Apparatus and method for imaging objects with wavefields

#Material on one (1) compact disc accompanying this patent and labeled COPY 1, a copy of which is also included and is labeled as COPY 2, is incorporated herein by reference. The compact disc has a software appendix thereon in the form of the following three (3) files: Appendix A.txt, Size: 16 Kbytes, Created: Aug. 13, 2001; Appendix B.txt, Size: 19 Kbytes, Created: Aug. 13, 2001; and Appendix C.txt, Size: 1 Kbytes, Created: Aug. 13, 2001.

#A portion of the disclosure of this patent document contains material to which a claim of copyright protection is made. The copyright owner(s) has/have no objection to the facsimile reproduction by any one of the patent document or the patent disclosure as it appears in the Patent and Trademark Office patent file or records, but reserves all other rights in the copyrighted word.

#It has long been known that elastic, electromagnetic or acoustic waves in homogeneous and layered environments in the frequency range of a fraction of a cycle per second up to hundreds of millions of cycles per second and higher can be propagated through many solids and liquids. Elastic waves are waves that propagate through solids, and have components of particle motion both parallel (longitudinal, or pressure, wave) and perpendicular (shear wave) to the direction of propagation of the wave energy itself. In contrast to this, acoustic waves are those waves that generate particle motion that is exclusively parallel to the propagation of wave energy. Electromagnetic waves have components of variation of field strength solely in the direction perpendicular to the direction of propagation. All of these types of waves may be used to image the acoustic longitudinal wavespeed and absorption, the electromagnetic wavespeed and absorption, the shear wavespeed, and the density of the material through which the wave energy has travelled.

#In order that the manner in which the above-recited and other advantages and objects of the invention are obtained, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:

#FIG. 1 is a side-elevational view shown partially in cross section which schematically illustrates an acoustic scanner which may be used with the apparatus and method of the present invention;

#FIG. 1A is a two dimensional view of a cross-borehole geometry imaging method, according to the present invention, using inverse scattering;

#Definition 1. An inverse scattering imaging method is any imaging method which totally or partially uses wave equation modeling and which utilizes a nonlinear operator relating the inversion data to the image components.

#Definition 2. The inversion data is defined by that transformation of the wavefield data which is the range of the nonlinear operator. The domain of the nonlinear operator is the image components.

#Definition 3. A parabolic propagation step is an arithmetic operation which computes the wavefield on a set of surfaces given the wavefield on another, disjoint set of surfaces using a parabolic differential (or difference?) equation in the derivation of the arithmetic operation.