LASNE et al.: PHASE SIGNATURE FOR DETECTING WET SUBSURFACE STRUCTURES

1689

Fig. 11.  Two-dimensional cross section of the two-layer geoelectrical model

of the Pyla dune.

curves reproduce fairly well the phase difference observed on

the field in Fig. 4.

The phase difference appears to be very sensitive to the rms

height of the sand­paleosoil interface as shown in Fig. 10(d). On

the contrary, we can see in Fig. 10(e) that the average

weakly increases with respect to the water content of the pale-

osoil layer. We can also see in Fig. 10(e) that the maximum of

occurs for different sand thicknesses when the pale-

osoil permittivity changes: it corresponds to a sand layer thick-

, 2.6 m for

ness of 2.08 m for

, and 3.2 m for

. As a comparison, the

maximum value of 23 for the copolarized phase difference ob-

served for the Pyla dune in Fig. 4 occurs for a sand thickness of

2.9 m. Nevertheless, our two-layer IEM model finds a maximum

around 6 , meaning that a phase difference

value for

Fig. 12.  Variations of the backscattered signals as a function of time for a

was not taken into account. We show in the following, using

given receiver at 1.6 GHz. Arrows indicate the reflections corresponding to each

numerical FDTD simulations, that a phase difference compo-

interface.

nent at the sand­paleosoil interface should be added, leading to

in (19) different for H and V polarizations.

a value

and 3) in addition to the classical Liao absorbing layers: they

provide absorption of the incident and scattered waves arriving

on the vertical sides of our geoelectrical model.

VI. FDTD NUMERICAL SIMULATIONS

The moisture interface between the two layers corresponds to

the roughness profile of the wet paleosoil and characterizes the

A. Geoelectrical Model of the Dune

geometrical distribution of moisture in the dune. In most cases,

Besides semiempirical and analytical modeling, we tried to

roughness in arid regions is related to the surface morphology

reproduce the observed phenomenon using a more accurate ge-

and geology. Lots of studies, based on theoretical, empirical,

ometrical and electrical description of the Pyla dune as input to

and numerical models, relate to surface roughness for geological

an "exact" FDTD electromagnetic code.

applications and its implication on the analysis of SAR images

Capabilities of L-band SAR systems to penetrate bare soils

[17], [29]­[33]. It has been shown that a soil moisture profile

are mainly related to the petrology and water content of the soil

could be regarded as roughness and then described by means of

material, which constrain the electrical behavior of each geo-

classical statistical parameters related to the spatial distribution

logical layer [28]. We need to establish, then, a geoelectrical

and magnitude of "height" variations. Even if the current trend

model of the dune in order to numerically simulate the propa-

is a fractal characterization of surface roughness [29], [34], we

gation of microwaves. Based on GPR data and laboratory mea-

consider here a conventional model for roughness characteriza-

surements of Pyla dune samples [24], we established a two-layer

tion, using a Gaussian autocovariance function [27] that can be

three-dimensional model of the Pyla dune subsurface as shown

characterized by its rms height  and correlation length .

in Fig. 11. In this model, each of the two layers has been con-

For our geoelectrical model, we assumed a smooth air­dune

sidered as electrically homogeneous. It should be noticed that

interface and a sand­paleosoil roughness characterized by a

dielectric constants of the two main layers (dry sand and pale-

Gaussian autocovariance function

of the following form:

osoil) have been measured in laboratory at a frequency of 1.6

GHz [24]. In order to reduce signal reflections at the simulation

(20)

space boundaries, we considered three absorbing layers (1, 2,