The fractal method application for space maps analysis

<p>To estimate surface soil moisture from Sentinel-1 backscattering, accurate estimation of soil roughness is a key. However, it is usually error source, due to complexity of surface heterogeneity. This study investigates the fractal methods that takes multi-scale roughness into account. Fractal models are widely recognized as one of the best approaches to depict soil roughness of natural system. Unlike the conventional approach of fractal method that uses local roughness measured in the field or Digital Elevation Model information seldom considering a stochastic characteristic of soil surface, fractal surface is generated with the roughness spatially inverted from Synthetic Aperture Radar (SAR) backscatter. Assuming that the land surface in study site is on small to intermediate scales, pseudo-roughness is spatially estimated by modelling SAR roughness with the one-sided power-law spectrum. In addition, it is assumed that both multiple and single scales of roughness affect SAR backscatter in an integrative way. For validation, soil moisture is retrieved with this time-varying roughness. Based upon local validation and cost minimization, as compared with an inversion approach of surface scattering models (Integral Equation Model), a fractal method seems geometrically more sensible than an inversion, based upon a spatial distribution and a priori knowledge in the field. Although inverted roughness is used as an input, fractal model does not reproduce the same roughness. Results will show local point validation, fractal surface, and estimation of coefficients, and various spatial distribution data. This study will be useful for future satellite missions such as NASA-ISRO SAR mission.</p>

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Prediction of oil-water relative permeability with a fractal method in ultra-high water cut stage

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2018.11.011 ◽

2019 ◽

Vol 130 ◽

pp. 1045-1052 ◽

Cited By ~ 3

Author(s):

Cuo Guan ◽

Wenrui Hu ◽

Yiqiang Li ◽

Ruicheng Ma ◽

Zilin Ma

Keyword(s):

Relative Permeability ◽

High Water ◽

Fractal Method ◽

Oil Water ◽

High Water Cut Stage ◽

High Water Cut ◽

Water Cut

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The Offshore Wave Simulation Based on the Improved P-M Spectrum and Multiple Fractal Interpolation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1030-1032.1832 ◽

2014 ◽

Vol 1030-1032 ◽

pp. 1832-1836

Author(s):

Ying Li ◽

Rui Zhou ◽

Hao Kuan Li ◽

Ming Wang

Keyword(s):

Shallow Water ◽

Interpolation Method ◽

Fractal Interpolation ◽

Fractal Method ◽

Growth State ◽

Water Factor ◽

Proposed Model ◽

Simulation Based ◽

Offshore Wave ◽

The Waves

The Pierson - Moskowitz model is only applicable to full growth state of the waves, and it has low authenticity and hopping phenomenon under the condition of offshore shallow water. This paper proposes a simulation model of offshore wave based on the improved P-M spectrum and multiple fractal interpolation methods. In order to calculate the sea wave with shallow water, a spectrum peak regulation factor and a depth of the water factor are introduced to the P - M spectrum model. Based on this model, the wavelength and wave speed are used as the initial values of wave height. Then, the amplitude and the number of iterations in diamond square fractal method are controlled to obtain the fractal static sea. In order to reduce the influence of the hopping phenomenon to the simulation authenticity, meanwhile, a multiple dynamic non-uniform interpolation method is proposed. The experimental results show that the proposed model can simulate offshore wave with better effect and in real time.

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Grid preparation for magnetic and gravity data using fractal fields

Nonlinear Processes in Geophysics ◽

10.5194/npg-19-291-2012 ◽

2012 ◽

Vol 19 (2) ◽

pp. 291-296 ◽

Cited By ~ 4

Author(s):

M. Pilkington ◽

P. Keating

Keyword(s):

Potential Field ◽

Fourier Transforms ◽

Gravity Data ◽

Fractal Model ◽

Data Sets ◽

Spectral Character ◽

Aeromagnetic Survey ◽

Fractal Method ◽

Gravity Measurements ◽

Interpretive Method

Abstract. Most interpretive methods for potential field (magnetic and gravity) measurements require data in a gridded format. Many are also based on using fast Fourier transforms to improve their computational efficiency. As such, grids need to be full (no undefined values), rectangular and periodic. Since potential field surveys do not usually provide data sets in this form, grids must first be prepared to satisfy these three requirements before any interpretive method can be used. Here, we use a method for grid preparation based on a fractal model for predicting field values where necessary. Using fractal field values ensures that the statistical and spectral character of the measured data is preserved, and that unwanted discontinuities at survey boundaries are minimized. The fractal method compares well with standard extrapolation methods using gridding and maximum entropy filtering. The procedure is demonstrated on a portion of a recently flown aeromagnetic survey over a volcanic terrane in southern British Columbia, Canada.

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Fractal Application in Micro Rock Mechanics of Low-Permeability Oil Reservoirs and Its Relationship with Enlarging Producing Reserves by Gemini Surfactant Flooding

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.29-32.170 ◽

2010 ◽

Vol 29-32 ◽

pp. 170-176 ◽

Cited By ~ 1

Author(s):

Heng Wei ◽

Lei Wei ◽

Jian Hui Yin ◽

Fu Ling Yin ◽

Jun Han Liu ◽

...

Keyword(s):

Rock Mechanics ◽

Gemini Surfactant ◽

Fractal Dimensions ◽

Oil Reservoirs ◽

Low Permeability ◽

Surfactant Flooding ◽

High Permeability ◽

Fractal Method ◽

Pore Structures ◽

Conventional Methods

Low permeability oil reservoirs were usually considered low quality reserves. However, low permeability oil reservoirs account for more and more percent of the proven reserves year by year in China. Conventional methods for analyzing medium-hign permeability cores are not suitable to low-permeability cores. Based on fractal method and the mercury injection curve data, the fractal dimensions of the pore structures of low permeability oil reservoirs are different from those of medium-high permeability oil reservoirs. The fractal dimensions of the pore structures of low permeability oil reservoirs are less than 2. Low permeability oil reservoirs which were not able to be developed are able to be developed by gemini surfactant flooding. This helps more and more low quality reserves be turned into producing reserves.

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