Modelling and removal of time-varying sea-surface and overburden effects in multicomponent data

In her industrial PhD project, Elsa's work will be divided in three phases. In the first phase she will generalize the time domain integral equation to include also the source ghost and build from receiver ghost and modelled subsurface reflectivity (without sea surface effects) any order of sea surface multiples. The second phase of this project will be based on the same theoretical background, but here Elsa will seek for inverting the integral equations and building a tool to remove the time-varying sea state effects from seismic data. And finally, in the third phase of this project, removal of time-varying sea state effects will be applied on a real data example and the impact on 4D repeatability will be evaluated. Based on the same physical principles as used in the receiver ghost modeling, in the first reporting period, the theoretical formulation for modeling the source ghost in the presence of a time-varying rough sea-surface has been derived. The source ghost is expressed as a surface integral of the source wavefield, containing the direct wave and sea surface reflectivity, and the subsurface reflectivity. Note, as sea surface is time-varying also the sea surface reflectivity will be time varying and simple principles like source-receiver reciprocity will fail to work. To solve the problem, a generalization of the source-receiver reciprocity is needed, which takes also the reversal of the sea surface time function into account. Elsa went on to design an algorithm, which was finally implemented in Matlab. First results of the combined source and receiver ghost modeling were shown at PGS Technology Day (2016) to a larger group of geophysicist from different companies. Furthermore, also the theoretical background for removing the source ghost has been developed based on the same integral formulation, and simple controlled data examples were run to study the performance of the new source deghosting. The modeling of the rough sea surface ghost effects together with the ghost effect removal is documented in the extended abstract for the EAGE (2017) conference. In the second reporting period, a first paper on modeling the effects of a time-varying sea surface on seismic data has been published in Geophysics (2017). This paper documents the theoretical formulation of all the sea surface related ghosts, including the source-receiver ghost as an extension to the previously derived source ghost and receiver ghost. A detail explanation of the algorithm is presented, along with benchmark testing to validate the method. The ghost effects of the wavefield propagating in a geologically complex subsurface have been modelled and the differences between time-varying and static sea surface have been highlighted. Continuing on the theoretical derivation for the source deghosting, the prototype has been finalized and compared to conventional approaches assuming for different application scenarios. The results of this investigation were presented at the Lofoten seminar (2017) and at the PGS Technology Day (2017). Finally, in order to account for all time-varying sea surface effects, the modeling has been extended to include also the free-surface multiples. Prototype codes for modelling all sea surface effects have been implemented in Matlab and first synthetic testing has been performed. The development of a method for simultaneously removing the sea-surface multiples, the source ghost, and the source signature from data acquired under realistic weather conditions has been now finalized. This method is based on a data driven multidimensional one step deconvolution, with deconvolution operator derived from the measured data after decomposition in up-going and down-going wavefield components. The performance of this method for removing all sea surface effects has been investigated using synthetic data of increasing complexity. Part of this study has been presented at EAGE in June 2018 and at PGS Technology Day (2018). A comprehensive study including the theoretical derivation has been compiled in Elsa's second paper, which was submitted on December 2018 to Geophysics. From July to end of September 2018, Elsa had a 3-month research stay at Colorado School of Mines. The research project had as main objective to analyze the feasibility of using blended data in simultaneous removal of multiples, source ghost, and source signature under rough weather conditions. In the third reporting period, a third paper has been written and submitted to Geophysics (April 2019). It covers a synthetic application of the inversion algorithm developed in paper II on source deghosting and demultiple analyzed over different weather conditions. Furthermore, the algorithm was also tested on OBC data and the results compared to the well-known P-Z summation. Part of the study will be presented at EAGE in June 2019. Finally, the last couple of months were dedicated to writing the PhD thesis.

A new method of data modeling for time-varying sea surface has been developed. We showed that: - Time-varying sea surface effects can be modeled accurately using an extended version of the Rayleigh reciprocity theorem - Source-receiver reciprocity is no longer valid in its stationary form Our synthetic results show: - Ghosts and sea-surface multiples are largely affected by the sea surface movements - The error made by considering stationary sea surface increases with time. - For rough weather conditions, also the processing tools need to be adapted. We develop a method to remove sea surface effects from seismic data. Based on our theoretical derivation. Finally, we have demonstrated the sea surface effects removal by our simultaneous source deghosting and demultiple method and observe: - Our inversion is an efficient scheme independently of the weather conditions - Application on OBC field data is successful, despite the small frequency band available.

A start to accurately handle the receiver ghost from time-varying rough sea surfaces has been made by Elsa Cecconello (and supervisors) in her master thesis. To this end we first derived an acoustic reciprocity based integral method in time domain and employed this method to couple the up-going subsurface reflection data with the time-varying sea surface reflectivity on a plane interface below the sea surface. In order to compute the time-varying sea surface reflectivity, we derived a similar integral equation with connecting interface at the sea surface. This method for computing the receiver ghost is benchmarked for both frozen and moving sea surfaces and an expanded abstract has been submitted for EAGE (Cecconello et al., 2016). In her industrial PhD project, Elsa's work will be split in three phases: 1) In the first phase she will generalize the time domain integral equation to include also the source ghost and build from receiver ghost and modelled subsurface reflectivity (without sea surface effects) any order of sea surface multiples. The modelling of surface related multiples will be achieved by a series development of the new integral equation, where each term represents one order of multiples, and each integrant contains the modelled time varying rough sea-surface reflectivity and the time-invariant subsurface reflectivity. The latter may be obtained by any adequate modelling method (e.g., finite difference, plane-layer ray tracing, general ray tracing). This modelling algorithm will be implemented and the generated prototype validated using well defined case studies. 2) The second phase of this project will be based on the same theoretical background, but here we will seek for inverting the integral equations and building a tool to remove the time-varying sea state effects from seismic data. 3)) In the third phase, removal of time-varying sea state effects will be applied on a real data example and the impact on 4D repeatability will be evaluated.