  Tree roots detection is a popular application of the Ground-penetrating radar
(GPR). Normally, the ground surface above the tree roots is assumed to be flat,
and standard processing methods based on hyperbolic fitting are applied to the
hyperbolae reflection patterns of tree roots for detection purposes. When the
surface of the land is undulating (not flat), these typical hyperbolic fitting
methods becomes inaccurate. This is because, the reflection patterns change
with the uneven ground surfaces. When the soil surface is not flat, it is
inaccurate to use the peak point of an asymmetric reflection pattern to
identify the depth and horizontal position of the underground target. The
reflection patterns of the complex shapes due to extreme surface variations
results in analysis difficulties. Furthermore, when multiple objects are buried
under an undulating ground, it is hard to judge their relative positions based
on a B-scan that assumes a flat ground. In this paper, a roots fitting method
based on electromagnetic waves (EM) travel time analysis is proposed to take
into consideration the realistic undulating ground surface. A wheel-based (WB)
GPR and an antenna-height-fixed (AHF) GPR System are presented, and their
corresponding fitting models are proposed. The effectiveness of the proposed
method is demonstrated and validated through numerical examples and field
experiments.
