Low-frequency seismic deghosting Lasse Amundsen 1 and Hongbo Zhou 2 ABSTRACT We evaluated a solution to seismic deghosting that de- ghosts the low-frequency components of the seismic pressure data. In an approximation that neglected the dependence on wavenumbers, the low-frequency deghosted pressure field was computed trace-by-trace as the sum of the pressure field and its scaled temporally integrated and temporally differ- entiated fields. We gave simple numerical examples that de- monstrated the concept. The method was found to deghost data up to a frequency that is typically half of the second notch frequency. On the low-frequency side, the deghosting method was limited by the signal-to-noise ratio. The low- frequency deghosting technique can be appropriate to apply to the part of seismic data that have penetrated and reflected beneath complex and attenuating overburdens such as ba- salt, salt, and chalk. INTRODUCTION In marine seismic exploration, a source ghost is an event starting its propagation upward from the source, and a receiver ghost ends its propagation moving downward at the receiver. They both have a reflection at the sea surface, which leads to a reduction of the useful frequency bandwidth and therefore damages seismic resolution. The sea surface ghost reflections modulate the spectrum of con- ventional pressure seismic data reducing energy at the so-called notch frequencies f n ¼ nc 2z ; n ¼ 0; 1; 2;:::; (1) where c is the speed of sound in water and z is the source or receiver depth. The first notch is always at zero frequency. The second and following notches are steered by depth z. As a result, there is a strong loss of useful low-frequency energy in pressure seismic data, in addition to similar losses at the second and higher notch frequen- cies. The usable seismic pressure bandwidth is normally between the first and second notch. The ghost removal process is known as deghosting. Deghosting has been a long-standing problem in the seismic industry but has recently obtained significant industry attention, with proposed so- lutions that range from new seismic acquisition methods to proces- sing methods that are applicable to conventional data. Receiver-side deghosting is equivalent to computing the upgo- ing component of the pressure field, which can be done from measurements of pressure and vertical component of the particle velocity. Several vendors offer such seismic measurements (Vaage et al., 2005; Tenghamn et al., 2007; Caprioli et al., 2012). Receiver- side deghosting techniques for conventional data are described in, e.g., Amundsen (1993), Amundsen et al. (2005), and Weglein et al. (2002), who derive a deghosting method from Green’s theorem. Amundsen et al. (2000) apply Green’s theorem for deghosting of ocean bottom seismic data. Ramirez and Weglein (2009) give a tutorial on Green’s theorem as a comprehensive framework for data reconstruction, regularization, wavefield separation, seismic interferometry, and wavelet estimation. After receiver-side deghosting, the source ghost is still present in the seismic data. Most published approaches to source deghosting are based on vertical source array acquisition, in which sources are towed in a complex over/under fashion. The reader is referred to the procedures suggested by Moldoveanu (2000, 2001), Moldoveanu et al. (2007), Robertsson et al. (2011), and those published in Vaage (2005). Recently, a so-called ghost-free solution has been intro- duced based on the GeoSource solution, which requires a time and depth distributed source, using subsources deployed at different depths and fired with specific time delays (Parkes and Hegna, 2011; Petroleum Geo-Services, 2011). Their method removes the source ghost, although mathematically it is not fully wave-theoretically founded because it involves a spectral normalization step at the Manuscript received by the Editor 17 July 2012; revised manuscript received 3 October 2012; published online 20 March 2013. 1 Statoil Research Centre, Norway, and The Norwegian University of Science and Technology, Department of Petroleum Engineering and Applied Geophysics, Norway. E-mail: lam@statoil.com. 2 Statoil Gulf Services, Inc., Houston, Texas, USA. E-mail: hzh@statoil.com. © 2013 Society of Exploration Geophysicists. All rights reserved. WA15 GEOPHYSICS, VOL. 78, NO. 2 (MARCH-APRIL 2013); P. WA15–WA20, 5 FIGS. 10.1190/GEO2012-0276.1 Downloaded 04/23/16 to 182.59.60.122. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/