The first Inverse-Scattering-Series internal multiple elimination method for a multi - dimensional subsurface Yanglei Zou, Chao Ma, Arthur B. Weglein, M-OSRP/Physics Dept./University of Houston SUMMARY information. If the multiple to be removed is isolated from other events, then the energy minimization adaptive subtrac- The ISS (Inverse-Scattering-Series) internal-multiple attenua- tion can fill the gap between the attenuation algorithm ampli- tion algorithm (Ara´ ujo et al. (1994),Weglein et al. (1997) and tude prediction and the internal multiples plus, e.g., all prepro- Weglein et al. (2003)) is the most effective algorithm today cessing factors that are outside the assumed physics of the sub- for internal multiple removal. It is the only multi-dimensional surface and acquisition. However primary and multiple events method that can predict the correct time and approximate am- can often interfere with each other in both on-shore and off- plitude for all internal multiples at once, without any subsur- shore seismic data. In these cases, the criteria of energy mini- face information. When combined with an energy minimiza- mization adaptive subtraction may fail and completely remov- tion adaptive subtraction, the ISS internal-multiple attenuation ing internal multiples becomes more challenging and beyond algorithm can effectively eliminate internal multiples when the the current capability of the petroleum industry. primaries and internal multiples are separated. However, under For dealing with this challenging problem, Weglein (2014) many offshore and onshore circumstances where internal mul- proposed a three-pronged strategy including tiples are often proximal to or interfering with primaries, the criteria of energy minimization adaptive subtraction can fail 1. Develop the ISS prerequisites for predicting the refer- (e.g., the energy can increase when a multiple is removed from ence wave field and to produce de-ghosted data. a destructively interfering primary and multiple). Therefore, Weglein (2014) proposed a three-pronged strategy for provid- 2. Develop internal-multiple elimination algorithms from ing an effective response to removing internal multiples with- ISS. out damaging interfering primaries. Currently, there is no ca- 3. Develop a replacement for the energy-minimization cri- pability available in the petroleum industry that addresses that teria for adaptive subtraction. type of serious and frequently occurring challenge. A major component of the strategy is to develop an internal-multiple To achieve the second part of the strategy, that is, to upgrade elimination algorithm that can predict both the correct am- the ISS internal-multiple attenuation algorithm to elimination plitude and correct time for all internal multiples. The ini- algorithm, the strengths and limitations of the ISS internal- tial idea to achieve an elimination algorithm is developed by multiple attenuation algorithm are noted and reviewed. The Weglein and Matson (1998) by removing attenuation factors ISS internal-multiple attenuation algorithm always attenuates (the difference between the predicted internal multiples and all internal multiples from all reflectors at once, automatically true internal multiples) using reflection data. There are early and without any subsurface information. That unique strength discussions in Ram´ ırez (2007). Based on the ISS attenuation always present and is independent of the circumstances and algorithm and the initial idea for elimination, Herrera and We- complexity of the geology and the play. However, there are glein (2012) formulated an ISS algorithm for a normal incident two well-understood limitations of this ISS internal-multiple wave on a 1D earth, that eliminate first-order internal multi- attenuation algorithm ples generated by the shallowest reflector and further attenu- ates first-order internal multiples from deeper reflectors. Zou 1. It may generate spurious events due to internal multi- and Weglein (2014) then advanced and extended these initial ples treated as sub-events. contributions for the pre-stack and for all first order internal multiples generated at all reflectors. In this paper, we further 2. It is an attenuation algorithm not an elimination algo- extend the 1-D elimination algorithm and provide the first ISS rithm. multi-dimensional elimination method for all first order inter- nal multiples. The first item is a shortcoming of the leading order term (the term used to derive the current attenuation algorithm), when taken in isolation, but is not an issue for the entire ISS internal- multiple removal capability . It is anticipated by the ISS and INTRODUCTION higher order ISS internal multiple terms exist to precisely re- move that issue of spurious events prediction. When taken to- The ISS (Inverse-Scattering-Series) allows all seismic process- gether with the higher order terms, the ISS internal multiple ing objectives, e.g., free-surface-multiple removal and internal- removal algorithm no longer experiences spurious events pre- multiple removal to be achieved directly in terms of data, with- diction. Ma et al. (2012) , H. Liang and Weglein (2012) and out any need for or estimation of the earth’s properties. The Ma and Weglein (2014) provided those higher order terms for ISS internal-multiple attenuation algorithm is the only method spurious events removal. today that can predict the correct time and approximate and well-understood amplitude for all first-order internal multiples In a similar way, there are higher order ISS internal multiple generated from all reflectors, at once, without any subsurface terms that provide the elimination of internal multiples when
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