Modeling non-Rayleigh speckle distribution in SAR images

Fig. 3. Frequency response of a simple logging device. the curves present a constant behavior at low frequencies and at relatively high frequency values they increase with frequency. It can be verified that the points at which the curves start to deviate from the constant line are related to those frequency values at which the skin depth in the formation becomes comparable to the length of the tool. It can be concluded from these results that in the typical range of operational frequencies, which is between 10 and 100 Hz for such type of devices, the measurement is substantially affected only for the case of the saltwater sand formation. The time-harmonic field analysis procedure presented here constitutes a new methodology that presents some important advantages over the conventional direct-current analysis techniques. It allows one to study the electric logging systems at their real frequencies of operation without the necessity of electrostatic assumptions. As may be concluded from the simulation results, the validity of the electrostatic assumption cannot be always presupposed. In particular, special care must be exercised when dealing with conductive formations. The presented time harmonic field analysis procedure also provides a means for studying the suitability of frequency-based radial resistivity sounding. REFERENCES [1] J. Hallenburg, Geophysical Logging for Mineral and Engineering Applications. New York: Wiley, 1984. [2] J. Lovell and W. Chew, " Response of a point source in a multicylin-drically layered medium, " IEEE Trans. Diffraction of ax-isymmetric waves in a borehole by bed boundary discontinuities, " Geo-phys. An efficient solution for the response of electrical well logging tools in a complex environment, " IEEE Trans. [7] Q.-H. Liu, " Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary number of horizontal dis-continuities, " On calculating electromagnetic fields for induction logging problems by deformation of the integration path into the complex plane of the integration variable, " Geol. Abstract—In non-Rayleigh distributed radar images, the number of scatterers can be viewed as a Poisson distributed random variable, with the mean itself random. When this mean is Gamma distributed, then the image classically satisfies the distribution. We add three new possible distributions for this mean: inverse Gamma, Beta of the first kind, and Beta of the second kind. We show that new intensity distributions so obtained can be estimated, with the interest of the extension validated on a real image.