High resolution seismic from band limited data using the scaling laws of the wavelet transforms

2006 ◽  
Author(s):  
K. R. Sandhya Devi
Keyword(s):  
High Resolution ◽  
Wavelet Transforms ◽  
Scaling Laws ◽  
Limited Data ◽  
Band Limited

High-resolution seismic signals from band-limited data using scaling laws of wavelet transforms

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA143-WA152 ◽  
Author(s):  
K. R. Devi ◽  
Herb Schwab
Keyword(s):  
High Resolution ◽  
Power Law ◽  
Seismic Data ◽  
Wavelet Transforms ◽  
Scaling Laws ◽  
Scaling Law ◽  
Well Log ◽  
Seismic Signals ◽  
Local Scaling ◽  
Seismic Wavelet

Time-scale spectra, obtained from seismic data wavelet transforms, are useful in analyzing local scaling properties of seismic signals. In particular, the wavelet transform modulus maxima (WTMM) spectra, obtained by following the local extrema of wavelet transforms along a constant phase line, describe characteristics of discontinuities such as interfaces. They also show a smooth behavior as a function of scale and thus allow us to derive local scaling laws. We use scaling behavior of WTMM spectra to enhance the bandwidth of seismic data. An analysis of well-log scaling behaviors and the seismic data shows that, whereas the WTMM spectrum of well logs at each interface exhibits a power-law behavior as a function of scale, the corresponding seismic signal spectrum shows a more complicated behavior, arising from seismic wavelet effects. Under the assumption that local well-log power-law behavior holds in general, a scaling law for seismic signals can be derived in terms of parameters that describe subsurface scaling effects and the seismic wavelet. A stable estimation of these parameters can be carried out simultaneously, as a function of time and over the seismic bandwidth, using the modified scaling law. No well-log information is needed to derive the seismic wavelet. Then wavelet transforms can be corrected for seismic wavelet effects and a high-resolution signal reconstructed. This reconstructed high-resolution signal can be used to map features that might not be obvious in the original seismic data, such as small faults, fractures, and fine-scale variations within channel margins.

Splash formation by spherical drops

2001 ◽  
Vol 427 ◽  
pp. 73-105 ◽  
Author(s):  
LIOW JONG LENG
Keyword(s):  
High Resolution ◽  
Quantitative Data ◽  
Water Surface ◽  
High Speed ◽  
Scaling Laws ◽  
Capillary Wave ◽  
Water Drop ◽  
Qualitative And Quantitative ◽  
High Resolution Images ◽  
The Impact

The impact of a spherical water drop onto a water surface has been studied experimentally with the aid of a 35 mm drum camera giving high-resolution images that provided qualitative and quantitative data on the phenomena. Scaling laws for the time to reach maximum cavity sizes have been derived and provide a good fit to the experimental results. Transitions between the regimes for coalescence-only, the formation of a high-speed jet and bubble entrapment have been delineated. The high-speed jet was found to occur without bubble entrapment. This was caused by the rapid retraction of the trough formed by a capillary wave converging to the centre of the cavity base. The converging capillary wave has a profile similar to a Crapper wave. A plot showing the different regimes of cavity and impact drop behaviour in the Weber–Froude number-plane has been constructed for Fr and We less than 1000.

COMPARATIVE ANALYSIS OF SPECTRA OF THE 2000-YEAR NORTHERN HEMISPHERE AVERAGE SURFACE AIR TEMPERATURE RECONSTRUCTIONS

2021 ◽  
pp. 5-13
Author(s):  
N. M. DATSENKO ◽  
◽  
D. M. SONECHKIN ◽  
B. YANG ◽  
J.-J. LIU ◽  
...  
Keyword(s):  
High Resolution ◽  
Northern Hemisphere ◽  
Air Temperature ◽  
Wavelet Transforms ◽  
Spectral Composition ◽  
Low Frequency ◽  
Surface Air Temperature ◽  
Temporal Variations ◽  
Continuous Wavelet Transforms ◽  
Stable Estimation

