Wavelet Transform Modulus Maxima Lines Research Articles

An empirical law for wavelet maxima interpretation of potential fields: Application to the Uinta Mountains range

Wavelet methods have been used in potential fields study to estimate source properties such as depth or structural index, through the analysis of Wavelet Transform Modulus Maxima Lines (WTMML) intersections and slopes at high scales. Little has been done on the study of maximum points of the wavelet diagram, that we call here Maximum Wavelet Coefficient Scales (MWCS). Previous works have shown interesting correlations between MWCS and source depths, depending on the wavelet used in regards to the source nature and the data derivative order. In this paper, we introduce an empirical law involving spectral parameters that have not been studied so far, which allows analytical calculation of the MWCS, knowing the source characteristics and using certain wavelets. In return, the study of MWCS allows recovering source characteristics from the use of a single wavelet, without prior knowledge on the source.We demonstrate through synthetic models that the new capability of predicting the source type and depth according to the wavelet coefficient behaviour allows new ways of potential fields' sources characterization and identification. We show an application of the formula on a real case example in the Uinta Mountains (Utah, USA).

Wavelet-Based Multifractal Analysis of DEMETER Satellite Data Before the L’Aquila Earthquake of 2009

The main goal of this paper is to demonstrate the multifractal behavior of the ionospheric plasma signals recorded by the ISL instrument installed onboard of the DEMETER satellite before the L’Aquila earthquake of 2009. Multifractal analysis is performed using the so-called the wavelet transform modulus maxima lines (WTMM) method. Signals to be analyzed are: density of electrons and ions, temperature of electrons, and the potential of the plasma. WTMM analysis of the data recorded during April 4, 2009 which recognizes many ionospheric disturbances before the L’Aquila earthquake clearly shows the multifractal behavior of the ionosphere plasma physical response. WTMM analysis of data recorded by the DEMETER satellite two months after the L’Aquila earthquake main shock shows the monofractal behavior of the plasma response.

Heterogeneities analysis using the generalized fractal dimensions and the continuous wavelet transform. Application to the KTB boreholes

The main goal of this paper is to identify heterogeneities from well logs data using the wavelet-based multifractal analysis. Firstly, the wavelet transform modulus maxima lines method is applied with a moving window of 128 samples to the raw well logs data. After that, the generalized fractal dimensions that correspond to the three first moments of the function of partition are estimated. Application to synthetic and real well logs data of the main and pilot Kontinentales Tiefbohrprogramm de Bundesreplik Deutschland wells shows that the information and the correlation dimensions can be used for heterogeneities analysis and lithofacies segmentation form well logs data.

A wavelet-based multifractal analysis of seismic data for facies identification. Application on the pilot KTB borehole

The main goal of this paper is to identify reflection from seismic data using the multifractal formalism. Firstly, the wavelet transform modulus maxima lines method is applied with a sliding window of 128 samples at the seismic seismogram data. After that, we estimate the generalized fractal dimension. Application at the noisy synthetic seismic seismogram of the pilot Kontinentales Tiefbohrprogramm de Bundesreplik Deutschland borehole shows that the three fractal dimensions related to the three first moments are a good tool that can separate between reflection dues to the change of facies and random noise.

Automatic lithofacies segmentation using the wavelet transform modulus maxima lines combined with the detrended fluctuation analysis

The main goal of this paper is to design and develop a new technique and software tool that help automatic lithofacies segmentation from well logs data. Lithofacies is a crucial problem in reservoir characterization and our study intends to prove that techniques like wavelet transform modulus maxima lines (WTMM) and detrended fluctuation analysis (DFA) approaches allow geological lithology segmentation from well logs data. On the one hand, WTMM prove to be useful for delimitation of each layer. We based on its sensitivity on the presence of more than one texture. On the other hand, DFA is used to enhance the estimation of the roughness coefficient of each facies. We have used them jointly to segment the lithofacies of boreholes located in the Algerian Sahara. Obtained results are encouraging to publish this method because the principal benefit is economic.

Fractal analysis revisited by the continuous wavelet transform of AVO seismic data

The main goal of this paper is to establish reservoirs media heterogeneities by the wavelet transform modulus maxima lines. First, we gathered amplitude versus offsets (AVO) amplitudes at the top of the reservoirs, then we calculated the 2D wavelet transform after we calculated its maxima, and we estimated the Holder exponent at each maxima. Variation of the Holder exponent can give more information about lithology and fluid nature at any point.

