scholarly journals Fast interpolation method for surfaces with faults by multi-scale second-derivative optimization

2020 ◽  
Vol 75 ◽  
pp. 62
Author(s):  
Michel Léger ◽  
Vincent Clochard
Keyword(s):  
Seismic Data ◽  
Single Unit ◽  
Input Data ◽  
Structural Model ◽  
Interpolation Method ◽  
Second Derivative ◽  
Multi Scale ◽  
Surface Interpolation ◽  
First Derivative ◽  
Fault Network

We present a smooth surface interpolation method enabling to take discontinuities (e.g. faults) into account that can be applied to any dataset defined on a regular mesh. We use a second-derivative multi-scale minimization based on a conjugate gradient method. Our multi-scale approach allows the algorithm to process millions of points in a few seconds on a single-unit workstation. The interpolated surface is continuous, as well as its first derivative, except on some lines that have been specified as discontinuities. Application in geosciences are numerous, for instance when a structural model is to be built from points picked on seismic data. The resulting dip of interpolation extends the dip of the input data. The algorithm also works if faults are given by broken lines. We present results from a synthetic and real examples taking into account fault network.

What can machine learning do for seismic data processing? An interpolation application

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. V163-V177 ◽  
Author(s):  
Yongna Jia ◽  
Jianwei Ma
Keyword(s):  
Machine Learning ◽  
Seismic Data ◽  
Input Data ◽  
Interpolation Method ◽  
Window Size ◽  
Tight Frame ◽  
Training Data ◽  
Low Rank ◽  
Support Vector ◽  
Data Sets

Machine learning (ML) systems can automatically mine data sets for hidden features or relationships. Recently, ML methods have become increasingly used within many scientific fields. We have evaluated common applications of ML, and then we developed a novel method based on the classic ML method of support vector regression (SVR) for reconstructing seismic data from under-sampled or missing traces. First, the SVR method mines a continuous regression hyperplane from training data that indicates the hidden relationship between input data with missing traces and output completed data, and then it interpolates missing seismic traces for other input data by using the learned hyperplane. The key idea of our new ML method is significantly different from that of many previous interpolation methods. Our method depends on the characteristics of the training data, rather than the assumptions of linear events, sparsity, or low rank. Therefore, it can break out the previous assumptions or constraints and show universality to different data sets. In addition, our method dramatically reduces the manual workload; for example, it allows users to avoid selecting the window size parameters, as is required for methods based on the assumption of linear events. The ML method facilitates intelligent interpolation between data sets with similar geomorphological structures, which can significantly reduce costs in engineering applications. Furthermore, we combine a sparse transform called the data-driven tight frame (so-called compressed learning) with the SVR method to improve the training performance, in which the training is implemented in a sparse coefficient domain rather than in the data domain. Numerical experiments show the competitive performance of our method in comparison with the traditional [Formula: see text]-[Formula: see text] interpolation method.

Effects of incomplete parameterization on full-wavefield viscoelastic seismic data for petrophysical reservoir properties

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. O9-O17 ◽  
Author(s):  
Upendra K. Tiwari ◽  
George A. McMechan
Keyword(s):  
Seismic Data ◽  
Input Data ◽  
Elastic Model ◽  
Quality Factors ◽  
Noise Levels ◽  
Reservoir Properties ◽  
Estimated Parameters ◽  
Model Parameterization ◽  
The Earth ◽  
Incomplete Model

In inversion of viscoelastic full-wavefield seismic data, the choice of model parameterization influences the uncertainties and biases in estimating seismic and petrophysical parameters. Using an incomplete model parameterization results in solutions in which the effects of missing parameters are attributed erroneously to the parameters that are included. Incompleteness in this context means assuming the earth is elastic rather than viscoelastic. The inclusion of compressional and shear-wave quality factors [Formula: see text] and [Formula: see text] in inversion gives better estimates of reservoir properties than the less complete (elastic) model parameterization. [Formula: see text] and [Formula: see text] are sensitive primarily to fluid types and saturations. The parameter correlations are sensitive also to the model parameterization. As noise increases in the viscoelastic input data, the resolution of the estimated parameters decreases, but the parameter correlations are relatively unaffected by modest noise levels.

scholarly journals Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 52
Author(s):  
Tongtong Liu ◽  
Lingli Cui ◽  
Chao Zhang
Keyword(s):  
Frequency Conversion ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Operating Efficiency ◽  
Planetary Gearbox ◽  
Noise Interference ◽  
Multi Scale ◽  
Morphological Filtering ◽  
Diagnosis Method ◽  
Simulation Signal