The spectral composition of temporal variations in the Northern Hemisphere mean surface air temperature is estimated and compared in 2000-year paleoclimatic reconstructions. Continuous wavelet transforms of these reconstructions are used for the stable estimation of energy spectra. It is found that low-frequency parts of the spectra (the periods of temperature variations of more than 100 years) based on such high-resolution paleoclimatic indicators as tree rings, corals, etc., are similar to the spectrum of white noise, that is never observed in nature. This seems unrealistic. The famous reconstruction called “Hockey Stick” is among such unrealistic reconstructions. Reconstructions based not only on high-resolution but also on low-resolution indicators seem to be more realistic, since the low-frequency parts of their spectra have the pattern of red noise. They include the “Boomerang” reconstruction showing that some warm periods close to the present-day one were observed in the past.

scholarly journals Quasi-Band-Limited Coronagraph for Extended Sources

2021 ◽  
Vol 10 (01) ◽  
pp. 2150002
Author(s):  
Igor Loutsenko ◽  
Oksana Yermolayeva
Keyword(s):  
High Resolution ◽  
High Ratio ◽  
Gravitational Lens ◽  
High Resolution Imaging ◽  
The Sun ◽  
Extended Source ◽  
Amplitude Image ◽  
Extended Sources ◽  
Resolution Imaging ◽  
Band Limited

We propose a class of graded coronagraphic “amplitude” image masks for a high throughput Lyot-type coronagraph that transmits light from an annular region around an extended source and suppresses light, with extremely high ratio, from elsewhere. The interior radius of the region is comparable with its exterior radius. The masks are designed using an idea inspired by approach due M. J. Kuchner and W. A. Traub (“band-limited” masks) and approach to optimal apodization by D. Slepian. One potential application of our masks is direct high-resolution imaging of exo-planets with the help of the Solar Gravitational Lens, where apparent radius of the “Einstein ring” image of a planet is of the order of an arc-second and is comparable with the apparent radius of the sun and solar corona.

scholarly journals On inertial-range scaling laws

1996 ◽  
Vol 306 ◽  
pp. 167-181 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Scaling Laws ◽  
State Energy ◽  
Three Dimensional ◽  
Inertial Range ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Unified Framework ◽  
Asymptotic Nature

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

Robust wavelet estimation and blind deconvolution of noisy surface seismics

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. V37-V46 ◽  
Author(s):  
Mirko van der Baan ◽  
Dinh-Tuan Pham
Keyword(s):  
Blind Deconvolution ◽  
General Purpose ◽  
Sufficient Accuracy ◽  
Wiener Filtering ◽  
Challenging Problem ◽  
Limited Data ◽  
Wavelet Estimation ◽  
Seismic Wavelet ◽  
Principal Frequency ◽  
Band Limited

Robust blind deconvolution is a challenging problem, particularly if the bandwidth of the seismic wavelet is narrow to very narrow; that is, if the wavelet bandwidth is similar to its principal frequency. The main problem is to estimate the phase of the wavelet with sufficient accuracy. The mutual information rate is a general-purpose criterion to measure whiteness using statistics of all orders. We modified this criterion to measure robustly the amplitude and phase spectrum of the wavelet in the presence of noise. No minimum phase assumptions were made. After wavelet estimation, we obtained an optimal deconvolution output using Wiener filtering. The new procedure performs well, even for very band-limited data; and it produces frequency-dependent phase estimates.

Wind Inhomogeneities in Wolf-Rayet Stars. I. Search for Scaling Laws Using Wavelet Transforms

1996 ◽  
Vol 466 ◽  
pp. 392 ◽  
Author(s):  
Sebastien Lepine ◽  
Anthony F. J. Moffat ◽  
R. N. Henriksen
Keyword(s):  
Wavelet Transforms ◽  
Scaling Laws

Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R57-R74 ◽  
Author(s):  
Santi Kumar Ghosh ◽  
Animesh Mandal
Keyword(s):  
First Principles ◽  
Acoustic Impedance ◽  
Linear Equations ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Limited Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Profile ◽  
Band Limited

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.

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