Relating source-receiver interferometry to an inverse-scattering series to derive a new method to estimate internal multiples

Abstract

We have evaluated an explicit relationship between the representations of internal multiples by source-receiver interferometry and an inverse-scattering series. This provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect. A downside of the existing representations is that their computational cost is extremely high, which can be a precluding factor especially in 3D applications. Using our insight from source-receiver interferometry, we have developed an alternative, computationally more efficient way to predict internal multiples. The new formula is based on crosscorrelation and convolution: two operations that are computationally cheap and routinely used in interferometric methods. We have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set.

Adaptive overburden elimination with the multidimensional Marchenko equation

“…In all cases, the mechanism for the internal multiple retrieval is closely related to that from other IME schemes, such as the method of Jakubowicz (1998), the ISS (Weglein et al, 1997), the work of Ten Kroode (2002), and source-receiver interferometry (Löer et al, 2016). In each of these methodologies, the data are crosscorrelated twice to retrieve internal multiple reflections.…”

“…As shown by Ten Kroode (2002), the ISS methodology can be rewritten by truncating integrals in time, under the assumption of traveltime monotonicity. This result has been modified further by Löer et al (2016), leading to the following first-order prediction mechanism for internal multiples: …”

“…These truncations are often designed, such that the so-called "lower-higher-lower" (LHL) condition is obeyed, meaning that the second reflection point should always be located higher than the first and third reflection points for an event to be a (first-order) internal multiple. In the term ͡ M f1 that is described in equation 40, the required truncations are imposed in a way that is closely related to the multiple elimination scheme of Ten Kroode (2002) and Löer et al (2016), which can be derived from source- . The dashed lines indicate the depth (in practice unknown) and traveltime t 2 (picked) of horizon Λ f .…”

“…The difference between both equations is a consequence of the different objectives of the IME schemes. Ten Kroode (2002) and Löer et al (2016) aim to remove all reflections that originate from a subsection of the data that is truncated at t − ϵ, where t is the output time. Because the truncation is applied just before the output time, the primaries are preserved.…”

“…Unlike in IME, all internal multiples are estimated at once, rather than through layer stripping. The ISS methodology can be interpreted as a migration-demigration process (Verschuur, 2013;Löer et al, 2016). Because any error in the macro model that is encountered during migration is compensated during demigration, the methodology appears to be relatively insensitive for errors in the macro model.…”