‘ghosts’. Lindsey (1960) presented a ghost removal or deghosting solution by observing that a downgoing source signal of unit amplitude followed by a ghost with time lag τ0


by applying the inverse filter D = 1/G to the data: D G = 1 . Here, r0


coefficient at the overlying boundary, k = ω/c is the wavenumber, ω=2πf is the


circular frequency, f is the frequency, c is the propagation velocity, and z is the source depth. In marine seismic surveying, the time


Figure 5.11: A plane wave with angle ϑ to the surface is incident at the receiver (red circle). The ghost is delayed with time τ = 2z/(c cosϑ). The rays that are normal to the plane wave denote the direction of the wave.


20 m 6 m


domain pressure pulse that is emitted by the single airgun in the vertical direction is called the pressure signature. Te pressure pulse that travels upward from the source is reflected downward at the sea surface and joins the initially downward-travelling pressure pulse. Tis delayed pulse, reflected at the sea surface, is called the source ghost. Also on the receiver side the sea surface


acts as an acoustic mirror, causing receiver ‘ghost’ effects in recorded seismic data. While the reflections from the subsurface move upward at the receiver, the receiver ghosts end their propagation moving downward at the receiver.


5.2.4 Ghost Effect on P


Figure 5.12: Ghost responses that modulate pressure recordings for deep-tow at 20m and shallow-tow at 6m. The ghost amplifies some frequencies (amplitude >0 dB) and attenuates other frequencies (amplitude <0 dB). By towing deeper, the pressure signal is improved below ~30 Hz. Although deep-tow yields nice low-frequency characteristics, the second notch at 37.5 Hz has a detrimental effect on resolution.


In the following, we discuss receiver ghosts – source ghosts are discussed in Section 3.1.3. We assume that the reflection coefficient at the sea surface is r0 Consider conventional pressure


=-1.


recordings at depth z. As seen from Figure /cosθ relative to an incident plane


5.11, the ghost is delayed with traveltime τ = τ0


Hydrophone Geophone


wave that has a propagation angle θ to the surface. Te composite signal (primary and ghost), that is the ghost function, in


the frequency domain then can be written G-


=1-exp(iωτ). Te frequency spectrum of this


composite signal, |G- has zeroes or ‘notches’ at frequencies fn


(f)|=2sin(2πfzcosθ/c), =nc/


Figure 5.13: Receiver ghost responses for hydrophone and geophone at 18.75m depth. The geophone has maximum response (+6 dB) where the hydrophone has notch, and vice versa. For the low frequencies, the real geophone signal is too noisy, and deghosting is achieved in processing using the geophone-hydrophone model.


200


(2zcosθ) (n=0,1,2,...), where the interference between signal and ghost is destructive. Te first notch is always at 0 Hz. Te second and following notches are steered by the depth z. As a result there is a strong loss of useful low-frequency energy in pressure seismic data, in addition to similar losses at the second and higher notch frequencies. On the other hand, constructive interference occurs at frequencies lying exactly in the middle of adjacent notch frequencies,


=2z/c, here represented in


frequency domain by the function G = 1 + r0 exp(iωτ0


), can be eliminated theoretically is the reflection


Lasse Amundsen


Lasse Amundsen


Lasse Amundsen


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