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Collaborating Authors
ABSTRACT We have developed a new method for the direct current resistivity interpretation, based on the continuous wavelet transform (CWT) of electric potential-difference data. It exploits the main properties of the CWT, such as stability versus noise, and does not require a starting model or other a priori information such as a model weighting function or constraints. Because the approximate integral equation of the resistivity problem has the same form as the forward problem for potential fields, the authors analyze geoelectric data (with dipole-dipole configuration) using the wavelets belonging to the Poisson kernel semigroup. They find that the CWT analysis of the measured electric potential difference is able to identify buried bodies, defining their depth, position, and extent. Such parameters are estimated with no prior knowledge of the resistivity contrast between the bodies and the background. We consider several synthetic models, such as dikes, compact bodies, and contacts. In general, the depth and the lateral thickness of the buried bodies are estimated with good accuracy, using a diagram relating the singular point estimations to the different values of the dipole separation factor n. Thanks to the good results obtained from synthetic data, we test the method with data generated during laboratory experiments. In two laboratory-scale models, our method displays a better precision compared with smoothness-constrained least-squares inversion in identifying the exact position of the edges of a buried body. Finally, we find that combining CWT and inversion is advantageous: after constraining the inverse problem with a priori information from the CWT analysis, we obtain an improved inverse model.
- Geophysics > Electromagnetic Surveying (0.93)
- Geophysics > Gravity Surveying (0.93)
ABSTRACT Spectral analysis has been used for studying a variety of geologic structures and processes, such as estimation of the depth to the crystalline basement or estimation of the Curie temperature isotherm from magnetic anomalies. However, the analysis is not standard because it refers to different theoretical frameworks, such as statistical ensembles of homogeneous sources and uncorrelated or fractal randomly distributed sources. We have aimed to unify the approaches by reformulating all of the common spectral expressions in the form of a product between a depth-dependent exponential factor and a factor, which we call the spectral correction factor, that incorporates all of the a priori assumptions for each method. This type of organization might be useful for practitioners to quickly select the most appropriate method for a given study area. We also establish a new formula for extending the Spector and Grant method to the centroid depth estimation. Practical constraints on the depth estimation and intrinsic assumptions/limitations of the different approaches are examined by generating synthetic data of homogeneous ensemble sources as well as random and fractal models. We address the statistical uncertainty of depth estimates using ordinary error propagation on the spectral slope. Critical parameters, such as the window size, are also analyzed in terms of the type of method used and the geologic complexity. We find that the window size is smaller for the centroid/modified centroid methods and larger for the spectral peak, defractal, and nonlinear parameter depth estimation methods. In any case, the window size can be large in tectonically stable regions and relatively small over volcanically, tectonically, and geothermally active areas. Finally, we estimate and discuss the depth to the magnetic top and bottom in the Adriatic Sea region (eastern Italy) in the context of the heat flow, Moho depth, and gravity data of the region.
- Europe (1.00)
- Asia > Middle East > Saudi Arabia (1.00)
- Africa > Middle East > Egypt (1.00)
- (5 more...)
- Geology > Structural Geology > Tectonics > Plate Tectonics (1.00)
- Geology > Structural Geology > Tectonics > Compressional Tectonics > Fold and Thrust Belt (1.00)
- Geology > Rock Type (1.00)
- Geology > Geological Subdiscipline (1.00)
- Geophysics > Magnetic Surveying > Magnetic Acquisition (0.71)
- Geophysics > Magnetic Surveying > Magnetic Processing (0.64)
- Oceania > Australia > Western Australia > Canning Basin (0.99)
- Africa > Nigeria > Sokoto Basin (0.99)
- North America > United States > Kansas > Grant Field (0.93)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Geologic modeling (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)
- (2 more...)
- Information Technology > Artificial Intelligence > Vision > Image Understanding (1.00)
- Information Technology > Data Science > Data Quality (0.93)
- Information Technology > Artificial Intelligence > Representation & Reasoning (0.87)
- Information Technology > Artificial Intelligence > Machine Learning (0.68)
ABSTRACT This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.
Measures of Scale Based On the Wavelet Scalogram And Its Applications to Gas Detection
Li, Hongbing (China University of Mining & Technology and Petrochina Company Limited) | Zhao, Wenzhi (Petrochina Company Limited) | Cao, Hong (Petrochina Company Limited) | Yao, Fengchang (Petrochina Company Limited)
ABSTRACT This paper derives a scalogram formula of seismic wave in wavelet domain from the wavelet theory and the propagating equation of seismic wave in an anelastic medium. From the scalogram formula we present a method for estimating seismic attenuation based on scale shift data and define the centroid of scale for characterizing attenuation. In the absorbing medium, seismic attenuation decreases with scale in the wavelet domain, the small-scale energies of the seismic signal are attenuated more rapidly than the large-scale energies as waves propagate. As a result, both the peak scale and the centroid of the signal''s scalogram experience a upshift during propagation. Under the assumption of a frequency-independent model, this upshift of the peak scale and the centroid of scale are inversely proportional to the quality factor. The peak scale shift method is applicable in any seismic survey geometry where the signal bandwidth is broad enough. The centroid of scale can be used as an attribute to qualitatively characterize the seismic attenuation. Tests of therotical model and real data for gas detection are presented.
Investigations of heterogeneities using The continuous wavelet transform (CWT) is used sonic log data is an exciting and fruitful area for to evaluate local variations of the powerlaw exponents practical application of the CWT.