Multifractal Analysis Revisited by the Continuous Wavelet Transform Applied in Lithofacies Segmentation from Well-Logs Data

The main goal of this paper is to use the wavelet transform modulus maxima lines (WTMM) and the detrended fluctuations analysis (DFA) methods to establish a new technique of lithofacies segmentation from well logs data. The WTMM is used to delimitate lithoafacies boundaries and the DFA is used to provide an exact estimation of the roughness coefficient of lithofacies. Application of the proposed idea at the synthetic and real data of a borehole located in Berkine basin shows that the proposed technique can enhance reservoirs characterization.

Detection of glitches and signal reconstruction using Hölder and wavelet analysis

We present a method based on a local regularity analysis for detecting and removing artefact signatures in noisy interferometric signals. Using Hölder and wavelet transform modulus maxima lines analysis (WTMML) [S. Mallat, W. Hwang, Singularities detection and processing with wavelets, IEEE Transaction on Information Theory 38 (1992) 617–643] in suitably selected regions of the time-scale half-plane, we can estimate the regularity degree of the signal. Glitches that are considered as a discontinuity on the signal show Hölder component lower than a fixed threshold defined for a continuous signal. After detection and signature removal, the signal is then locally reconstructed using Mallat reconstruction formulae. The method has been tested with Herschel SPIRE FTS proto-flight model calibration observations and shows remarkable results. Optimization of the detection parameters has been performed on the correlation coefficient, the scale domain for Hölder exponent estimation and reconstruction for SPIRE FTS signals.

Scale-adaptive detection and local characterization of edges based on wavelet transform

In this paper, we present an edge detection and characterization method based on wavelet transform. This method relies on a modelization of contours as smoothed singularities of three particular types (transition, peak and line). Using the wavelet transform modulus maxima lines of the edge models, position and descriptive parameters of each edge point can be inferred. Indeed, on the one hand, the proposed algorithm allows to detect and locate edges at a locally adapted scale. On the other hand, it is able to identify the type of each detected edge point and to measure both its amplitude and smoothness degree. The latter parameters represent, respectively, the contrast and the blur level of the edge point. Evaluation of the method is performed on both synthetic and real images. Synthetic data are used to investigate the influence of different factors and the sensitivity to noise, whereas real images allow to highlight the performance and interests of the method. In particular, we point out that the measured smoothness degree provides a cue to recover depth from defocused images or a cue to diffusion measurements in images of cloud structures. Moreover, from an indoor scene, we demonstrate the relevance of type identification for segmentation purposes.

Joint application of continuous and discrete wavelet transform on gravity data to identify shallow and deep sources

The discrete wavelet transform (dwt), using the good property of localization of wavelet bases has been used as a powerful tool in filtering and denoising problems. The continuous wavelet transform (cwt) exploits the upward continuation properties of the field horizontal derivative and allows the location of potential field singularities in a simple geometrical manner. Within the cwt space-scale framework, the lines formed by joining, at different scales, the modulus maxima of the wavelet coefficients (multiscale edge detection method) intersect each other at the position of the point source or along the edges of the causative body. As long as the multiscale edge detection method is applied to experimental data the procedure may, however, fail, since the observed anomalies are the superposition of effects of sources having different density contrast, geometrical size and depths. We show that wavelet transform modulus maxima lines attributed to deep sources do not converge toward the true depths, but yield completely erroneous solutions. On the other hand, use of nth-order derivatives of the potential field allows the enhancement of the shallowest source effects, preventing us from obtaining information on the deeper ones. In this paper we therefore try to overcome this problem by a joint application of cwt and dwt. A localized dwt filter coupled to compactness criterion allows the separation of the effects due to the deeper sources from those of the shallower ones. Hence, the multiscale edge detection method, applied separately to the original and the filtered signals enabled the estimation of the depth of shallower and deeper sources, respectively. This analysis, performed on the gravity anomalies of Sardinia (Italy), has given estimations of the depths to both the Campidano graben and the Moho discontinuity, in good agreement with previous interpretations of gravity and seismic data.