Lele Zhang

Electromagnetic Marchenko equations for a dissipative heterogeneous medium

We present a three-dimensional scheme that can be used to compute a vertical radar profile from reflection and transmission data measured at two parallel surfaces of a dissipative medium. From this double-sided data set the reflection response of a fictitious medium with negative dissipation can be computed. The measured reflection response and the computed reflection response in the medium with negative dissipative can be used to construct two focusing wavefields. One focuses at the chosen location in the subsurface of the actual dissipative medium and the other one focuses inside the medium with negative dissipation at the same location. This location is then the virtual receiver location for the vertical radar profile Greens function. Because the up- and downgoing parts of the Greens function are retrieved separately, these are very useful for imaging and inversion. We show with a numerical example that the method works well in a one-dimensional configuration.

Single- and Double-Sided Marchenko Imaging Conditions in Acoustic Media

In acoustic reflector imaging, we deploy sources and receivers outside a volume to collect a multisource, multioffset reflection response in order to retrieve the internal reflectivity of that volume. It has been shown that Greens functions inside the volume can be retrieved by single-sided wavefield focusing of the acquired reflection data, using so-called focusing functions, which can be computed by solving a multidimensional Marchenko equation. Besides the reflection data, this methodology requires a background model of the propagation velocity. We present several imaging conditions to retrieve the internal reflectivity of an acoustic medium with correct amplitudes and without artifacts, using the Greens functions and focusing functions that are derived from the Marchenko equation. We distinguish three types of imaging: 1) imaging by deconvolution, 2) imaging by double focusing, and 3) imaging by cross correlation. In all cases, reflectors can be approached either from above or from below. Imaging by deconvolution or double focusing requires single-sided illumination (meaning that sources and receivers are deployed at a single boundary above the volume only), whereas imaging by cross correlation requires double-sided illumination (meaning that sources and receivers are placed at two boundaries enclosing the volume). In order to achieve double-sided illumination, the required reflection response at the lower boundary can either be physically recorded or it can be retrieved from the reflection response at the upper boundary. When imaging by deconvolution or double focusing, the internal reflectivity is retrieved solely from primary reflections. When imaging by cross correlation, multiple reflections are focused at the image points, such that they contribute physically to the retrieved reflectivity values. This special feature can be beneficial for imaging weakly illuminated sections of strongly heterogeneous media.

Artefact-Free Imaging by a Revised Marchenko Scheme

Summary A revised Marchenko scheme that avoids the need to compute the Green’s function is presented for artefact-free image of the subsurface with single-sided reflection response as input. The initial downgoing Green’s function which can be modelled from a macro model is needed for solving the revised Marchenko equations instead of its inverse. The retrieved upgoing focusing function can be correlated with the modelled initial downgoing Green’s function to image the medium without artefacts. The numerical example shows the effectiveness of the revised scheme in a 2D layered case.

Electromagnetic Marchenko scheme based internal multiple elimination for lossless media

Iterative substitution of the Marchenko equation has been introduced recently to integrate internal multiple reflection in the seismic and electromagnetic imaging process. In the so-called Marchenko imaging, solving the Marchenko equation at each imaging point is required to meet this objective. It makes the scheme seriously expensive. Inspired by this limitation, we present an Electromagnetic Marchenko equation based one dimensional scheme to eliminate the internal multiples of the single-sided lossless surface ground penetrating radar data layer by layer, such that the conventional imaging schemes can be applied to get the internal multiple related artifacts free imaging result without the need of solving Marchenko equation at each imaging point. We show with an example that the method works well for a sample in a synthetic waveguide that could be used for measurements in laboratory and field.

Electromagnetic Marchenko imaging in 1D

We present a one-dimensional scheme to compute an image of a dissipative medium from two single-sided reflection responses without using any model information. One reflection response is measured at or above the top reflector of a dissipative medium and the other is computed as if measured at or above a medium with negative dissipation. The reflection response of a medium with negative dissipation can be computed from measured double-sided reflection and transmission data from a dissipative medium. These two reflection responses together can be used to construct two focusing wavefields. One focuses at the chosen location in the subsurface of the dissipative medium and the other inside the medium with negative dissipation. From the focusing functions and reflection responses the Greens functions for a virtual receiver can be computed. The Greens function are used to construct the image. We show with a numerical example that the method works well for a synthesised layered sample in a waveguide that could be used for measurements in a laboratory.