Ghosts have always held some degree of fascination, thanks to hundreds of books and movies devoted to the subject. One of the scariest films of all time is The Exorcist, a 1973 horror film which deals with the demonic possession of a young girl and her mother’s desperate attempts to win back her daughter through an exorcism. Ghosts are also present in seismic recordings and must also be exorcised.

To understand how geophysical priests exorcize seismic ghosts, either through developing sensor technologies or new data processing methods, you need to understand what ghosts are and how they band-limit seismic data. Like John Malkovich, geophysicists do not lack confidence, but we believe our profession may never be fully successful in catching and exorcizing the seismic ghosts. The real-world problem is too tough. We give you the history.

### Broadband Seismic Towed-Streamer Methods

Conventional marine seismic acquisition techniques record data over a useable frequency range of typically 8 to 80 Hertz. A seismic section with this bandwidth can resolve reflectors separated by about 20–25 ms. This resolution is adequate for mapping medium to large geological structures with simple stratigraphy. However, in areas having complex geological features, conventional data hide the details required to fully assess the exploration potential.

One of the major factors hampering marine seismic resolution is the ghost effect – the result of reflections from the sea surface. Ghost reflections interfere constructively or destructively with the primary reflections, thereby limiting useable bandwidth and data integrity due to notches at particular frequencies. The notch frequencies depend on the respective depths of the source and receiver. For example, a depth of 6m produces a notch at 0 and 125 Hz, while a 20m depth produces notches at 0, 37.5, 75, and 112.5 Hz (See figure at the end of this article). Some control can be exercised in acquisition by varying the depth of the source and streamers, but the full bandwidth remains compromised.

Acquisition and processing solutions to address the receiver ghost problem were introduced in the mid-1950s, with significant technological progress having been made over the last five years. Major developments include the hydrophone-geophone (P-Z) streamer; over/under streamers; slanted streamer; GeoStreamer, P-Z; BroadSeis, variant of slanted streamer; and the multicomponent streamer, IsoMetrix.

Hydrophones measure pressure (P) changes, while geophones and accelerometers are sensitive to particle motion. The hydrophone is omni-directional and measures the sum of upgoing and downgoing pressure waves. The vertically oriented geophone (Z) has directional sensitivity and measures their difference.

### Significant Developments

By 1956, Haggerty from Texas Instruments had patented methods for canceling the ghost reflections and reverberations in the water-layer by deploying hydrophones and geophones, and over/under streamers. His analysis was based on the theory of standing waves. Today, history shows that Haggerty was 50 years ahead of time.

Pavey and Pearson from Sonic Engineering Company described in 1966 how the frequency components that are canceled on hydrophone recordings due to the ghost can be replaced by the use of geophones. However, it was found that the combination of P and Z signals tended to degrade the S/N-ratio of the lower frequencies in the seismic band. The Z-sensor had high noise caused by the specific mounting of the sensor and the rotation of the towed cable.

Berni in Shell Oil (1982–85) developed the geophone principles further. The first successful P-Z marine streamer, PGS’ GeoStreamer, was described by Vaage et al. (2005). In addition to the deghosting advantage, the GeoStreamer reduces weather noise and increases acquisition efficiency by extending the weather acquisition window.

In 1976 Parrack from Texaco patented the use of streamers that are spaced apart vertically to cancel the downgoing ghost signals from the sea surface. The first practical 2D applications of the over/under streamer method started in 1984 in the North Sea, driven by ideas from Sønneland in Geco. The method was introduced as a means to reduce the weather downtime by deploying two streamers on top of each other at large depths, such as 18m and 25m, to minimize the effect of swell noise. In addition, it allowed deghosting. The over/under acquisition, however, had limited applications during that period due to deficiencies in marine acquisition technology related to lack of streamer control in vertical and horizontal planes.

With the introduction of new marine acquisition technology that has accurate positioning and advanced streamer control, the over/under method has been used for the last six years, mainly for 2D applications.

Slant streamer marine acquisition was first proposed by Ray and Moore (1982) from Fairfield Industries. The novel idea of this method was to have variable receiver depths along streamers and, inherently, variable ghosts from receiver to receiver, and to take advantage of this in the stacking process. However, slant streamer acquisition was not successful at that time due to inadequate data processing algorithms, particularly for the ghost-removal process.

Today, variants of the slant streamer idea have been implemented by CGGVeritas (BroadSeis) and by WesternGeco (ObliQ).

The concept of multicomponent towed streamers was introduced by Robertsson et al. (2008). The system, now called IsoMetrix, measures pressure with hydrophones, and particle acceleration in y- and z-directions with micro electromechanical systems (MEMS) accelerometers. Based on these measurements crossline wavefield reconstruction and deghosting can be performed (GEO Expro Vol. 9, No. 5).

