A multiple elimination technique was tested in Elf’s Butabul Concession in Western Oman. The multiples mask the main exploration target, the Permian-Carboniferous Haushi reservoir. The technique is based on inversion in a curvature-time domain. The common mid-point gathers are transformed into this new domain and a mute is then applied to eliminate the multiples. The resulting function is then transformed back to the space-time (x-t) domain. The technique was tested on a newly-acquired, high-resolution seismic line. The survey is approximately 100 kilometers and traverses a low relief seismic prospect south of the Rabkha-1 well. Special high-resolution field acquisition parameters were used to maximize the effective separation of real events from multiples. To prevent aliasing the source and trace spacing were 12.5 and 25 meters, respectively. The Rabkha-1 well was used to select the best mute in the curvature-time domain. The mute required only minor adjustments over the line. The technique proved effective in eliminating the multiples and the resulting interpretation convinced the explorationists not to drill the prospect.


The Butabul Concession in Western Oman produces oil from the Permian-Carboniferous Haushi sandstone reservoir in Sahmah field (Figures 1 and 2). The remaining exploration targets in this area are mainly low relief structures. These targets are difficult to image due to strong multiple interference which completely masks several primary reflections including the Haushi reservoir. Also the primary reflections from the Haushi reservoir below the Permian Khuff carbonates is weak (Figure 3).

The application of conventional multiple elimination techniques, such as deconvolution and filtering (in the T-p, f-t and f-k domains) fails to solve this problem. This failure is due to the similarity of the primary and multiple velocities as well as their frequency spectra and nearly flat geological dips.

Thorson and Claerbout (1985) developed a technique for eliminating multiples in the curvature-time domain (T-p domain). In this paper we use this method, known as the inverted Deltastack process, to eliminate multiples from a specially designed high-resolution seismic line.


Figure 4 shows a common mid-point (CMP) gather from the seismic line acquired in Butabul concession. In the inverted Deltastack process, dip moveout (DMO) is first applied to the traces. At this stage the seismic information is described in the (x, t) domain. The traces are then decomposed in a curvatur-time domain (T, p) where T is the zero offset time and p is the focusing time. Figure 5 shows the CMP gather from Figure 4 in the (T, p) domain, where the vertical axis is the zero offset time and the horizontal axis is sampled in curvature intervals.

The curvature-time domain is based on hyperbolas defined by Eric de Bazelaire (1988) as:





T = t0= zerooffsettimep = tp=zero focusing timeVo=constant velocity in input medium

As Yilmaz (1989) showed for the parabolic radon transform, these hyperbolas are also invariant along the time axis. A hyperbolic radon transform (de Bazelaire et al., 1991) can similarly be defined with the advantage of reducing computation time for the transform algorithm (as compared to a classical hyperbolic transform).

This transformation is followed by an inversion process to enhance the resolution of events (Canadas et al., 1991). The inversion is only performed on a residual normal moveout correction made on a preliminary velocity model. Processing using this method is cost-effective for large datasets. This step optimally defines a mute in the curvature-time domain which selects only events identified as primary reflections.

After applying the mute, the multiple-free function is converted back from the (T, p) domain to a stacked trace in the (x, t) domain. This process is reproduced for each common mid-point (CMP) trace providing a multiple-free section.

The next step consists in the definition of the mute, shown as the region the two green lines in Figure 5. The energy inside the two lines is passed and elsewhere it is rejected. This leads to a clear separation between primaries, highlighted in orange, and multiples circled in red. The mutes must be calibrated in at least one well.

The Rabkha-1 well was used to calibrate the mute. In Figure 5 the synthetic seismogram from Rabkha-1 is also shown. The mute is checked every 40 CMP’s and updated if necessary. The mutes and CMP’s in the (T, p) domain are verified at line intersections to ensure the consistency of the analysis. During this verification stage the timing of several events were stable in the (T, p) domain. As a result the adjustment of the mute pattern was minor which indicated that the analyses was generally consistent and robust.


The efficiency of the multiple suppression technique described here can be optimized by designing the acquisition parameters to match the geophysical objective. For this study, the parameters were set for a target at 2.0 seconds two-way-time. A fold of 240 was chosen to obtain a very high signal/noise ratio. This high fold also helps focus events in the inversion process which improves computational convergence.

