Description of surface roughness as an approximate self-affine random structure

Yordanov, O.I.; Ivanova, K.

doi:10.1016/0039-6028(95)00157-3

Cited by 22 publications

(6 citation statements)

References 19 publications

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“…Since after the roughness measurement of the study sites, the geometric parameters are considered to be calculated on some arbitrary linear profiles, the ACF for a linear profile of the samples can be realised in the form of [32]:…”

Section: Power-law Inputs For the Iemmentioning

confidence: 99%

“…where k is the wavenumber and α has a limited amount; D < α < D + 2, D is the topological dimension, and for the linear profile, it is considered one (D = 1) [29,33], representing the slope of the linear best-fit of the power spectral density (PSD) on a logarithmic scale [29,32]. It is noted that this linear best-fit must be applied to the trendless profile.…”

Section: Power-law Inputs For the Iemmentioning

confidence: 99%

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Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

et al. 2017

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Abstract:Microwave remote sensing can measure surface geometry. Via the processing of the Synthetic Aperture Radar (SAR) data, the earth surface geometric parameters can be provided for geoscientific studies, especially in geological mapping. For this purpose, it is necessary to model the surface roughness against microwave signal backscattering. Of the available models, the Integral Equation Model (IEM) for co-polarized data has been the most frequently used model. Therefore, by the processing of the SAR data using this model, the surface geometry can be studied. In the IEM, the surface roughness geometry is calculable via the height statistical parameter, the rms-height. However, this parameter is not capable enough to represent surface morphology, since it only measures the surface roughness in the vertical direction, while the roughness dispersion on the surface is not included. In this paper, using the random fractal geometry capability, via the implementation of the power-law roughness spectrum, the precision and correctness of the surface roughness estimation has been improved by up to 10%. Therefore, the random fractal geometry is implemented through the calculation of the input geometric parameters of the IEM using the power-law surface spectrum and the spectral slope. In this paper, the in situ roughness measurement data, as well as SAR images at frequencies of L, C, and X, have been used to implement and evaluate the proposed method. Surface roughness, according to the operational frequencies, exhibits a fractal or a diffractal behavior.

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Section: Power-law Inputs For the Iemmentioning

confidence: 99%

Section: Power-law Inputs For the Iemmentioning

confidence: 99%

Better Estimated IEM Input Parameters Using Random Fractal Geometry Applied on Multi-Frequency SAR Data

et al. 2017

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show abstract

“…In a number of studies investigating the roughness spectra of natural surfaces, it has been found that the measured spectra may be modeled reasonably well using a power law spectrum of the form (4) where is the offset, and is the spectral slope, which for 1-D profiles is bounded by [35], [36]. Surfaces with a (one-sided) power-law roughness spectrum, valid over the interval , are ideal random fractals.…”

Section: B Power-law Surfacesmentioning

confidence: 99%

“…A mathematical model for this is a power law spectrum with sharp cutoffs and . In this case, an ACF exists (e.g., [36], [37]). The shape of the ACF varies with the cutoff frequencies.…”

Section: B Power-law Surfacesmentioning

confidence: 99%