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 target-enclosed 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.

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