The Method of Average Modulus Based on Wavelet Transform to Recognize the Sequence Stratigraphy Boundaries with Logging Curves

2012 ◽  
Vol 500 ◽  
pp. 14-17
Author(s):  
Yun Liang Yu ◽  
Ye Bai ◽  
Jian Qiang Wang
Keyword(s):  
Fourier Series ◽  
Wavelet Transform ◽  
Sequence Stratigraphy ◽  
Scale Factor ◽  
Fourier Series Expansion ◽  
Spectral Energy ◽  
Wavelet Coefficients ◽  
Optimal Scale ◽  
Average Modulus ◽  
Wavelet Transforming

Choose a wavelet to transform the logging curves, which can obtain a series of scale and depth corresponding to wavelet coefficients. From the view of fourier series expansion and spectrum energy, the wavelet coefficients of optimal scale should be the largest proportion of total spectral energy. Based on the theory above, method of average modulus based on wavelet transform is put forwarded. Find the optimal scale factor through wavelet transforming of logging curves, and establish a correspondence between oscillations characteristic of wavelet coefficients curve of the optimal scale factor and sequence stratigraphy boundaries. This method provides a new way to recognize sequence stratigraphy boundaries.

The Meaning of Wavelet Transform in High Resolution Sequence Stratigraphy Study

2013 ◽  
Vol 411-414 ◽  
pp. 3035-3038
Author(s):  
Zhan Dong Li ◽  
Meng Li ◽  
Yan Liu
Keyword(s):  
Wavelet Transform ◽  
High Resolution ◽  
Sequence Stratigraphy ◽  
Wavelet Coefficient ◽  
Scale Factor ◽  
Sequence Stratigraphic ◽  
Natural Gamma ◽  
Set Up ◽  
Morlet Wavelet Transform ◽  
High Resolution Sequence Stratigraphy

Taking the division of Gao3 reservoir group strata sequence in Songliao basin of Daqing Changyuan Xingbei for example, this paper analyzed the applicability of the one-dimensional continuous wavelet transform in high resolution sequence division. By means of making morlet wavelet transform on the natural gamma logging curve, the connection between well curve signal and depth is transformed to the alter relationship between depth and the domains of scale, which obtains the wavelet coefficient curve. Then set up the corresponding relations between periodic oscillations characteristics of wavelet coefficient curve and sequence interface at all levels under the optimal scale factor. And the wavelet coefficients curve in best scale factor will eventually be used for the identification and division of the sequence. Practice has proved that the wavelet coefficient curve in the best factor can accurately identify the sequence interface at all levels, and the result is more accurate, objective and effective than manual calibration. So take advantage of wavelet transform in sequence stratigraphic classification provides a new way for high resolution sequence stratigraphy studies.

BESOV NORMS IN TERMS OF THE CONTINUOUS WAVELET TRANSFORM. APPLICATION TO STRUCTURE FUNCTIONS

1996 ◽  
Vol 06 (05) ◽  
pp. 649-664 ◽  
Author(s):  
VALÉRIE PERRIER ◽  
CLAUDE BASDEVANT
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Besov Spaces ◽  
Inversion Formula ◽  
Structure Functions ◽  
Continuous Wavelet ◽  
Wavelet Coefficients ◽  
Small Scales ◽  
Besov Norms

The continuous wavelet transform is extended to Lp spaces and an inversion formula is demonstrated. From this the Besov spaces can be characterized by the behavior at small scales of the wavelet coefficients. These results apply to the measurement of structure functions.

scholarly journals Characterizing wavelet coefficients with decomposition for medical images

2021 ◽  
pp. 26-32
Author(s):  
Jabbar Abed Eleiwy ◽  
Keyword(s):  
Wavelet Transform ◽  
Medical Images ◽  
Wavelet Coefficients

In this paper, applications Discrete Laguerre Wavelet Transform were used where satisfactory results were obtained, where the efficiency of our proposed theory was proved, and the examples used will prove this. Three physical samples were selected that were compressed using the proposed wavelets, and good results were obtained that prove the efficiency of the method used. Three physical samples were selected that were compressed using the proposed wavelets, and good results were obtained that prove the efficiency of the method used.

scholarly journals Optimal multistage relaxation with automatic parameter selection

2021 ◽  
Author(s):  
Alvin Wong
Keyword(s):  
Fourier Series ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Convergence Time ◽  
Fourier Series Expansion ◽  
End User ◽  
Local Flow ◽  
Flow Problems ◽  
User Expertise ◽  
Complex Fourier Series

