GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 125 The demultiple results using the two best performing Radon transform algorithms tested are displayed in Figs. 3b and 3c. As already observed on the synthetic data, we see that the standard parabolic Radon transform from ProMAX is more efficient in attenuating far-offset multiples, but it seems to create more artifacts at near-offset. Conclusion. Two existing problems in the Radon transform computation are the artifacts generated in the transform domain and the long computing time. The limited offset range in t-x domain leads to far-from-ideal, low-resolution Radon transforms with butterfly structures, that make less effective this algorithm in attenuating the multiples on seismic data. Different ways of computing the standard Radon transform and different sparse Radon transform methods are compared in this work according to their performances in giving a high resolution transform and in the demultiple operation. For what concern the standard Radon transform, the conjugate gradient method is more efficient in the multiple attenuation than the damped least squares or the singular value decomposition methods. Concerning the sparse Radon transforms, although in τ-q domain FDS-RT provides a lower signal to noise ratio and a worse vertical and horizontal resolution than TFDS-RT and ISS-RT, in t-x domain it better preserves the weak seismic events and causes the smallest amplitude attenuation along the offset axis. The experiments that we carried out on both synthetic and real data show that our implementation of FDS-RT is the most suitable algorithm in the multiple attenuation between all the Radon transform algorithms tested. To deal with the long computing time problem, the MPI package from Octave-Forge can be used to parallelize the Radon transform algorithms. Taking the ISS-RT code as an example, with 6 processors we achieved a 3.17 times speedup when we set the iteration in the FDS-RT part as 200 and split the frequencies into 25 parts. As a final remark note that the number of parameters required by the aforementioned algorithms is very different, varying from 3 for the TFDS-RT up to 10 for the ISS-RT with FDS-RT calculating the initial model. This could have a great impact on the processing of seismic data. Acknowledgments. We would like to thank Dr. Angelo Sajeva and Dr. Mattia Aleardi for the beneficial discussions during the work. We would like to thank Signal Analysis and Imaging Group from Department of Physics, University of Alberta for their SeismicLab package. We gratefully acknowledge Landmark Graphics Corporation for the use of their ProMAX® software. References Lu W. K.; 2013: An accelerated sparse time-invariant Radon transform in the mixed frequency-time domain based on iterative 2D model shrinkage. Geophysics, vol. 78, issue 4, p. V147-V155. Oldenburg D. W. and Li Y. G.; 2005: Inversion for applied geophysics: a tutorial. Investigations in geophysics, 13, 89-150. Sacchi M. and Ulrych T.; 1995: High-resolution velocity gathers and offset space reconstruction. Geophysics, 60, 1169-1177. Schonewille M. A. and Duijndam A. J. W.; 2001: Parabolic Radon transform, sampling and efficiency. Geophysics, 66, 667-678. Strang G.; 1986: Introduction to applied mathematics. Wellesley-Cambridge Press. Trad D., Ulrych T. and Sacchi M.; 2003: Latest views of the sparse Radon transform. Geophysics, 68, 386-399. Turner G.; 1990: Aliasing in the tau-p transform and the removal of spatially aliased coherent noise. Geophysics, 55(11), 1496-1503. Yilmaz Ö.; 2001: Seismic data analysis. Society of Exploration Geophysicists.