### Ghosts

The effect of the sea or land surface is a well-known obstacle in seismic exploration and has been addressed since the outset of reflection seismology (Leet, 1937). Van Melle and Weatherburn (1953) dubbed the reflections from energy initially reflected above the level of the source, by optical analogy, ‘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 τ_{0}=2z/c, here represented in frequency domain by the function G = 1 + r_{0} exp(iωτ_{0}) can be eliminated theoretically by applying the inverse filter D = 1/G to the data: D G = 1 . Here, r0 is the reflection 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 domain pressure pulse that is emitted by the single airgun in the vertical direction is called the pressure signature. The pressure pulse that travels upward from the source is reflected downward at the sea surface and joins the initially downward-traveling pressure pulse. This 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.

### Ghost Effect on P

In the following, we discuss receiver ghosts – source ghosts were discussed in GEO ExPro Vol. 7, No. 1 on Marine Seismic Sources. We assume that the reflection coefficient at the sea surface is r_{0}=-1.

Consider conventional pressure recordings at depth z. As seen from the illustration on the page opposite, the ghost is delayed with travel time τ = τ_{0}/cosθ relative to an incident plane wave that has a propagation angle θ to the surface. The composite signal (primary and ghost), that is the ghost function, in the frequency domain then can be written G_{-}=1-exp(iωτ).

The frequency spectrum of this composite signal, |G_{-}(f)|=2sin(2πfzcosθ/c), has zeroes or ‘notches’ at frequencies f_{n}=nc/(2zcosθ) (n=0,1,2,...), where the interference between signal and ghost is destructive. The first notch is always at 0 Hz. The 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 intermediate adjacent notch frequencies, leading to maxima in the amplitude at these frequencies.

One of the goals in broadband marine seismic acquisition is to deliver data rich in both low and high frequencies. The challenge of increasing low-frequency while maintaining high-frequency content is caused by the receiver ghost effect. Towing streamers shallowly favors the higher frequencies at the expense of attenuating the low frequencies, while towing streamers deeper favors the lower frequencies, at the expense of attenuating frequencies within the seismic bandwidth.

### Ghost Effect on Z

Today’s most advanced streamer technologies record both particle velocities and pressure. The hydrophone is omni-directional and measures the sum of upgoing and downgoing pressure waves. The vertically oriented geophone has directional sensitivity and measures their difference. Therefore, in Z-recordings the ghost has opposite sign compared to that in P-recordings: G_{+} = 1 + exp(iωτ). Its frequency spectrum reads |G_{+}(f)|=2cos(2πfzcosθ/c), and has notches at frequencies f_{n} = (2n+1)c/(4zcosθ), lying mid-between the notches in the P-recordings. Thus, hydrophones and geophones give complementary information. Where the hydrophone has zero sensitivity due to the ghost, the Z-geophone has its maximum sensitivity, and vice versa.

Let R denote the ’reflection response’ of the subsurface (including the source ghost). Then P~R G_{–} and Z~R G_{+}. It now follows that you can exorcize the receiver ghost by summing P and Z (when Z is properly scaled to P) since (1/2)(P+Z)=R. Thus, receiver side deghosting, equivalent to computing the upgoing component of the pressure field, can be done from PZ measurements. This is a fundamental basis of both PGS’s GeoStreamer solution and WesternGeco’s IsoMetrix solution.

### Deghosting by PZ Summation

However, for low frequencies, below 15–20 Hz, depending on the particular acquisition system and weather, the Z recordings are too noisy to be used in PZ summation. The solution to this problem was developed and implemented by PGS in the GeoStreamer. The straightforward combination of the two equations, P~R G
_{–} and Z~R G_{+}, gives the Z-P relationship, first published in Geophysics by Amundsen (1993): Z~(G_{+} /G_{–})P.

Thus, for the low frequencies where Z is noisy, Z can be estimated from P by deghosting the pressure (multiplying P by 1/G_{–}) and ghosting the result (multiplying by G_{+}). Then, this estimate of Z is used at low frequencies whereas the Z measurements are used at higher frequencies in deghosting. The Z-P model is used also in 3D deghosting of WesternGeco’s IsoMetrix measurements, not to replace low-frequency Z data but rather to further constrain the cross-line reconstruction problem.

We observe that P-Z sensor streamers have no direct benefits for low frequency recording as they use only the hydrophone at low frequencies; the geophones are used to infill the higher frequency ghost notches. To get high-quality pressure measurements at low frequencies, the cables must be towed deep where the pressure ghost notch has minimum effect and the S/N ratio is good.