This research developed a numerical method that solves complicated fluid flow problems without requiring end-user expertise with the solver. This method is capable of obtaining a spatially accurate solution in the same time or better as a skilled user with a conventional solver. An explicit preconditioned multigrid solver was used in this research with a multistage relaxation method. The prosposed method utilizies a database with optimized relaxation method parameters for different local flow and mesh conditions. The parameters are optimized for the relaxation such that the error modes in a complex Fourier series expansion of the residual can be quickly reduced. The convergence time and iteration count of this method was compared against the same solver using default input values, as well as a pre-optimized solver, to simulate a skilled user for various geometries. Improvements in both comparisons were demonstrated.

scholarly journals Optimal multistage relaxation with automatic parameter selection

2021 ◽  
Author(s):  
Alvin Wong
Keyword(s):  
Fourier Series ◽  
Relaxation Method ◽  
Accurate Solution ◽  
Convergence Time ◽  
Fourier Series Expansion ◽  
End User ◽  
Local Flow ◽  
Flow Problems ◽  
User Expertise ◽  
Complex Fourier Series

This research developed a numerical method that solves complicated fluid flow problems without requiring end-user expertise with the solver. This method is capable of obtaining a spatially accurate solution in the same time or better as a skilled user with a conventional solver. An explicit preconditioned multigrid solver was used in this research with a multistage relaxation method. The prosposed method utilizies a database with optimized relaxation method parameters for different local flow and mesh conditions. The parameters are optimized for the relaxation such that the error modes in a complex Fourier series expansion of the residual can be quickly reduced. The convergence time and iteration count of this method was compared against the same solver using default input values, as well as a pre-optimized solver, to simulate a skilled user for various geometries. Improvements in both comparisons were demonstrated.

An Improved Fourier–Ritz Method for Analyzing In-Plane Free Vibration of Sectorial Plates

2017 ◽  
Vol 84 (9) ◽  
Author(s):  
Siyuan Bao ◽  
Shuodao Wang ◽  
Bo Wang
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Displacement Function ◽  
Accurate Solution ◽  
Previous Method ◽  
Fourier Series Expansion ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Radial Variable

A modified Fourier–Ritz approach is developed in this study to analyze the free in-plane vibration of orthotropic annular sector plates with general boundary conditions. In this approach, two auxiliary sine functions are added to the standard Fourier cosine series to obtain a robust function set. The introduction of a logarithmic radial variable simplifies the expressions of total energy and the Lagrangian function. The improved Fourier expansion based on the new variable eliminates all the potential discontinuities of the original displacement function and its derivatives in the entire domain and effectively improves the convergence of the results. The radial and circumferential displacements are formulated with the modified Fourier series expansion, and the arbitrary boundary conditions are simulated by the artificial boundary spring technique. The number of terms in the truncated Fourier series and the appropriate value of the boundary spring retraining stiffness are discussed. The developed Ritz procedure is used to obtain accurate solution with adequately smooth displacement field in the entire solution domain. Numerical examples involving plates with various boundary conditions demonstrate the robustness, precision, and versatility of this method. The method developed here is found to be computationally economic compared with the previous method that does not adopt the logarithmic radial variable.

A SIMPLE MODEL FOR ORIENTATIONAL ORDERING OF A SILVER MONOLAYER ELECTRODEPOSITED ON A C(0001) SURFACE

1995 ◽  
Vol 02 (04) ◽  
pp. 489-494 ◽  
Author(s):  
E.E. MOLA ◽  
A.G. APPIGNANESSI ◽  
J.L. VICENTE ◽  
L. VAZQUEZ ◽  
R.C. SALVAREZZA ◽  
...  
Keyword(s):  
Experimental Data ◽  
Fourier Series ◽  
Simple Model ◽  
Series Expansion ◽  
Unit Cell ◽  
Fourier Series Expansion ◽  
Crystal Formation ◽  
Substrate Potential ◽  
Weber Type ◽  
Orientational Ordering

The model for the angular orientational energy (AOE) has been extended to hexagonal submonolayer domains of Ag electrodeposited at a constant overpotential on a C(0001) surface. These domains which are characterized by an epitaxy angle θ=15±5° and an Ag−Ag distance d Ag−Ag =0.330± 0.016 nm, can be considered as precursors of 3D Ag crystal formation, according to a Volmer-Weber type mechanism. Calculations are based upon a simple Hamiltonian evaluated by introducing the concept of the commensurable unit cell. A Fourier series expansion for the substrate potential was used. Results from the model predict the existence of a commensurable cell in agreement with the experimental data derived from STM imaging.

Sign in / Sign up

Export Citation Format

Share Document