On the Reduced Noise Sensitivity of a New Fourier Transformation Algorithm

Dobróka, Mihály; Szegedi, H.; Molnar, J. Somogyi; Szűcs, Péter

doi:10.1007/s11004-014-9570-x

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…The greatest advantage of the method is that even with the introduction of relatively few (several times ten) expansion coefficients, a suitable resolution can be achieved so that the problem to be solved leads to an overdetermined inverse problem. The method has been used in several fields: gravitational Völgyesi 2008, 2010), DC geoelectric (Gyulai et al 2010(Gyulai et al , 2017, magnetotelluric (Dobróka et al 2013), borehole geophysics (Dobróka and Szabó 2010;Dobróka et al 2016), data processing (Vass and Dobróka 2010;Dobróka et al 2015), induced polarization (Turai et al 2010;Turai and Dobróka 2011). In this paper the method of series expansion based inversion is used to evaluate induced polarization data measured on ore-bearing rock cores in laboratory, to determine the time constant spectrum and to isolate the individual polarization effects.…”

Section: Data Processing By Series Expansion Based Inversion Methodsmentioning

confidence: 99%

Evaluation of induced polarization measurements using a new inversion method

et al. 2021

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In this paper, a new inversion method is proposed to process laboratory-measured induced polarization (IP) data. In the new procedure, the concept of the series expansion-based inversion is combined with a more general definition of the objective function. The time constant spectrum of the IP effect is assumed a line spectrum approximated by a series of Dirac’s delta function resulting in a square-integrable forward problem formula. This gives the applicability of the generalized objective function. The expansion coefficients as unknowns represent the model parameters of the inversion procedure. We use the new inversion procedure on an apparent polarizability dataset measured on a rock sample originated from the Recsk ore complex, northeast Hungary. The inversion results was compared to those of three additional laboratory datasets, which were measured on samples rich in ore minerals collected from the same area. The results are compared to those given by the traditional series expansion-based least squares method. It is shown that the newly proposed method gives more accurate and stable parameter estimation.

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Section: Data Processing By Series Expansion Based Inversion Methodsmentioning

confidence: 99%

Evaluation of induced polarization measurements using a new inversion method

et al. 2021

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“…The Hermite functions meet this criterion with an additional advantage as discussed in the 1D. Dobróka et al (2015) showed that the elements of the Jacobian matrix can be considered as the inverse Fourier transform of the basis function system. Therefore, they can be calculated more easily if the basis functions are chosen from the eigenfunctions of the inverse Fourier transformation.…”

Section: The 2d Irls-ftalgorithmmentioning

confidence: 99%

“…To achieve this, a more robust inversion algorithm with higher noise reduction capabilities is required. Dobróka et al (2015) presented an inversion based 1D Fourier transformation method known as the Iteratively Reweighted Least Squares Fourier Transform (IRLS-FT) which proved to be an effective tool for noise reduction. It was shown that the noise sensitivity of the continuous Fourier transform (and its discrete variants DFT and FFT) was sufficiently reduced by using robust inversion.…”

Section: Introductionmentioning

confidence: 99%

Inversion-based fourier transformation used in processing non-equidistantly measured magnetic data

Nuamah

2019

Acta Geod Geophys

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A comprehensive robust inversion-based Fourier transformation algorithm has been proposed based on the advantages of Hermite functions for processing even in random-walk data known as the iteratively reweighted least squares fourier transformation (IRLS-FT) method. By using Hermite functions as the basis functions of discretization, the Fourier spectrum was discretized using a series expansion of which the expansion coefficients were given by a solution of a linear inverse problem. The method enabled a quicker determination of the Jacobi matrix as the Hermite functions were considered as the eigenfunctions of the inverse fourier transformation. The process was robustified using the iteratively reweighted least squares (IRLS) method with Steiner weights. The result was a very efficient, robust and resistant procedure with a higher noise reduction capability irrespective of the data acquisition protocols, thus, whether regular or irregular sampling procedure was used in acquiring the data. The Fourier transformation operation was employed in developing the new method because it facilitated data conversion from time to frequency domain. To reduce the noise sensitivity of the IRLS-FT as characterized by the traditional DFT method, the Fourier transformation was formulated as an overdetermined inverse problem permitting the required noise reduction tools to be applied. Traditionally, geophysical data are acquired on a regular equidistant grid, but the continual improvement in survey equipment's and processing tools permits non-equidistant measurements. The new applicability of the IRLS-FT is demonstrated in the reduction to the pole of synthetic magnetic data generated in the regular equidistant array and subsequently randomized to produce non-equidistant measurements along a survey line. In one dimensional study, the IRLS-FT processed waveforms were similar for both equidistant and non-equidistant sampling. An application on magnetic data showed a similar anomaly generation for DFT processed equidistant sampling and IRLS-FT processed non-equidistant sampling, indicating the new method is applicable irrespective of the sampling protocol applied in the field survey or data acquisition process. This data processing abilities of the IRLS-FT method simplifies and fasten field data acquisition as measurements are not necessarily taken on a regular grid, which gives it a competitive advantage over the traditional DFT method.

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“…However, the noise sensitivity of the processing method must be taken into account as the noise recorded in the time domain is adequately transformed into the frequency domain. In order to provide significant reduction of the impact of data noise and outliers in data processing, a more robust method known as the Steiner Iteratively Reweighted Least Square Fourier Transformation (S-IRLS-FT) was developed by Dobróka et al (2015). The algorithm was evaluated on several levels including an application on magnetic data set (Dobróka et al 2017) to prove its noise reduction capability.…”

Section: Introductionmentioning

confidence: 99%

Legendre polynomial-based robust Fourier transformation and its use in reduction to the pole of magnetic data

et al. 2021

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A new inversion based Fourier transformation technique named as Legendre-Polynomials Least-Squares Fourier Transformation (L-LSQ-FT) and Legendre-Polynomials Iteratively Reweighted Least-Squares Fourier Transformation (L-IRLS-FT) are presented. The introduced L-LSQ-FT algorithm establishes an overdetermined inverse problem from the Fourier transform. The spectrum was approximated by a series expansion limited to a finite number of terms, and the solution of inverse problem, which gives the values of series expansion coefficients, was obtained by the LSQ method. Practically, results from the least square method are responsive to data outliers, thus scattered large errors and the estimated model values may be far from reality. A definitely better option is attained by introducing Steiner’s Most Frequent Value method. By combining the IRLS algorithm with Cauchy-Steiner weights, the Fourier transformation process was robustified to give the L-IRLS-FT method. In both cases Legendre polynomials were applied as basis functions. Thus the approximation of the continuous Fourier spectra is given by a finite series of Legendre polynomials and their coefficients. The series expansion coefficients were obtained as a solution to an overdetermined non-linear inverse problem. The traditional DFT and the L-IRLS-FT were tested numerically using synthetic datasets as well as field magnetic data. The resulting images clearly show the reduced sensitivity of the newly developed L-IRLS-FT methods to outliers and scattered noise compared to the traditional DFT. Conclusively, the newly developed L-IRLS-FT can be considered to be a better alternative to the traditional DFT.

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On the Reduced Noise Sensitivity of a New Fourier Transformation Algorithm

Cited by 9 publications

References 8 publications

Evaluation of induced polarization measurements using a new inversion method

Evaluation of induced polarization measurements using a new inversion method

Inversion-based fourier transformation used in processing non-equidistantly measured magnetic data

Legendre polynomial-based robust Fourier transformation and its use in reduction to the pole of magnetic data

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