Wave equation receiver deghosting: A provocative example

Abstract

The problem of counteracting the effects of the receiver ghost in marine data has generally been addressed either by making complementary measurements such as hydrophone pairs or hydrophone and particle velocity sensors or by estimation of the effect through the so-called ghost model.Here, we discuss a technique based on the wave equation that accomplishes up/down wavefield separation based on a single measurement that does not rely on the spectral ghost model and does not rely on statistical or other means of estimating missing frequencies. While it is a distinct advantage to record multiple measurements, such systems are limited in availability and, moreover, significant legacy data exist that could benefit from deghosting. We briefly review the theory for wave equation receiver deghostingfirst presented by Beasley et al., (2013) and then present examples that confirm the accuracy of the approach. We illustrate a significant difference between this approach and many other approaches that use single measurements. Using the notch frequency in a mono-frequency plane wave example, we show that our approach accurately reconstructs the upgoing wavefield without benefit of information from other frequencies; a task that we expect would pose challenges to other single-measurement approaches.

Three‐dimensional receiver deghosting of seismic streamer data using L1 inversion and redundant extended radon dictionary

“…Rickett (2014) used joint interpolation deghosting to achieve genuinely 3D deghosting. Beasley, Coates and Ji (2013a); Beasley et al (2013b); and Beasley and Coates (2014) proposed a wave equation deghosting method, which strives to honour wave propagation and causality as much as possible.…”

“…For 3D receiver deghosting, almost all the reported methods require dense wavefield sampling, but in real data acquisition, the crossline interval is normally much larger than the inline interval (typically, the ratio of inline interval to crossline interval varies between 1:4 and 1:16), which violates this fundamental assumption. As a trade-off, most methods choose either to work only on dense 2D inline data (Beasley et al 2013a(Beasley et al , 2013bBeasley and Coates 2014;Berkhout and Blacquiere 2014) or make a 1D propagation assumption (Soubaras 1996). Rickett (2014) utilised interpolation in his method explicitly as an independent operation; however, interpolation for real data is not trivial, which makes it difficult to optimally apply both steps without a propagation of errors.…”

Integrated receiver deghosting and closed-loop surface-multiple elimination

“…To remove the receiver ghost, Ferber et al (2013) combine pressure data with an estimate of the particle velocity data. Beasley et al (2013) and Robertsson et al (2014) use the fact that the upcoming waves arrive earlier than the downgoing ghost waves, leading to causal deghosting filters. Ferber and Beasley (2014) use this principle to shift the ghost events out of the time window.…”

Using Ghost Reflections Rather than Removing Them

“…Many methods for deghosting have been proposed. E.g., Soubaras (2010) carries out joint deconvolution to a direct and a mirror migration result; Wang and Peng (2012) introduce a bootstrap method based on modelled mirror data; apply a frequency-domain spatial deconvolution; Beasley et al (2013) and Robertsson et al (2014) exploit causality: upcoming waves arrive earlier than the corresponding downgoing 'ghost' waves; Ferber and Beasley (2014) shift the ghost events out of the time window. Some examples specifically focussing at the source side are Mayhan and Weglein (2013) and .…”