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clockwise motion, their resultant vector may at some instances form a cardioid pattern and appear to turn in the opposite direction. We interpret this as the effect of interference of twoclosely arriving wavelets. This is also caused by noise interference in low amplitude zones.Because of these reversals, instantaneous frequency will have unusual magnitudes and fluctuations.

Instantaneous Frequency Envelope Weighted To suppress spurious values of instantaneous frequency in areas with poor signal quality thevalue of instantaneous frequency is multiplied by the normalized value of the instantaneousenvelope and averaged over a short time window:

where T is the smoothing time window.

Thin Bed Indicator The locations where instantaneous frequencies jump or become negative are of a particular interest. As we have discussed earlier these jumps are indicative of closely arrivingreflections. The time derivative of the phase function therefore becomes an indicator for thin

beds when the variations are large, whereas smooth variations will correspond to variations in bedding characteristics, which we will have to investigate further. The thin bed indicator is,therefore, computed as the difference between instantaneous and time averaged frequencies:

Acceleration of the Phase The time derivative of instantaneous frequency, by definition, gives the instantaneousacceleration. We can compute this both from instantaneous frequency and from time averaged instantaneous frequency. It is obvious that the time derivative of instantaneous frequency willaccentuate the local frequency jumps, and hence will make the thin bed indicators more

prominent. It should also indicate to some degree the effect of absorption by showing thefrequency dispersion of seismic signals going through unconsolidated or quickly deposited

layers:

Band Width

Barnes (1992) suggested that instantaneous bandwidth can be computed as

where d[env(t)]/dt is the time derivative of theenvelope. This equation measures the absolute value of the rate of change of envelopeamplitude. The bandwidth is expressed in terms of octaves.

Dominant Frequency RMS frequency of the amplitude spectrum represents a biased mean towards the dominantfrequency band. This attribute will be computed if you select the DominantFrequency toggleon the interface.

Instantaneous Q Barnes (1992) suggested that instantaneous quality factor q(t) can be defined by the

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expression where decay(t) is the instantaneous decay rate,which is defined as the derivative of the instantaneous envelope divided by the envelope.

Except for a factor of , decay(t) is similar to the instantaneous bandwidth.

Normalized Amplitude The normalized amplitude is computed as the cosine of instantaneous phase. This attribute hasall of the details of instantaneous phase while avoiding the jumps inherent in it. The display of this attribute emphasizes the lateral continuity of seismic events. The attribute has noamplitude information and its values vary between 1 and +1.

Envelope Modulated Phase Since instantaneous phase information is independent of amplitude information, all events,including those with very low amplitudes, are displayed with the same intensity. In order toshow the instantaneous phase of the more significant events, we have combined envelopeamplitude information with the phase information.

Relative Acoustic Impedance This attribute is computed by continuous integration of the original seismic trace with thesubsequent application of low cut filter. This attribute will be computed if you select theRelativeAcousticImpedance toggle on the interface.