of the weighted sum (Saragiotis and Scholtz 2009). Since the estimation of C k S k is based on cross‐correlation, the better the initial estimate is, the better C k S k are estimated as there is less energy leakage.…”

Section: Definitions and The Convolutional Modelmentioning

confidence: 99%

“…Furthermore, in order to calculate the ratios C k S k C 1 S 1 , it may be beneficial to have a better estimate of the pilot harmonic phase spectra. Other initial estimates of the pilot harmonics phase spectra have been proposed (Scholtz 2002;Saragiotis and Scholtz 2009). Such phase spectra can be obtained from the ground force estimated as the mass weighted sum of the baseplate and reaction mass accelerations.…”

Section: Correlation Of H(t) With the M-th Harmonic H M (T) Yieldsmentioning

confidence: 99%

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On the accuracy of the ground force estimated in vibroseis acquisition

Saragiotis

Scholtz

Bagaini

2009

Geophysical Prospecting

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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.

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