Correlation Theory of Stationary and Related Random Functions

Yaglom, A. M.

doi:10.1007/978-1-4612-4628-2

Cited by 323 publications

(232 citation statements)

References 0 publications

Supporting

Mentioning

229

Contrasting

Unclassified

Order By: Relevance

“…[32] The accuracy of the experimental spectral density can be estimated as follows. For each periodogram value P i , the quantity (2 P i P f ð Þ ), where P( f ) is the true value of power spectral density at frequency f, has the c 2 (2) distribution with 2 degrees of freedom [Yaglom, 1987]. Therefore, the periodogram estimate has the mean hP i i = P( f ) and the variance var(P i ) = s 2 i = P 2 ( f ).…”

Section: Experimental Scintillation Spectramentioning

confidence: 99%

Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements

et al. 2007

View full text Add to dashboard Cite

[1] Exploitation of stellar scintillation allows studying air density irregularities in the stratosphere. In this paper, we develop a methodology for reconstruction of internal gravity wave (IGW) and turbulence parameters using scintillation measurements by the Global Ozone Monitoring by Occultation of Star (GOMOS) fast photometers on board the Envisat satellite. The forward model is based on a two-component spectral model of air density irregularities: the first component corresponds to the gravity wave spectrum, while the second one describes locally isotropic turbulence resulting from internal gravity wave breaking. The retrieval of parameters of IGW and turbulence spectra is based on the maximum likelihood method. The developed algorithm is tested on simulated and real data, and its accuracy is assessed. It is shown that the measured scintillation spectra are in good agreement with the proposed model and that structure characteristics and inner and outer scales of the anisotropic component can be reconstructed from scintillation spectra. The developed method can provide information about global distribution of parameters of IGW and turbulence spectra in the stratosphere at altitudes from 25 to 50 km.Citation: Sofieva, V. F., A. S. Gurvich, F. Dalaudier, and V. Kan (2007), Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,

show abstract

Section: Experimental Scintillation Spectramentioning

confidence: 99%

Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements

et al. 2007

View full text Add to dashboard Cite

show abstract

“…Then T,(x, y, z) and ~( x , y, z) are regarded as the outcome of some kind of random experiment. Their spectral representations are given by Fourier-Stieltjes integrals (Yaglom 1986) in the following sense: W where R(x) is the random function in the space domain and Z ( d u ) is a complex random measure determined for any interval du and having the properties…”

Section: Modelmentioning

confidence: 99%

Curie-temperature depth estimation using a self-similar magnetization model

Maus¹,

Gordon²,

Fairhead³

1997

Geophysical Journal International

147

129

View full text Add to dashboard Cite

S U M M A R YThe Earth's crust is magnetized down to the Curie-temperature depth at about 10 to 50 km. This limited depth extent of the crustal magnetization is discernible in the power spectra of magnetic maps of South Africa and Central Asia. At short wavelengths, the power increases as rapidly towards longer wavelengths as expected for a self-similar magnetized crust with unlimited depth extent. Above wavelengths of about 100 km the power starts increasing less rapidly, indicating the absence of deep-seated sources. To quantify this effect we derive the theoretical power spectrum due to a slab carved out of a self-similar magnetization distribution. This model power spectrum matches the power spectra of South Africa and Central Asia for a self-similarity parameter of p = 4 and Curie temperature depths of 15 to 20 km.

show abstract

“…Also, because the result contains only lowfrequency components by construction, it is much smoother than the original covariance function. Computationally, this process is very efficient; however, the resulting covariance function is not a member of the set of parametric covariance functions commonly used in geostatistics (for references to the frequency analysis of covariance functions, see Yaglom 1987;Stein 1990;Chilès and Delfiner 1999;and Schabenberger and Gotway 2005). The behavior of the covariance kernel C ð1Þ in Fig.…”

Section: Ordinary Krigingmentioning

confidence: 99%

Geostatistical Smoothing of Areal Data: Mapping Employment Density with Factorial Kriging. 面状数据的地统计滤波：采用因子克里格方法制作就业密度图

Nagle

2010

Geographical Analysis

View full text Add to dashboard Cite

This article summarizes area‐to‐point (ATP) factorial kriging that allows the smoothing of aggregate, areal data into a continuous spatial surface. Unlike some other smoothing methods, ATP factorial kriging does not suppose that all of the data within an area are located at a centroid or other arbitrary point. Also, unlike some other smoothing methods, factorial kriging allows the user to utilize an autocovariance function to control the smoothness of the output. This is beneficial because the covariance function is a physically meaningful statement of spatial relationship, which is not the case when other spatial kernel functions are used for smoothing. Given a known covariance function, factorial kriging gives the smooth surface that is best in terms of minimizing the expected mean squared prediction error. I present an application of the factorial kriging methodology for visualizing the structure of employment density in the Denver metropolitan area.

show abstract

Correlation Theory of Stationary and Related Random Functions

Cited by 323 publications

References 0 publications

Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements

Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements

Curie-temperature depth estimation using a self-similar magnetization model

Geostatistical Smoothing of Areal Data: Mapping Employment Density with Factorial Kriging. 面状数据的地统计滤波：采用因子克里格方法制作就业密度图

Contact Info

Product

Resources

About