## 1 Introduction
### Comparisons Between the Two Models  
An analysis of the terminology in [PERSON]'s model and [PERSON] and [PERSON]'s model revealed that both are identical. In [PERSON]'s model, the parameters of the weight and range resolution functions are not displayed. Furthermore, the expression \(h_{v}-(z-z_{0})\) is designated as \(\text{s}_{z}\). The particle density \(\rho_{0}\) is assumed to be constant in both equations. The symbols (\(\text{r}_{1}\text{-r}_{2}\)) and (\(\text{R}_{1}\text{-R}_{2}\)) in both equations appear identical, as do the notations \(Imf\), \(Im<f_{f}>\).  
Without the arguments, correlation equation can be given as  
\[<E(R_{1})E^{*}(R_{2})>=\rho_{0}A^{4}<f^{2}>\int\mid W_{r}\mid^{2}\mid W_{n} \mid^{2}e^{ik(\text{r}_{1}-\text{r}_{2})}e^{-\frac{8\pi\rho}{6\cosh}Im<f>s_{z }}dr_{1}^{3} \tag{12}\]  
Comparing both models, the only parameters needed to equate are the terms \(\frac{\mid f_{R}(\hat{0})\mid^{2}\mid f(0^{+})\mid^{2}\mid f_{T}(\hat{i})\mid^ {2}}{4\pi\hat{R}^{2}R_{1}R_{2}}\) and \(A^{4}\) that makes the Equations (2) and (12) equal. The list of the terms used both in the [PERSON] and [PERSON] model is given in Table 1.  
Figure 4: The four paths of the bi-static field. (**a**) Direct incidence–direct scattered field; (**b**) reflected–direct field; (**c**) direct—reflected field; (**d**) reflected–reflected field [21; 22].  
[PERSON]'s model, characterized by a homogeneous randomly oriented volume, serves as a valuable foundation for considering \"interferometry\" (INSAR), \"polarimetry\" (POLSAR) and \"polarimetric interferometry\" (POLINSAR). Each model scenario presented in [13] includes a summary of its parameters and observations. The decrease in specular amplitude caused by roughness is represented by the term \(\Gamma_{\text{rough}}\).  
\[\Gamma_{\text{rough}}\equiv expexp\left[-2k^{2}\sigma_{\text{H}}^{2}coscos \ \theta_{sp1,\ R}\ \right] \tag{13}\]  
where \(\sigma_{\text{H}}\) is the expected Gaussian-distributed ground heights standardly derivable. Although it always multiplies the reflection coefficient, the ground roughness term is added for completeness; therefore, by itself, \(\sigma_{\text{H}}\) will not appear as a parameter. The whole path length is included in the equal phases of the ground-volume and volume-ground components. The length of this path, \(\hat{R}_{1}\rightarrow\hat{R}_{sp1,\hat{R}}\rightarrow\hat{R}(x,y,z) \rightarrow\hat{R}_{1}\), is approximately equivalent to \(2\left|\hat{R}_{1}-\hat{R}(x,y,z_{0})\right|.\) The cross-correlation is obtained by utilizing the equivalence of these path lengths.  
[PERSON]'s discrete model demonstrates that the interferometric cross-correlation yields four fundamental terms, as elucidated in [17]. The various combinations of ground-volume and volume-ground that are interrelated are illustrated by the four ground terms in the cross-correlation. Due to attenuation in the vegetation, components related to ground-volume-ground returns (two specular reflections) are omitted as they are often negligible. Bistatic fields in the [PERSON] model and the corresponding scattering mechanisms used in the [PERSON] model are listed in Table 2. Besides these bistatic fields, [PERSON]'s model addresses an alternative scattering mechanism, specifically the reflected-reflected bistatic field which is not addressed in [PERSON]'s model.