Seismic reflection data can be redatumed to a specified boundary in the subsurface by solving an inverse (or multidimensional deconvolution) problem. The redatumed data can be interpreted as an extended image of the subsurface at the redatuming boundary, depending on the subsurface offset and time. We retrieve targetenclosed extended images by using two redatuming boundaries, which are selected above and below a specified target volume. As input, we require the upgoing and downgoing wavefields at both redatuming boundaries due to impulsive sources at the earth's surface. These wavefields can be obtained from actual measurements in the subsurface, they can be numerically modeled, or they can be retrieved by solving a multidimensional Marchenko equation. As output, we retrieved virtual reflection and transmission responses as if sources and receivers were located at the two target-enclosing boundaries. These data contain all orders of reflections inside the target volume but exclude all interactions with the part of the medium outside this volume. The retrieved reflection responses can be used to image the target volume from above or from below. We found that the images from above and below are similar (given that the Marchenko equation is used for wavefield retrieval). If a model with sharp boundaries in the target volume is available, the redatumed data can also be used for two-sided imaging, where the retrieved reflection and transmission responses are exploited. Because multiple reflections are used by this strategy, seismic resolution can be improved significantly. Because target-enclosed extended images are independent on the part of the medium outside the target volume, our methodology is also beneficial to reduce the computational burden of localized inversion, which can now be applied inside the target volume only, without suffering from interactions with other parts of the medium.

For a robust way of estimating time shifts near horizontal boreholes, we have developed a method for separating the reflection responses above and below a horizontal borehole. Together with the surface reflection data, the method uses the direct arrivals from borehole data in the Marchenko method. The first step is to retrieve the focusing functions and the updown wavefields at the borehole level using an iterative Marchenko scheme. The second step is to solve two linear equations using a least-squares minimizing method for the two desired reflection responses. Then, the time shifts that are directly linked to the changes on either side of the borehole are calculated using a standard crosscorrelation technique. The method is applied with good results to synthetic 2D pressure data from the North Sea. One example uses purely artificial velocity changes (negative above the borehole and positive below), and the other example uses more realistic changes based on well logs. In the 2D case with an adequate survey coverage at the surface, the method is completely data driven. In the 3D case inwhich there is a limited number of horizontal wells, a kinematic correct velocity model is needed, but only for the volume between the surface and the borehole. Possible error factors related to the Marchenko scheme, such as an inaccurate source wavelet, imperfect surface multiples removal, and medium with loss are not included in this study.

In the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross-correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter-source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter-source seismic interferometry using nontransient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill-bit signals) are not available, it is required that the drill-bit signals are the same and that the phases of the virtual reflections at drillbit positions can be retrieved by deconvolution interferometry or by cross-coherence interferometry. Further, for this case, classic interferometry by cross-correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic-whiledrilling processing techniques such as pilot cross-correlation and pilot deconvolution to remove the drill-bit signatures in the data and then applying cross-correlation interferometry. Therefore, provided that pilot signals are reliable, drill-bit data can be redatumed from surface to borehole depths using this inter-source interferometry approach without any velocity information of the medium, and we show that a well-positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.