Multiple Suppression

We have developed two effective data-driven multiple suppression tools, **SRME** (Surface Related Multiple Elimination) and **MWD** (Model based Water layer related Demultiple), to address different geology and survey conditions for marine data.

**SRME** predicts multiple models by convolving seismic data with itself both in time and space based on Huygens principle, and then the multiple is adaptively subtracted from the input data. The method can model all kinds of surface related multiples including water layer related multiples and peg-leg multiples. In our implementation, seismic data is regularized on-the-fly using local interpolation technique and there is no need to run expensive external interpolation, therefore the efficiency is greatly improved.

**MWD** is similar to** SRME** except that the data is not convolved with itself but with a green function of the water bottom primary reflection. The technique has advantages over** SRME** when the water bottom depth is roughly less than half the near offset, where surface–related multiples can be very challenging to attenuate. The missing near-offset data is analytically computed using the water bottom model and water velocity, assuming the water bottom is locally flat. The wavelet of the modeled multiples is more similar to that of the input because the green function can have white spectrum, which makes it easier to apply adaptive subtraction without touching primaries.

The following generalizes the pros and cons of these two methods:

- Both are data driven, not dependent on velocity difference between primaries and multiples.
**SRME**can model more types of surface-related multiples, but it needs good sampling of near offset.**MWD**needs lower requirement of near offset sampling, but it needs good knowledge of water bottom.**MWD**has advantage in adaptive subtraction, because the model wavelet is more similar to input.**SRME**is more suitable for deep-water data because it is difficult for MWD to compute accurate Green’s function when bigger aperture is required and the local flatness assumption is compromised.

We have developed two kinds of adaptive subtraction methods. The first method is based on least-squares matching in the time and space domain. In this method we try to compute an optimal filter for the input multiple model to minimize the difference between the filtered model and the original input data. We have also developed an advanced subtraction method, FFTSUB. This method decomposes both input and model into different dips and frequency bands, then filters the models to match data within each band based on minimum energy criterion, and finally, all filtered models are summed together to form the final filtered model. The decomposition-matching approach enables us to fit data separately for different frequencies and dips, thereby maximum subtraction can be achieved.

Near channel before MWD** **

Near channel after MWD

Shots before SRME

** **

**Shots after SRME**

Stack before SRME

Stack after SRME** **

**IME**

The IME algorithm can be understood as SRME followed by a travel time correction. Mathematically, each multiple contribution can be formulated as a convolution between a common shot trace and a common receiver trace and then correlating with a third trace connecting a receiver of the common shot gather and a source of the common receiver gather. We have developed a spectrum-preserving IME by replacing the cross-correlation step with a horizon-based phase correction in the space and temporal frequency domain. The method has the following advantage over the conventional method

- There is no need to construct cross-correlation gathers in the algorithm. Therefore, the computational cost is significantly reduced.
- The phase correction procedure does not affect the frequency content of the model which helps to preserve the amplitude spectrum.
- There is no need to apply internal mutes to the cross-correlation gather in the model prediction. The resulting model contains fewer artifacts than that of a conventional method.

Raw multiple model comparison of two IME methods. (a) Input shot gather. (b) Multiple model computed using the conventional method (Jacubowitz, 1998). (c) Multiple model computed using the spectrum-preserving IME.

Amplitude spectrum comparison of different IME methods.

**High Resolution Radon Transform (HRRT) Multiple Suppression**

- Uses the Radon transform to perform noise attenuation (usually the attenuation of multiples). It discriminates signal from noise by moveout of seismic events that have been fit to a family of curves – parabolic, hyperbolic or linear.
- In this high-resolution implementation, the forward Radon uses a sparseness constraint to improve focusing in the Radon domain. In principle, a sparse Radon Panel generates better separation between signal and noise.
- It is implemented in the time domain which allows for sparsity in both the time and moveout dimensions.
- Typically, the signal is muted in the Radon domain, and then the noise is inverse transformed back to offset-time. This predicted noise is then subtracted from the input data to leave an estimate of the signal. Other muting strategies are possible with this tool.

**Hyperion Radon Multiple Suppression**

- Hyperbolic Radon transform in time domain.
- Must provide accurate stacking velocities.
- Works on un-NMOed CDP gathers (avoids stretch).
- Optionally designs on super gathers. Number of surrounding CDPs used reduces as the fold increases.
- Does not turn off in regions of low fold. The amount of multiple attenuation reduces gradually with fold.
- Protects against primary removal through “Primary weighting”. This means you can be aggressive with the multiple mute.
- Parameter selection easy. Does not require tau-p mute picking.

**Apex Shifted Diffracted Multiple Suppression**

- This tool provides attenuation of diffracted multiples by performing an apex-shifted Radon transform for CDP gathers in offset-time.
- It computes a parabolic Radon transform at the offset of the apex for a single multiple arrival in a CDP. All multiples that have that offset shift for the apex will be estimated in one pass.
- An apex shifted multiple should appear as a point in Radon space but in real data it is a smeared blob in Tau-q. A transformed apex event in Radon space can be selected using a rectangular box specified by a rectangle in Tau and Q space. All transformed data outside that rectangular box is muted. After muting and applying the inverse Radon transform, the output in offset-time should be the isolated apexes.
- After the isolated apexes are found, an adaptive subtraction tool can be run to remove the apexes as noise.

**Land SRME**

We have implemented **SRME **algorithm for land data. There are several challenges to applying data-driven demultiple methods to land data: uneven surface, poor spatial sampling and signal-noise ratio. We have addressed these problems using strategies in different stages of the demultiple process. In the preprocessing stage, we precondition the data by applying harsh noise attenuation algorithms to remove linear noise and random noise. The data is corrected to a floating datum and then regularized using a local interpolation method. In the subtraction stage, different kinds of matched filters are applied to balance preserving primaries and removing multiples to obtain optimal solutions. As an option, we can use horizons as guide to apply target-oriented SRME so that only the target zone is processed, and the rest is protected.

The example below illustrates a very difficult surface multiple problem in the Cambay Basin of India.

**Input to SRME**

**Output from SRME**

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