A short spacing of 12.5 meters (m) between vibrator points (VP) and 25 m between traces (stack array) was used. This spacing not only gives an accurate coverage of the subsurface layers but also avoids spatial aliasing when transforming between the (x, t) domain to the (T, p) domain.

In order to increase the signal to noise ratio the positioning accuracy was set for a maximum tolerance of 3 m. Each VP and each trace barycenter position were surveyed at their actual position while recording. This accurate positioning reduces the risk of blurring in the u(T, p) functions which may lead to an imprecise separation of the events.

The input signal was improved by reducing even and odd harmonics. This was accomplished by summing four phase-encoded VP’s with a phase rotation of +90° between each point.

In the pre-processing multiples were preserved in order to identify them clearly in the (T, p) domain. Nevertheless, strong dipping noise trains were removed with a classical F-K filter in order to eliminate their interference with the hyperbolic events. Otherwise the data processing sequence prior to the 240 fold dip moveout was conventional.


Figure 6 shows the original stack after DMO where strong multiple interference is evident. The multiple energy is nearly ten times greater than the underlying primaries. On these records the interpretation of the three major events (intra- Khuff, Haushi sandstone and base Haushi limestone) is either impossible or very inaccurate. The section in Figure 7 has been cleared from most of the multiple interferences, providing a clear definition of the major events.

The events of interest can be readily interpreted in the sections with inversion down to two seconds with no spatial aliasing The focusing depth limit of this method is actually set by the acquisition parameters. A longer antenna would increase the aperture of the acquisition pattern and make it possible to focus even deeper events.

The demultiple process has also widened the bandpass of the seismic signal, making the definition of the resulting events sharper. In the inverted section (Figure 7) the bandpass filter is 15 Hertz wider than the one of the traditional DMO section. This demonstrates a significant increase in good signal bandwidth which was previously overshadowed by the low frequency multiples.

We can see the fold effect on the right side of Figure 7 around 1.5 seconds. The reflection pattern which appears near the border tends to vanish to the left, giving way to a different reflection pattern appearance. The reflections on the right of the section are a mix of primaries and multiples which could not be separated in the curvature-time domain due to poor fold. As the fold increases, the separation became more effective and the three main events can be more readily interpreted. The same effect can be observed where a lateral fault crosses the line, the real fold then decreases and the multiples interferences tend to appear below the fault plane.


We have shown that by applying inversion and multiple suppression in the curvature-time domain results in an improved seismic image. The interpretation of the target seismic events was only possible after applying this technique. The resulting interpretation indicated that the seismic lead lacked structural closure.


The authors wish to thank the associates Sumitomo Petroleum Development Co. Ltd. and Wintershall A.G. for encouraging this work and granting permission to make it public. We also wish to thank Compagnie Génerale de Géophysique for their quality seismic acquisition work and the Ministry of Petroleum and Minerals of the Sultanate of Oman for their authorization to publish this paper.


Cherif Benkara-Mostefa is Exploration Manager in Oman with Elf. He has 15 years of exploration and petroleum industry experience with the company. Cherif has a MSc and DEA of Geology from Grenoble University.

Cyril Saint-Andre is a Processing Geophysicist with Elf. His industry experience includes 4 years as Geophysicist with Elf where he is in charge of land/marine processing and supervision. Cyril has an Engineering degree from the Engineer Science Institute of Clermont II University. His areas of professional interest include seismic and signal processing.

Eric de Bazelaire is Scientific Advisor with Elf. He has 15 years of petroleum and exploration industry experience with Elf, following 11 years of research in optics at the Ecole Polytechnique and GESSY Laboratories. Eric is a member of the SEG, EAEG, SFP and SFO. He has an Engineering degree from Ecole Supérieure d’Optique and a PhD in Physics. His areas of professional interest include optics, signal processing and geophysics.

Marc Girard is an Acquisition Supervisor with Elf Aquitaine Production. He has 13 years of exploration experience with Elf where he is involved in the supervision of 2-D and 3-D land acquisitions worldwide. He has a MSc in Geophysics from ENSPM. His areas of professional interest include seismic acquisition and signal analysis.