THE ESTIMATION OF MAGNETOTELLURIC IMPEDANCE TENSOR ELEMENTS FROM MEASURED DATA

Geophysics ◽  
1971 ◽  
Vol 36 (5) ◽  
pp. 938-942 ◽  
Author(s):  
W. E. Sims ◽  
F. X. Bostick ◽  
H. W. Smith
Keyword(s):  
Mean Square Error ◽  
Random Noise ◽  
Measured Data ◽  
Impedance Tensor ◽  
Mean Square ◽  
Signal To Noise ◽  
One Dimensional ◽  
Additional Information ◽  
The One ◽  
Mean Square Error Criterion

Six different estimates of the magnetotelluric impedance tensor elements may be computed from measured data by use of auto‐power and cross‐power density spectra. We show that each of the estimates satisfies a mean‐square error criterion. Two of the six estimates are relatively unstable in the one‐dimensional case when the incident fields are unpolarized. For the remaining four estimates, it is shown that two are unaffected by random noise on the H signal, but are biased upward by random noise on the E signal. The remaining two estimates are unaffected by random noise on the E signal, but are biased downward by random noise on the H signal. Computation of all of the estimates provides a measure of the total amount of noise present, as indicated by a stability coefficient for the estimates. In the absence of additional information as to the relative signal‐to‐noise ratios of the E and H signals, we suggest that a mean estimate be used. A numerical example is included.

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

scholarly journals Audio steganography based on least significant bits algorithm with 4D grid multi-wing hyper-chaotic system

2022 ◽  
Vol 12 (1) ◽  
pp. 320
Author(s):  
Hussein Abdulameer Abdulkadhim ◽  
Jinan Nsaif Shehab
Keyword(s):  
Mean Square Error ◽  
Chaotic System ◽  
Signal To Noise Ratio ◽  
Secret Message ◽  
Security Level ◽  
Mean Square ◽  
Signal To Noise ◽  
Protection Level ◽  
Voice Message ◽  
Least Significant Bits

Although variety in hiding methods used to protect data and information transmitted via channels but still need more robustness and difficulty to improve protection level of the secret messages from hacking or attacking. Moreover, hiding several medias in one media to reduce the transmission time and band of channel is the important task and define as a gain channel. This calls to find other ways to be more complexity in detecting the secret message. Therefore, this paper proposes cryptography/steganography method to hide an audio/voice message (secret message) in two different cover medias: audio and video. This method is use least significant bits (LSB) algorithm combined with 4D grid multi-wing hyper-chaotic (GMWH) system. Shuffling of an audio using key generated by GMWH system and then hiding message using LSB algorithm will provide more difficulty of extracting the original audio by hackers or attackers. According to analyses of obtained results in the receiver using peak signal-to-noise ratio (PSNR)/mean square error (MSE) and sensitivity of encryption key, the proposed method has more security level and robustness. Finally, this work will provide extra security to the mixture base of crypto-steganographic methods.

scholarly journals An Image Steganography Algorithm using Fractional Discrete Wavelet Transform with Advanced Encryption System

2020 ◽  
Vol 9 (5) ◽  
pp. 541-546
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Mean Square Error ◽  
Signal To Noise Ratio ◽  
Image Steganography ◽  
Discrete Wavelet ◽  
Mean Square ◽  
Signal To Noise ◽  
Noise Ratio

The research constitutes a distinctive technique of steganography of image. The procedure used for the study is Fractional Random Wavelet Transform (FRWT). The contrast between wavelet transform and the aforementioned FRWT is that it comprises of all the benefits and features of the wavelet transform but with additional highlights like randomness and partial fractional value put up into it. As a consequence of the fractional value and the randomness, the algorithm will give power and a rise in the surveillance layers for steganography. The stegano image will be acquired after administrating the algorithm which contains not only the coated image but also the concealed image. Despite the overlapping of two images, any diminution in the grade of the image is not perceived. Through this steganographic process, we endeavor for expansion in surveillance and magnitude as well. After running the algorithm, various variables like Mean Square Error (MSE) and Peak Signal to Noise ratio (PSNR) are deliberated. Through the intended algorithm, a rise in the power and imperceptibility is perceived and it can also support diverse modification such as scaling, translation and rotation with algorithms which previously prevailed. The irrefutable outcome demonstrated that the algorithm which is being suggested is indeed efficacious.

scholarly journals Analysis and Implementation of Enhanced Image Inpainting method using adjustable patch sizes

2021 ◽  
Vol 9 (3) ◽  
pp. 310-317
Keyword(s):  
Mean Square Error ◽  
Patch Size ◽  
Signal To Noise Ratio ◽  
Image Inpainting ◽  
Absolute Difference ◽  
Mean Square ◽  
Patch Selection ◽  
Signal To Noise ◽  
Distance Method ◽  
Noise Ratio

Image inpainting is the process of reconstruction of the damaged image and removal of unwanted objects in an image. In the image inpainting process patch priority andselection of best patch playsa major role. The patch size is also considered for producing good results in the image inpainting. In this paper patch priority is obtained by introducing a regularization factor (ɷ). The best patch selection is acquired by using the Sum of Absolute Difference (SAD) distance method. The results of inpainting are investigated with adjustable patch sizes of 5×5, 7×7, 9×9, 11×11, and 13×13 for the proposed method. The performance of these adjustable patch sizes is observed by using Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). The best suitable patch size for good inpainting is announced based on the values of PSNR and MSE.

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