Kirchhoff Migration Images Research Articles

Imaging in lossy media

We study the effects of absorption in the medium on synthetic aperture imaging. We model absorption using the loss tangent, which is the imaginary part of the relative dielectric permittivity, and study two cases: (i) the loss tangent is known and (ii) the loss tangent is unknown. When the loss tangent is known and used in Kirchhoff migration (KM), we find that images of targets are range-shifted by approximately a central wavelength so that their predicted locations are closer to the synthetic aperture than they actually are. In contrast, we find that when the medium is unknown, the KM image does not exhibit this range-shift. Hence, we determine that it is better to not make use of any knowledge of the absorption when imaging. Using a recently developed transformation of KM images, which we call reciprocal-KM (rKM), we achieve tunably high-resolution images of targets through adjusting the value of a user-defined parameter ε. When rKM is applied to an imaging region containing two targets, we find that their predicted locations shift, especially in range, but within a fraction of central wavelength of their true locations.

A real-time microwave imaging of unknown anomaly with and without diagonal elements of scattering matrix

In this contribution, a real-time non-iterative microwave imaging of unknown anomaly from scattering matrix whose elements are scattering parameters measured at the dipole antennas considered. For this, we apply Kirchhoff migration imaging technique when the diagonal elements of scattering matrix are available or unavailable, and confirm that opposite to the traditional researches, one can obtain good result without diagonal elements. Simulation results with synthetic data are presented to support our confirmation.

A Kirchhoff migration imaging method based on grounded-source TEM virtual wave-fields and its applications

This research study was based on a Kirchhoff migration imaging method, and the aim of the study was to realize grounded-source transient electromagnetic virtual wave-field migration. Diffusion equations mainly characterize the induction characteristics of low-frequency electromagnetic waves which are not suitable for wave-fields. Wave equations mainly characterize wave reflections, refractions, and other propagation features, which are suitable for wave-field imaging processes. A unique mathematical transformation relationship exists between the diffusion fields of transient electromagnetic fields and seismic wave-fields. After the transformations from diffusion fields to virtual wave-fields are achieved, seismic interpretation methods can be used for the transient electromagnetic data interpretations. First, in order to realize Kirchhoff migration imaging based on transient electromagnetic wave-fields, precondition regularization methods are used for the wave-field inverse transformations. Then, after obtaining the wave-field data, dynamic correction methods are adopted to convert the grounded-source transient electromagnetic virtual wave-fields to quasi-seismic zero offset data. At that point, a Kirchhoff integral can be applied to realize the grounded-source transient electromagnetic quasi-seismic migration imaging. A theoretical model was used to test the method which was proposed in this study. The results showed that the Kirchhoff migration imaging was able to determine the geometric formations of underground dielectric interfaces, which fully demonstrated the applicability of the proposed method. Finally, migration imaging processing was performed on the data obtained from a mining area, and the imaging results were found to be consistent with the known geological data. Therefore, the feasibility of using a wave-field transform method and Kirchhoff migration imaging technology for grounded-source transient electromagnetic data interpretations was successfully confirmed.

Optimal waveform design for array imaging

We introduce and analyze several algorithms for optimal illumination in array imaging. We consider time reversal and Kirchhoff migration imaging in homogeneous media, in regimes where the signal-to-noise ratio is high (infinite). Extensions to coherent interferometric imaging in clutter are described briefly. We show with numerical simulations that the optimal illumination algorithms image selectively closely spaced point scatterers and extended scatterers with considerably better resolution than without the optimization. We analyze the imaging algorithms in the Fraunhofer diffraction regime for small and extended scatterers. Using the prolate spheroidal wavefunctions we also derive analytic expressions of optimal illuminations for imaging strips.

Crosswell imaging by two-dimensional oriented wave path migration

SUMMARY We apply a new imaging method, called oriented wave path migration, to 2-D prestack crosswell imaging. Compared to conventional crosswell imaging techniques, for example, Kirchhoff migration, which requires separation of the data into upgoing and downgoing waves prior to migration, oriented wave path migration automatically separates the wavefields during the migration process. Results with synthetic data show that oriented wave path migration can effectively locate the steeply dipping fault boundaries and noticeably improve the image resolution compared to the Kirchhoff migration method. Both oriented wave path and Kirchhoff migration images are suitable for geological interpretation. Results with field data show that oriented wave path migration generates quality images similar to the Kirchhoff migration method, all of which roughly correlate with the P-wave sonic logs.