5.1.3 Resolution and Wavelength
Te classic definition of resolution, given by the famous geophysicist Bob Sheriff, is the ability to distinguish two features from one another. Te seismic method is limited in
its ability to resolve or separate small features that are very close together in the subsurface. Te definition of ‘small’ is governed generally by the seismic wavelength, λ = v/f. Geophysicists can do little about a rock’s velocity, but they can change the wavelength by working hard to change the frequency. Reducing the wavelength by increasing the frequency helps to improve both temporal/vertical and spatial/ horizontal resolution. Resolution thus comes in two flavours. Te temporal resolution refers to the seismic method’s ability to distinguish two close seismic events corresponding to different depth levels, and the spatial resolution is concerned with the ability to distinguish and recognise two laterally displaced features as two distinct adjacent events. Figure 5.3 depicts two similar layers separated
a
by interfaces. Te measurable seismic signals that they produce may show as separate, distinguishable signals when they are well separated – a condition we call ‘resolved’. When the interfaces are close together, however, their effects on the seismic signals merge and it is difficult or maybe impossible to tell that two rather than just one interface is present – this condition we call ‘unresolved’. Te problem of resolution is to determine how to separate resolved from unresolved domains. Te yardstick for seismic resolution is the
dominant wavelength λ. A much used definition of ‘resolvable limit’ is the Rayleigh limit of resolution: the bed thickness must be a quarter of the dominant wavelength. Tis resolution limit is in agreement with conventional wisdom for seismic data that are recorded in the presence of noise and the consequent broadening of the seismic wavelet during its subsurface journey. Te dominant wavelength generally increases with depth because the velocity increases and the higher frequencies are more attenuated than lower frequencies. Te λ/4 limit is considered by many the
geophysical principle regarding the limiting resolution we can expect in determining how thin we can resolve bedding layers from seismic. However, we might be able to go beyond this limitation by focusing in on frequency’s ability to tune in on the layer thickness. For reflectors separated by less than λ/4 thickness, the amplitude of the composite reflection depends directly on the thickness of the reflecting layer. Tis composite amplitude variation can be used for estimating the thickness of arbitrary thin beds.
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Figure 5.3: Different limits of vertical resolution (d–f, after Kallweit and Wood, 1982; Zeng, 2008) for a step-wise acoustic impedance (AI) profile (a) giving rise to two reflection events R of same polarity (b). Resolution can be increased by increasing the high-frequency content of the seismic wavelet.
Te stepwise AI profile in Figure 5.3 represents a somewhat
uncommon model for reservoir geophysics. Te model of greater interest is the wedge model (see 5.4), which gives reflections of equal amplitude but opposite polarity. In this case λ/4 is known as the tuning thickness that corresponds to the maximum composite amplitude.
Figure 5.4: Wedge model (a) and its resolution. Observe that low frequencies (b) in the wavelet significantly reduce the side-lobe effects, improving interpretability.
b
c
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