Time-lapse POCS Differencing of time-lapse survey data using a projection onto convex sets algorithm Mostafa Naghizadeh and Kris Innanen ABSTRACT Irregular spatial sampling in time-lapse surveys can hamper the efforts to obtain op- timal difference sections due to very sparse common spatial samples in the baseline and monitor surveys. We exploit the similarities between baseline and monitor surveys via a Fourier-based reconstruction methods called projection onto convex sets (POCS) to ob- tain a reliable difference section. Simultaneous handling of baseline and monitor surveys provides a robust indicator of dominant harmonics in the difference section for a given frequency component. Synthetic and modeled data examples demonstrate the viability of the approach when baseline and monitoring data sets have so few as 30% common trace locations. INTRODUCTION Time-lapse seismic surveys have become an industry standard in exploration seismol- ogy. It consists of an operation to acquire and process multiple seismic surveys, repeated at the same location over a period of time (Lumley, 2001). It can be utilized for various purposes such as reservoir monitoring, CO2 sequestration, and environmental studies. The main problem with processing time-lapse seismic surveys lays in the fact that multiple surveys can not be acquired with the same exact geometry. Therefore, efficient process- ing methods are necessary in order to account for the mismatch between the baseline and monitor surveys. Imaging and migration of time-lapse surveys are the next step of identifying the sub- surface changes. This task can be carried out using joint imaging of baseline and monitor surveys as well as imaging of the difference section. The joint inversion provides the pos- sibility of using various regularization terms but it imposes very high computational costs. On the other hand, migrating the difference section is computationally less demanding but it is difficult to create a reliable differences section from real data sets due to the irregu- lar spatial sampling and presence of statics in seismic sections. This requires finding an optimal way of matching the baseline and monitor surveys to obtain a reliable difference section (Zabihi 2010). Also, maximally complete difference data sets will be of significant importance in implantation of time-lapse imaging based on scattering/perturbation theory, which is expressed in terms of linear and nonlinear operations on these data differences (Innanen et al., 2011). Fourier reconstruction and interpolation methods has attained spacial attention in seis- mic data processing community in recent years. Projection onto convex sets (POCS) (Abma and Kabir, 2005), minimum weighted norm interpolation (MWNI) (Liu and Sacchi, 2004) and anti-leakage Fourier transform (ALFT) (Xu et al., 2005) are few to name from many. These techniques rely on imposing sparseness constraints on the Fourier representation of the irregularly sampled seismic data in an attempt to recover seismic data on a regularly CREWES Research Report — Volume 23 (2011) 1