First order born scattering away from a fluid-filled borehole

• Published in: Journal of applied geophysics Vol. 192; p. 104310
• Main Authors: Geerits, Tim W., Linke, Maik, Hellwig, Olaf, Buske, Stefan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2021
• Subjects: Cylindrical waves; Elastic scattering; Fluid-filled borehole; Logging while drilling; Multipole source/receiver; Fluid-filled borehole; Multipole source/receiver; Logging while drilling; Elastic scattering; Cylindrical waves
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/j.jappgeo.2021.104310

In this paper we solve the forward scattering problem in the first order Born approximation as it applies to the multipole borehole acoustic measurement configuration. This configuration consists of a multipole source and an array of multipole receivers, both deployed on a mandrel (The tool), and where the latter is axially offset from the former by a certain distance. The tool is deployed in a fluid-filled borehole, penetrating the earth formations. Assuming an arbitrary elastodynamic scatterer away from the fluid-filled borehole, we derive explicit expressions for the far-field scattered wavefield in the borehole fluid. In principle, these expressions could be used as a fast forward operator in the development of a full waveform inversion technique. Subsequently, to further our understanding, we derive analytical expressions for the borehole fluid scattered pressure at ‘small’ source-receiver offsets, and where the scatterer is represented by a Heaviside step change in elastodynamic formation properties, having an arbitrary orientation relative to the borehole axis. Our expressions apply to tools having a multipole source and receiver of order n. Such a source/receiver consists of 2n sources/receivers, located on the circumference of the tool and azimuthally separated from one another by π/n radians. All sources may be fired with equal polarity or adjacent sources may be fired with alternate polarity. In the latter case we compare our analytical solution with 3-D finite difference simulations. We do this for the practically relevant dipole (n = 1) and quadrupole (n = 2) excitation, for the (specular) PP, SVSV and SHSH borehole acoustic scattered pressure contributions. We obtain excellent results as long as the elastodynamic contrast between scatterer and embedding is small (<30%). [Display omitted] •First order Born approximation in the presence of a fluid-filled borehole•Zero-offset analytical expressions for the scattered borehole acoustic pressure•Full multipole description•Comparison between zero-offset first order Born and 3-D finite difference results•Excellent agreement is obtained for a dipole and quadrupole excitation.