Theory of multisource crosstalk reduction by phase-encoded statics

Abstract

S U M M A R YFormulas are derived that relate the strength of the crosstalk noise in supergather migration images to the variance of time, amplitude and polarity shifts in encoding functions. A supergather migration image is computed by migrating an encoded supergather, where the supergather is formed by stacking a large number of encoded shot gathers. Analysis reveals that for temporal source static shifts in each shot gather, the crosstalk noise is exponentially reduced with increasing variance of the static shift and the square of source frequency. This is not too surprising because larger time shifts lead to less correlation between traces in different shot gathers, and so should tend to reduce the crosstalk noise. Analysis also reveals that combining both polarity and time statics is a superior encoding strategy compared to using either polarity statics or time statics alone.Signal-to-noise (SNR) estimates show that SNR stand. = √ G S for a standard migration image and SNR super = √ G I for an image computed by migrating a phase-encoded supergather; here, G is the number of traces in a shot gather, I is the number of stacking iterations in the supergather and S is the number of encoded/blended shot gathers that comprise the supergather. If the supergather can be uniformly divided up into Q unique sub-supergathers, then the resulting SNR of the final image is SNR sub-super = √ QG I , which means that we can enhance image quality but at the expense of Q times more cost. The importance of these formulas is that they provide a precise understanding between different phase encoding strategies and image quality.Finally, we show that iterative migration of phase-encoded supergathers is a special case of passive seismic interferometry. We suggest that the crosstalk noise formulas can be helpful in designing optimal strategies for passive seismic interferometry and efficient extraction of Green's functions from simulated supergathers.

Sparse least-squares reverse time migration using seislets

“…We simulate 256 shots using the true velocity model shown in Figure 3(a). Each shot is recorded with 512 receivers at a 20 m receiver interval with a total recording time of 10 s. We assume a fixed-spread acquisition geometry for both the sources and the receivers and blend all the 256 shotgathers into one supergather using the dynamic polarity and phase-encoding technique proposed by Schuster et al (2011) and Dai et al (2012). The velocity model shown in Figure 3(b) is used as the migration velocity model.…”

“…This approach, although very effective in reducing the computational cost, suffers from crosstalk noise which severely degrades the quality of the migrated image. Later, Dai and Schuster (2009) and Schuster et al (2011) extended the blended source migration technique to multisource least-squares migration and showed that the crosstalk noise can be mitigated by an iterative migration of supergathers.…”

Plane-wave least-squares reverse time migration for rugged topography

“…Schuster et al (2011), Dai et al (2012 employed a phase-encoding multisource approach to increase the computational efficiency. Dai and Schuster (2013), Li et al (2014a, b) performed plane-wave encoding to LSRTM and achieved a better suppression to crosstalk.…”

Least-squares reverse time migration of marine data with frequency-selection encoding

“…However, the random encoding functions used by Romero et al (2000), Krebs et al (2009), Schuster et al (2011) and Dai et al (2012), cannot be easily applied to a seismic survey with a marine streamer geometry (Routh et al, 2011;Huang and Schuster, 2012) because, although the calculated synthetic data are of fixed spread geometry, the observed data are recorded with a marine streamer geometry. Huang and Schuster (2012) proposed a frequency-selection encoding strategy for least-squares phase shift migration, which is applicable to marine data.…”

“…The phase-encoding technique (Romero et al, 2000;Krebs et al, 2009;Schuster et al, 2011) has been applied to increase the computational efficiency of seismic modeling and migration and it can reduce the cost of LSRTM to the level of conventional RTM. However, the random encoding functions used by Romero et al (2000), Krebs et al (2009), Schuster et al (2011) and Dai et al (2012), cannot be easily applied to a seismic survey with a marine streamer geometry (Routh et al, 2011;Huang and Schuster, 2012) because, although the calculated synthetic data are of fixed spread geometry, the observed data are recorded with a marine streamer geometry.…”