Ratio‐Euler deconvolution and its applications

Huang, Liang; Zhang, Henglei; Li, Chun‐Feng; Feng, Jiashi

doi:10.1111/1365-2478.13201

Cited by 5 publications

(3 citation statements)

References 46 publications

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“…The layer recognition method based on neural networks requires a large number of samples for model training, with a large amount of computation. Moreover, data from different regions cannot be shared for learning due to their different features, resulting in low adaptability and weak stability (Zhang et al, 2017). Moreover, several scholars have conducted research on the identification methods of different media layers.…”

Section: Introductionmentioning

confidence: 99%

Research on intelligent identification algorithm of coal and rock strata based on Hilbert transform and amplitude stacking

Zhu,

Xu,

Peng

et al. 2024

Geophysical Prospecting

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The high precision identification of coal–rock layers is a significant challenge in intelligent mining. There is a large amount of electromagnetic noise and metal reflector signals in the full space detection environment of mining roadway, which makes it hard to distinguish the reflected waves at interface from a set of echo signals generated by the interface due to the similar amplitudes among them. So the method of identifying layers solely based on amplitude characteristics has poor stability and accuracy in coal mining environments. This paper proposes a method for identifying coal–rock layers based on Hilbert transform and tracking–scanning–stacking technology. There are two steps to achieve the recognition of air–coal–rock interfaces. First, by analysing the instantaneous amplitude spectrum obtained from the Hilbert transform, the first extreme point that is always the maximum value within a wavelength range is determined as the rough position of the air–coal interface. To solve the problem of recognition errors caused by noise and energy dispersion, the density difference method is used to remove discrete points. Second, the precise position of the air–coal interface is determined by tracking the extreme points within the 1.5 wavelength range around the rough position, and using the amplitude stacking method to quantitatively analyse and compare the degree of energy concentration. The data between zero time and the reflected waves at the air–coal interface is removed to avoid the impact of them on the recognition of the coal–rock interface. Results of physical model experiments and actual coal mine experiments show that this method yields better results and has high stability compared to conventional recognition method. Moreover, the average relative thickness errors are 4.5% for air layer and 4.2% for coal layer.

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Section: Introductionmentioning

confidence: 99%

Research on intelligent identification algorithm of coal and rock strata based on Hilbert transform and amplitude stacking

Zhu,

Xu,

Peng

et al. 2024

Geophysical Prospecting

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“…Euler deconvolution is suitable for the semi-automatic estimation of source locations in large-scale potential field data [ 1 , 2 , 3 , 4 , 5 ]. It originates from the overdetermined system of Euler with a large condition number, which causes significant perturbations and often shows divergent trends in Euler solutions [ 6 , 7 , 8 , 9 , 10 ]. Therefore, many researchers use the standard deviation [ 6 ] or the truncation error [ 11 ] of the overdetermined system of Euler as criteria to filter out spurious solutions.…”

Section: Introductionmentioning

confidence: 99%

FFT-Based Probability Density Imaging of Euler Solutions

Cao,

Chen,

et al. 2024

Entropy

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When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming “tail”-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with only the structural index. The nonparametric estimation method based on the normalized B-spline probability density (BSS) is used to separate the Euler solution clusters and mark different anomaly sources according to the similarity and density characteristics of the Euler solutions. For display purposes, the BSS needs to map the samples onto the estimation grid at the points where density will be estimated in order to obtain the probability density distribution. However, if the size of the samples or the estimation grid is too large, this process can lead to high levels of memory consumption and excessive computation times. To address this issue, a fast linear binning approximation algorithm is introduced in the BSS to speed up the computation process and save time. Subsequently, the sample data are quickly projected onto the estimation grid to facilitate the discrete convolution between the grid and the density function using a fast Fourier transform. A method involving multivariate B-spline probability density estimation based on the FFT (BSSFFT), in conjunction with fast linear binning appropriation, is proposed in this paper. The results of two random normal distributions show the correctness of the BSS and BSSFFT algorithms, which is verified via a comparison with the true probability density function (pdf) and Gaussian kernel smoothing estimation algorithms. Then, the Euler solutions of the two synthetic models are analyzed using the BSS and BSSFFT algorithms. The results are consistent with their theoretical values, which verify their correctness regarding Euler solutions. Finally, the BSSFFT is applied to Bishop 5X data, and the numerical results show that the comprehensive analysis of the 3D probability density distributions using the BSSFFT algorithm, derived from the Euler solution subset of x0,y0,z0, can effectively separate and locate adjacent anomaly sources, demonstrating strong adaptability.

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“…Euler deconvolution is based on Euler's homogenous function theorem, which is widely used throughout mathematics and physics. It states that for homogenous functions (i.e., those in which all terms are raised to the same power) of degree N, then [8][9][10][11]…”

Section: Introductionmentioning

confidence: 99%

Using Euler Deconvolution as Part of a Mineral Exploration Project

Cooper

2024

Minerals

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Mineral exploration projects can make considerable use of a variety of geophysical techniques and datasets, including magnetic and gravity data. The interpretation of large quantities of data can be very time consuming, so semi-automatic interpretation techniques are often used to provide initial estimates of the parameters (primarily the location and depth) of the sources of anomalies. Euler deconvolution is a commonly used interpretation method for potential fields which has a number of advantages over many other techniques, such as working in the presence of remanent magnetisation, and not being restricted to a particular model such as a contact. A second-order version of Euler’s equation is introduced here, which is much less affected by trends in the data than the standard method and additionally produces depth parabolas, which simplify the interpretation of results. The method was applied to aeromagnetic data from a mineral exploration project in Southern Africa and provided plausible results.

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Ratio‐Euler deconvolution and its applications

Cited by 5 publications

References 46 publications

Research on intelligent identification algorithm of coal and rock strata based on Hilbert transform and amplitude stacking

Research on intelligent identification algorithm of coal and rock strata based on Hilbert transform and amplitude stacking

FFT-Based Probability Density Imaging of Euler Solutions

Using Euler Deconvolution as Part of a Mineral Exploration Project

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