Characterization of heterogeneities from sonic velocity measurements using the wavelet transform

1995 ◽  
Author(s):  
Xiao‐Ping Li ◽  
Johannes C. Haury
Keyword(s):  
Wavelet Transform ◽  
Sonic Velocity ◽  
Velocity Measurements

CHARACTERIZATION OF IMAGE SPACE OF A WAVELET TRANSFORM

2006 ◽  
Vol 04 (03) ◽  
pp. 547-557 ◽  
Author(s):  
CAIXIA DENG ◽  
YULING QU ◽  
LIJUAN GU
Keyword(s):  
Wavelet Transform ◽  
Truncation Error ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Image Space ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Scope Of Application

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.

scholarly journals Densified Pupil Spectrograph as High-precision Radial Velocimetry: From Direct Measurement of the Universe’s Expansion History to Characterization of Nearby Habitable Planet Candidates

2022 ◽  
Vol 163 (2) ◽  
pp. 63
Author(s):  
Taro Matsuo ◽  
Thomas P. Greene ◽  
Mahdi Qezlou ◽  
Simeon Bird ◽  
Kiyotomo Ichiki ◽  
...  
Keyword(s):  
Radial Velocity ◽  
Direct Measurement ◽  
High Precision ◽  
Resolving Power ◽  
Line Of Sight ◽  
High Dispersion ◽  
Velocity Measurements ◽  
Habitable Planet ◽  
Airy Disk

Abstract The direct measurement of the universe’s expansion history and the search for terrestrial planets in habitable zones around solar-type stars require extremely high-precision radial-velocity measures over a decade. This study proposes an approach for enabling high-precision radial-velocity measurements from space. The concept presents a combination of a high-dispersion densified pupil spectrograph and a novel line-of-sight monitor for telescopes. The precision of the radial-velocity measurements is determined by combining the spectrophotometric accuracy and the quality of the absorption lines in the recorded spectrum. Therefore, a highly dispersive densified pupil spectrograph proposed to perform stable spectroscopy can be utilized for high-precision radial-velocity measures. A concept involving the telescope’s line-of-sight monitor is developed to minimize the change of the telescope’s line of sight over a decade. This monitor allows the precise measurement of long-term telescope drift without any significant impact on the Airy disk when the densified pupil spectra are recorded. We analytically derive the uncertainty of the radial-velocity measurements, which is caused by the residual offset of the lines of sight at two epochs. We find that the error could be reduced down to approximately 1 cm s−1, and the precision will be limited by another factor (e.g., wavelength calibration uncertainty). A combination of the high-precision spectrophotometry and the high spectral resolving power could open a new path toward the characterization of nearby non-transiting habitable planet candidates orbiting late-type stars. We present two simple and compact highly dispersed densified pupil spectrograph designs for cosmology and exoplanet sciences.

CHARACTERIZATION OF PRECIPITATION BEHAVIOR IN NIMONIC 263 BY ULTRASONIC VELOCITY MEASUREMENTS

2009 ◽  
Author(s):  
G. V. S. Murthy ◽  
Kumar Anish ◽  
G. Sridhar ◽  
T. Jayakumar ◽  
R. N. Ghosh ◽  
...  
Keyword(s):  
Ultrasonic Velocity ◽  
Velocity Measurements ◽  
Precipitation Behavior

A Local Multiscale Characterization of Edges Applying the Wavelet Transform

1998 ◽  
pp. 261-277
Author(s):  
Carl J. G. Evertsz ◽  
Kathrin Berkner ◽  
Wilhelm Berghorn
Keyword(s):  
Wavelet Transform

scholarly journals Time-space characterization of droughts in the São Francisco river catchment using the Standard Precipitation Index and continuous wavelet transform

RBRH ◽  
2019 ◽  
Vol 24 ◽  
Author(s):  
Marcus Suassuna Santos ◽  
Veber Afonso Figueiredo Costa ◽  
Wilson dos Santos Fernandes ◽  
Rafael Pedrollo de Paes
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Large Scale ◽  
Continuous Wavelet ◽  
River Catchment ◽  
Time Space ◽  
L Moments ◽  
Space Characterization

ABSTRACT This paper focuses on time-space characterization of drought conditions in the São Francisco River catchment, on the basis of wavelet analysis of Standardized Precipitation Index (SPI) time series. In order to improve SPI estimation, the procedures for regional analysis with L-moments were employed for defining statistically homogeneous regions. The continuous wavelet transform was then utilized for extracting time-frequency information from the resulting SPI time series in a multiresolution framework and for investigating possible teleconnections of these signals with those obtained from samples of the large-scale climate indexes ENSO and PDO. The use of regional frequency analysis with L-moments resulted in improvements in the estimation of SPI time series. It was observed that by aggregating regional information more reliable estimates of low frequency rainfall amounts were obtained. The wavelet analysis of climate indexes suggests that the more extreme dry periods in the study area are observed when the cold phase of both ENSO and the PDO coincides. While not constituting a strict cause effect relationship, it was clear that the more extreme droughts are consistently observed in this situation. However, further investigation is necessary for identifying particularities in rainfall patterns that are not associated to large-scale climate anomalies.

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