Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

scholarly journals Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of Study: Charak Area, Iran)

2013 ◽  
Vol 2 (7) ◽  
pp. 80-85
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cm^3for the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area.

scholarly journals Comparison and Review of the Advantages of the Fractal Method (Variogram) With Respect to the Nettelton in Determining the Density of the Bouguer Plane in the Southern Hormozgan: Iran

2013 ◽  
Vol 3 (1) ◽  
pp. 1-8
Author(s):  
Samadi Hamid Reza ◽  
Teymoorian Asghar
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Geometry ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Common Method ◽  
Fractal Method ◽  
Optimal Density ◽  
Regional Geology

In this paper we describe a comparison between the methods of Variogram and Nettelton to establish the density of the Bouguer plane. The Nettelton’s method is a common method for determining the density along a profile which is based on the least chosen profile’s topographic resemblance with the chosen density of related to that profile of the region. The variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area in south of Hormozgan province can be determined which is 2/7 g/cm3forthe under-research area. The density of the Bouguer plane in the region by the Nettelton’s method has been calculated 2/3g/cm3. This determined optimal density has been used in correcting and reviewing its result in the case of Isostazy state and some very good results have been achieved which has an amazing coincidence with the regional geology and the drilled exploration wells in the area.

scholarly journals Application of Fractal Geometry to Study the Geological Structure of the Zarin Plain (Plain Razak)

2014 ◽  
Vol 3 (11) ◽  
pp. 135-144
Author(s):  
Khadijeh Faridi Nia ◽  
Asghar Teymoorian ◽  
Mojtaba Babaei
Keyword(s):  
Fractal Dimension ◽  
Density Dependence ◽  
Fractal Geometry ◽  
Bouguer Anomaly ◽  
Geological Structure ◽  
Optimal Density ◽  
The Relationship ◽  
Rigid Shell

One of the most important steps to obtain the specified density Bouguer anomaly corrections for the topography of the page Bouguer is the most commonly used way in which the relationship between topography and Bouguer anomaly in the method assumes that topography of the rigid shell instead Isoztasi balance is maintained. The method to determine the density of Bouguer provided by fractal analyze these are the lowest density dependence the topography of the area is considered as the optimal density and the fractal relationship to the topography of the fractal dimension using the Bouguer anomaly.

Application of fractal geometry measurements to the evaluation of fracture toughness of brittle intermetallics

1991 ◽  
Vol 6 (9) ◽  
pp. 1856-1861 ◽  
Author(s):  
Y. Fahmy ◽  
J.C. Russ ◽  
C.C. Koch
Keyword(s):  
Fracture Toughness ◽  
Surface Roughness ◽  
Fractal Dimension ◽  
Oxygen Content ◽  
Fractal Geometry ◽  
Single Parameter

Determination of the boundary fractal dimension of planar sections through particles produced by fracturing a series of brittle intermetallic V3Au materials with increasing oxygen content provides a single parameter that describes the surface roughness. This is observed to correlate with the measured fracture toughness, K1c, as determined with an indentation cracking test. The correlation agrees quantitatively with results obtained on several brittle ceramics by other workers.

A Three-Dimensional Fractal Analysis Method for Ground Monocrystal Sapphire Surface

2014 ◽  
Vol 1017 ◽  
pp. 187-192
Author(s):  
Qiu Yan Wang ◽  
Zhi Qiang Liang ◽  
Xi Bin Wang ◽  
Wen Xiang Zhao ◽  
Yong Bo Wu ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Ground Surface ◽  
Surface Characteristics ◽  
Surface Phenomenon ◽  
Analysis Method ◽  
Characterization Methods ◽  
Box Counting

Conventional characterization methods of grinding surface using surface roughness parameters, e.g., Ra, depend on either the resolution of the measuring instrument or the length of the sample. But fractal dimension (FD) as a scale-independent fractal parameter is effective to evaluate the ground surface at any length scale and represent lots of surface phenomenon at its relevant length scales. In this paper, a three-dimensional (3D) box-counting fractal analysis method is used to investigate ground surface morphology of monocrystal sapphire by calculating 3D fractal dimension of the ground surface. The results obtained show that fractal dimension decreases with the increasing surface roughness. For the ground surface with higher fractal dimension, its microtopography is more exquisite with minor defects. Once the fractal dimension become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the ground surface obtained in ductile mode has much higher fractal dimension than that in brittle mode. Therefore, the fractal analysis method has the potential to reveal the ground surface characteristics of monocrystal sapphire.

