Data-driven deep local imaging using both surface and borehole seismic data Yi Liu ∗ , Norwegian University of Science and Technology; Joost van der Neut, Delft University of Technology; Børge Arntsen, Norwegian University of Science and Technology; Kees Wapenaar, Delft University of Technology SUMMARY Seismic interferometry(SI) is a proven data-driven redatuming method to create virtual sources for better illumination of the target area. It requires a physical receiver at the position of the created virtual source. With the development of the itera- tive Marchenko method, one can now use surface data alone to create a virtual source in the subsurface, but an estimate of the direct wavefield from those virtual source positions to the surface is needed, which means an adequately accurate smooth velocity model is nevertherless necessary. We show that when borehole data from a horizontal well is available, one can com- bine the principles of SI and the Marchenko method to formu- late several inversion-based redatuming schemes, such that no prior smooth velocity model is needed at all and that the ex- act forms of retrieving the reflection responses from above and from below can also be obtained. Furthermore, the internal multiples are accounted for using these exact forms. No sur- rounding acquisition geometry is required or multi-component well data is needed. We demonstrate the proposed schemes us- ing a synthetic gas cloud example. We then show the retrieved responses and the migrated images using only a local velocity model. The results show that given the same velocity uncer- tainty, these responses that are redatumed by data produce a better positioned image near the well than a surface seismic image. The proposed schemes can be beneficial for deep bore- holes and complex areas with big velocity uncertainties. INTRODUCTION Different types of borehole seismic data (Schuster et al., 2004; Bakulin and Calvert, 2006; Vasconcelos and Snieder, 2008b; Poletto et al., 2010) have been used to create virtual source data by applying seismic interferometry (SI) (Wapenaar and Fokkema, 2006; Curtis et al., 2006). Compared to other re- datuming methods, SI does not require any velocity informa- tion and the physical receivers are turned into virtual source (or vice versa). Known approaches to SI are crosscorrela- tion (CC) (Snieder, 2004), deconvolution (DC) (Vasconcelos and Snieder, 2008a), multidimensional deconvolution (MDD) (van der Neut et al., 2011) and crosscoherence (CH) (Nakata et al., 2011). Comprehensive and systematic comparisons among different approaches can be found in Wapenaar et al. (2011), Snieder et al. (2009), and Galetti and Curtis (2012). Taking a step beyond SI, the iterative Marchenko method (Brog- gini et al., 2012; Wapenaar et al., 2013) has been developed to create virtual sources in the subsurface from surface seismic data alone, which means the presence of physical receivers at depth is no longer needed. Various applications that use the Marchenko method for imaging are suggested by Wapenaar et al. (2014). However, the scheme does require an estimate of the direct wavefield from the virtual source positions to the surface, and the requirement on the accuracy of such estimate is yet to be studied. We show that when the data from a horizontal borehole is available, the direct wavefield can be obtained directly from the borehole data, thus making the whole Marchenko imag- ing scheme completely independent of any traveltime estima- tion errors. Further, by combining the principles of SI and the properties of the focusing functions in the Marchenko method, the exact formulations of retrieving the reflection responses from above and from below the well can be obtained. The internal multiples can also be properly accounted for. Com- pared to the scheme for imaging from below by Poliannikov (2011), whose approach is based on source-receiver interfer- ometry (SRI) (Curtis and Halliday, 2010), our scheme is an inversion-based scheme under one-sided illumination and can account for internal multiples. These schemes also do not re- quire multicomponent borehole data, both for imaging from above (Mehta et al., 2007) and from below (van der Neut and Wapenaar, 2015), but the surface related multiples are assumed to have been removed from both surface and borehole datasets. We start by introducing some of the properties of the focusing functions (Wapenaar et al., 2014). Then we use them to derive the equations for retrieving the reflection responses from above and from below, and suggest some approximations as alterna- tives for situations in which the focusing functions cannot be obtained. In total, we illustrate four schemes for imaging from above and two for imaging from below. We show the results using a synthetic gas cloud model. THEORY The focusing functions The two focusing functions f ± 1 (x|x ′ i , t ) and f ± 2 (x|x ′′ 0 , t ) have been studied in detail in Wapenaar et al. (2014). Here we will just show briefly some results. f ± 1 (x ′′ 0 |x ′ i , t ) describes a wave- field that focuses at position x ′ i at depth level i and is recorded at position x ′′ 0 at surface level 0, while f ± 2 (x ′ i |x ′′ 0 , t ) describes a wavefield that focuses at position x ′′ 0 and is recorded at position x ′ i . The superscripts + and − denote downgoing and upgoing, respectively. The two focusing functions are mutually related via  f + 1 (x ′′ 0 |x ′ i )=  f − 2 (x ′ i |x ′′ 0 ); (1) −   f − 1 (x ′′ 0 |x ′ i )  ∗ =  f + 2 (x ′ i |x ′′ 0 ), (2) where the focusing functions are now represented in the fre- quency domain, indicated by the  above (the angular fre- quency variable ω is omitted), and the superscript ∗ denotes the complex conjugate. Due of the causality arguments for the one-way Green’s function G − (x ′ i |x ′′ 0 , t ), G + (x ′ i |x ′′ 0 , t ) and the focusing function f + 2 (x ′ i |x ′′ 0 , t ) (Wapenaar et al., 2014), the fol- lowing relations apply, for t < t d (x ′ i , x ′′ 0 ), where t d is the direct