Round Trip Times Versus the Range of the Radargram Maxima of an Air-Coupled Bistatic GPR: Modeling and Fitting by a Hyperbola

For a circular cylinder in free space and for a monostatic configuration (transmitter and receiver are identical), from a geometrical way, it is well-known that the maxima of the ground-penetrating radar (GPR) radargram (or B-scan) cross section follows a hyperbola profile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t=w(x_{2})$ </tex-math></inline-formula> (time t versus receiver range <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x_{2}$ </tex-math></inline-formula>). For a buried object and for a coupled-air monostatic configuration, this statement is no longer valid. The purpose of this letter is to generalize the derivation of w to a bistatic (transmitter and receiver are distinct) configuration by investigating two approaches based on a geometrical way: The conventional midpoint approximation technique and a new more physical way based on the specular direction. In addition, a study is led on the fitting of w by a hyperbola and a polynomial function of the fourth degree. The resulting closed-form expressions are compared with the results obtained from the full-wave method of moments (MoM) to verify their accuracy.