scholarly journals Intergranular area microalloyed aluminium-silicate ceramics fractal analysis

2013 ◽  
Vol 45 (1) ◽  
pp. 117-126 ◽  
Author(s):  
J. Purenovic ◽  
V.V. Mitic ◽  
Lj. Kocic ◽  
V. Pavlovic ◽  
M. Randjelovic ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Electrical Properties ◽  
Fractal Analysis ◽  
Fractal Nature ◽  
Place Making ◽  
Richardson Method ◽  
Micro Morphology ◽  
Solid System ◽  
Aluminium Silicate

Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization.

A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness

2020 ◽  
Vol 60 (1) ◽  
pp. 184 ◽  
Author(s):  
Abbas Movassagh ◽  
Xi Zhang ◽  
Elaheh Arjomand ◽  
Manouchehr Haghighi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Hydraulic Fracturing ◽  
Fractal Analysis ◽  
Roughness Length ◽  
Variation Method ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Surface Profiles ◽  
Fractal Methods

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.

Fractal analysis with scanning probe microscopy

1992 ◽  
Vol 50 (2) ◽  
pp. 1046-1047
Author(s):  
Paul E. West ◽  
Sid Marchesse-Rugona ◽  
Zhuoning Li
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Physical Properties ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Optical Microscope ◽  
Two Dimensional ◽  
Atomic Force ◽  
Dimensional Measurements ◽  
Surface Profiles

Surface roughness determined qualitatively by direct visualization can be correlated to several physical properties. However, finding a suitable method of quantifying surface roughness, until recently, has been difficult. The concept of Fractal Dimension, recently popularized by Mandelbrot(1982) has been extremely successful in quantifying surface roughness and relating it to such measurable physical properties such as; cleanability, catalytic activity, rate of corrosion, and even flavor.Atomic Force Microscopes permit direct three dimensional measurements of surface microstructure. AFM images are obtained by measuring the motion of a sharp stylus as it is scanned across a surface. Because the AFM directly measures three dimensional topograms, it is ideally suited for two dimensional and three dimensional fractal analysis. Other microscope techniques such as the scanning electron or optical microscope give only two dimensional magnification and fractal measurements are not easily made.The Atomic Force Microscope enables us to obtain the fractal dimension of surface profiles as well as surface areas. For surface profiles we use a box counting method (Mandelbrot 1986, Chesters et al. 1989).

Application of Fractal Geometry in the Evaluation of Surface Microtexture of Soil Particles

2015 ◽  
Vol 797 ◽  
pp. 238-245
Author(s):  
Sylwia Szerakowska ◽  
Maria Jolanta Sulewska ◽  
Edward Stanisław Oczeretko ◽  
Jerzy Trzciński ◽  
Barbara Woronko
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Solid Phase ◽  
Complex Nature ◽  
Mathematical Tool ◽  
Soil Behaviour ◽  
Difficult Issue ◽  
Shape Of Particles

The shape of particles building the solid phase of soils is an important factor influencing soil behaviour. Three parameters defining the characteristics of particle shape: roundness, angularity and texture are the most commonly analyzed. The most difficult issue is texture determination due to its complex nature. Quantitative evaluation of this parameter creates serious problems, however, is not impossible. A new mathematical tool, such as fractal geometry, may be helpful. Through the use of power law, fractal analysis allows to designate fractal dimension that specifies the complexity of the tested object.

Bouguer density determination by fractal analysis

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 932-935 ◽  
Author(s):  
Freyr Thorarinsson ◽  
Stefan G. Magnusson
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Gravity Data ◽  
Bouguer Anomaly ◽  
New Method ◽  
Data Sets ◽  
Isostatic Compensation ◽  
Topographic Features ◽  
Density Determination ◽  
Density Values

Density values for the Bouguer reduction of two gravity data sets from Iceland are determined using a new method based on minimization of the roughness of the Bouguer anomaly surface. The fractal dimension of the surface is used as a gauge of the roughness. The analysis shows the size of topographic features supported by crust without isostatic compensation to be 25 to 30 km in southwest Iceland and 9 to 10 km inside the active rifting zone. The densities selected for these areas are 2490 and [Formula: see text], respectively.

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