Considerations on anisotropic models of image processing based on partial differential equations

Extracting fault, unconformity, and horizon surfaces from a seismic image is useful for interpretation of geologic structures and stratigraphic features. Although others automate the extraction of each type of these surfaces to some extent, it is difficult to automatically interpret a seismic image with all three types of surfaces because they could intersect with each other. For example, horizons can be especially difficult to extract from a seismic image complicated by faults and unconformities because a horizon surface can be dislocated at faults and terminated at unconformities. We have proposed a processing procedure to automatically extract all the faults, unconformities, and horizon surfaces from a 3D seismic image. In our processing, we first extracted fault surfaces, estimated fault slips, and undid the faulting in the seismic image. Then, we extracted unconformities from the unfaulted image with continuous reflectors across faults. Finally, we used the unconformities as constraints for image flattening and horizon extraction. Most of the processing was image processing or array processing and was achieved by efficiently solving partial differential equations. We used a 3D real example with faults and unconformities to demonstrate the entire image processing.

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Soliton Kernels for Solving PDEs

International Journal of Computational Methods ◽

10.1142/s0219876216400090 ◽

2016 ◽

Vol 13 (02) ◽

pp. 1640009 ◽

Cited By ~ 2

Author(s):

Marjan Uddin ◽

H. U. Jan ◽

Amjad Ali ◽

I. A. Shah

Keyword(s):

Image Processing ◽

Partial Differential Equations ◽

Differential Equations ◽

Response Surface ◽

Computer Experiments ◽

Time Dependent ◽

Response Surface Modeling ◽

Partial Differential ◽

Special Solutions ◽

Better Than

There are many important applications in the fields of computer experiments, response surface modeling, finance and image processing, where some special types of nonstandard kernels performed better than standard kernels. These kernels are more appropriate than standard kernels when looking at special solutions of partial differential equations (PDEs). For example some nonlinear time-dependent PDEs have soliton like solutions, so soliton kernels would more suit to approximate the solution. In this work, we recover the solution of equal width equation using soliton kernels.

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A New Image Demising Method Based on Partial Differential Equations

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.443.22 ◽

2013 ◽

Vol 443 ◽

pp. 22-26

Author(s):

Yong Xing Lin ◽

Xiao Yan Xu ◽

Xian Dong Zhang

Keyword(s):

Image Processing ◽

Partial Differential Equations ◽

Differential Equations ◽

Diffusion Equation ◽

Objective Function ◽

Thermal Diffusion ◽

Minimization Problem ◽

Iterative Process ◽

Function Minimization ◽

Partial Differential

In the paper, we discuss the image demising models, based on partial differential equations. It is through the use of the concept of variations in the calculus of the objective function minimization problem, defines the image processing tasks. The results show that the model expands 2d thermal diffusion equation. Therefore, it is easy to get solution is to use a simple iterative process.

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