The turn domain resampling (TDR) method is proposed in the paper on the basis of the existing angle domain resampling for solving the problem of non-fixed fault frequency under variable working conditions. TDR can select the appropriate sampling order according to the influence of frequency conversion, which avoided the error caused by the spline interpolation method. It can provide accurate parameters for the subsequent calculation of the equivalent frequency order. Variable multi-scale morphological filtering (VMSMF) method is proposed for the purpose of further reducing the interference of noise in resampling signal to feature extraction. VMSMF adaptively selects structural elements according to the parameter change of impact signal to make its scale more targeted. It only needs to calculate once using the optimal structural unit for a particular impact, and the filtering accuracy and operating efficiency have been greatly improved. The main steps of this article are as follows. First, the TDR is used to resample the original signal as to get the resampling signal which is still submerged by the strong noise. In the second step, VMSMF is used to filter the resampling signal to obtain the signal with less noise interference. Finally, the fault characteristics of the filtering signal was extracted and compared with the possible fault frequency calculated by the sampling parameters provided by resampling, so as to determine the fault type of the planetary gearbox. By analyzing the simulation signal and the experimental signal respectively, this method can find out the corresponding fault characteristics effectively.

scholarly journals Appraising structural interpretations using seismic data — Theoretical elements

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N29-N40
Author(s):  
Modeste Irakarama ◽  
Paul Cupillard ◽  
Guillaume Caumon ◽  
Paul Sava ◽  
Jonathan Edwards
Keyword(s):  
Seismic Data ◽  
Structural Model ◽  
Synthetic Data ◽  
Target Region ◽  
Structural Interpretation ◽  
Vertical Seismic Profiling ◽  
Seismic Image ◽  
Vsp Data ◽  
Phase Shift Data ◽  
Seismic Images

Structural interpretation of seismic images can be highly subjective, especially in complex geologic settings. A single seismic image will often support multiple geologically valid interpretations. However, it is usually difficult to determine which of those interpretations are more likely than others. We have referred to this problem as structural model appraisal. We have developed the use of misfit functions to rank and appraise multiple interpretations of a given seismic image. Given a set of possible interpretations, we compute synthetic data for each structural interpretation, and then we compare these synthetic data against observed seismic data; this allows us to assign a data-misfit value to each structural interpretation. Our aim is to find data-misfit functions that enable a ranking of interpretations. To do so, we formalize the problem of appraising structural interpretations using seismic data and we derive a set of conditions to be satisfied by the data-misfit function for a successful appraisal. We investigate vertical seismic profiling (VSP) and surface seismic configurations. An application of the proposed method to a realistic synthetic model shows promising results for appraising structural interpretations using VSP data, provided that the target region is well-illuminated. However, we find appraising structural interpretations using surface seismic data to be more challenging, mainly due to the difficulty of computing phase-shift data misfits.

Rapidly convergent Steffensen-based methods for unconstrained optimization

2019 ◽  
Vol 53 (2) ◽  
pp. 657-666
Author(s):  
Mohammad Afzalinejad
Keyword(s):  
Unconstrained Optimization ◽  
Newton's Method ◽  
Optimization Problems ◽  
Quadratic Model ◽  
Second Derivative ◽  
Rapid Convergence ◽  
First Derivative ◽  
Unconstrained Optimization Problems ◽  
Derivative Free ◽  
Steffensen Method

A problem with rapidly convergent methods for unconstrained optimization like the Newton’s method is the computational difficulties arising specially from the second derivative. In this paper, a class of methods for solving unconstrained optimization problems is proposed which implicitly applies approximations to derivatives. This class of methods is based on a modified Steffensen method for finding roots of a function and attempts to make a quadratic model for the function without using the second derivative. Two methods of this kind with non-expensive computations are proposed which just use first derivative of the function. Derivative-free versions of these methods are also suggested for the cases where the gradient formulas are not available or difficult to evaluate. The theory as well as numerical examinations confirm the rapid convergence of this class of methods.

scholarly journals Analysis of the Acid Detergent Fibre Content in Turnip Greens and Turnip Tops (Brassica rapa L. Subsp. rapa) by Means of Near-Infrared Reflectance

Foods ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 364 ◽  
Author(s):  
Sara Obregón-Cano ◽  
Rafael Moreno-Rojas ◽  
Ana María Jurado-Millán ◽  
María Elena Cartea-González ◽  
Antonio De Haro-Bailón
Keyword(s):  
Standard Error ◽  
Near Infrared ◽  
Mathematical Treatment ◽  
Second Derivative ◽  
Infrared Reflectance ◽  
Near Infrared Reflectance ◽  
First Derivative ◽  
Acid Detergent Fibre ◽  
Turnip Greens ◽  
Turnip Tops

Standard wet chemistry analytical techniques currently used to determine plant fibre constituents are costly, time-consuming and destructive. In this paper the potential of near-infrared reflectance spectroscopy (NIRS) to analyse the contents of acid detergent fibre (ADF) in turnip greens and turnip tops has been assessed. Three calibration equations were developed: in the equation without mathematical treatment the coefficient of determination (R2) was 0.91, in the first-derivative treatment equation R2 = 0.95 and in the second-derivative treatment R2 = 0.96. The estimation accuracy was based on RPD (the ratio between the standard deviation and the standard error of validation) and RER (the ratio between the range of ADF of the validation as a whole and the standard error of prediction) of the external validation. RPD and RER values were of 2.75 and 9.00 for the treatment without derivative, 3.41 and 11.79 with first-derivative, and 3.10 and 11.03 with second-derivative. With the acid detergent residue spectrum the wavelengths were identified and associated with the ADF contained in the sample. The results showed a great potential of NIRS for predicting ADF content in turnip greens and turnip tops.

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