Wave tracing: Ray tracing for the propagation of band-limited signals: Part 1 — Theory

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE377-VE384 ◽  
Author(s):  
Kenneth P. Bube ◽  
John K. Washbourne
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Characteristic Frequency ◽  
Fresnel Zone ◽  
Imaging Techniques ◽  
Real Data ◽  
New Approach ◽  
Head Waves ◽  
Band Limited ◽  
Ray Bending

Many seismic imaging techniques require computing traveltimes and travel paths. Methods to compute raypaths are usually based on high-frequency approximations. In situations such as head waves, these raypaths minimize traveltime but are not paths along which most of the energy travels. We have developed a new approach to computing raypaths, using a modification of ray bending that we call wave tracing; it computes raypaths and traveltimes that are more consistent with the paths and times for the band-limited signals in real data than the paths and times obtained using high-frequency approximations. Wave tracing shortens the raypath while keeping the raypath within the Fresnel zone for a characteristic frequency of the signal.

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 2 — Applications

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE385-VE393 ◽  
Author(s):  
John K. Washbourne ◽  
Kenneth P. Bube ◽  
Pedro Carillo ◽  
Carl Addington
Keyword(s):  
Ray Tracing ◽  
Real Data ◽  
Modeling Method ◽  
Simulation Accuracy ◽  
Arrival Times ◽  
Velocity Models ◽  
Depth Images ◽  
Snell’S Law ◽  
Band Limited ◽  
Snell's Law

Modeling seismic propagation is critically important to our work; unfortunately, we often must trade simulation accuracy for reduced computational expense. We present a new seismic-modeling method that is as simple and computationally efficient as Snell’s law ray tracing but provides propagation paths and arrival times more consistent with finite-bandwidth data. We refer to this modeling method as wave tracing and apply it to nonlinear traveltime tomography and depth imaging. By replacing Snell’s law ray tracing with wave tracing, we get better ray coverage, more robust and faster ray bending (fewer iterations), and a much more robust and faster algorithm for nonlinear tomography (fewer iterations, too). A very significant benefit is increased stability and robustness of tomographic inversion with respect to small changes in model parameterization and regularization. A related benefit is the increased stability of depth images with respect to small changes in velocity, which can increase confidence in interpretation. The velocity models that result from wave tracing match picked arrival times in band-limited data better and generate improved depth images. These advantages of wave tracing relative to conventional Snell’s law ray tracing have been tested on both synthetic and real data examples for crosswell seismic geometry.

Fresnel volume ray tracing

Geophysics ◽  
1992 ◽  
Vol 57 (7) ◽  
pp. 902-915 ◽  
Author(s):  
Vlastislav Červený ◽  
José Eduardo P. Soares
Keyword(s):  
Ray Tracing ◽  
High Frequency ◽  
Fresnel Zone ◽  
Body Wave ◽  
Low Frequency ◽  
Algebraic Manipulation ◽  
Ray Method ◽  
Propagator Matrix ◽  
Paraxial Ray ◽  
Fresnel Volumes

The concept of “Fresnel volume ray tracing” consists of standard ray tracing, supplemented by a computation of parameters defining the first Fresnel zones at each point of the ray. The Fresnel volume represents a 3-D spatial equivalent of the Fresnel zone that can also be called a physical ray. The shape of the Fresnel volume depends on the position of the source and the receiver, the structure between them, and the type of body wave under consideration. In addition, the shape also depends on frequency: it is narrow for a high frequency and thick for a low frequency. An efficient algorithm for Fresnel volume ray tracing, based on the paraxial ray method, is proposed. The evaluation of the parameters defining the first Fresnel zone merely consists of a simple algebraic manipulation of the elements of the ray propagator matrix. The proposed algorithm may be applied to any high‐frequency seismic body wave propagating in a laterally varying 2-D or 3-D layered structure (P, S, converted, multiply reflected, etc.). Numerical examples of Fresnel volume ray tracing in 2-D inhomogeneous layered structures are presented. Certain interesting properties of Fresnel volumes are discussed (e.g., the double caustic effect). Fresnel volume ray tracing offers numerous applications in seismology and seismic prospecting. Among others, it can be used to study the resolution of the seismic method and the validity conditions of the ray method.

Band-limited beam propagator and its application to seismic migration

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S311-S319 ◽  
Author(s):  
Shaoyong Liu ◽  
Hanming Gu ◽  
Bingkai Han ◽  
Zhe Yan ◽  
Dingjin Liu ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Ray Tracing ◽  
Seismic Wave ◽  
Fresnel Zone ◽  
Seismic Wave Propagation ◽  
Ray Method ◽  
Ray Tracing Method ◽  
Band Limited ◽  
And Migration ◽  
Tracing Method

The ray-tracing technique under the high-frequency assumption has been widely used in seismic wave propagation and migration. However, the practical use of conventional ray tracing is limited in complicated media especially when seismic data are band limited. Besides, the ray-tracing method also suffers from shadow zones in complex media. To alleviate these problems, we have developed a band-limited beam propagator and we apply it in seismic wave propagation and migration, which is flexible to implement and can be friendly to extract angle gathers. To derive the band-limited beam propagator, the band-limited ray-tracing method is adopted to compute the central ray of the beam. These rays in the first Fresnel zone are weighted to obtain the band-limited ray based on the assumption of a local plane wave. Then, the band-limited ray is extended to the band-limited beam propagator using the paraxial approximation. Because the beam propagator has a certain beam width perpendicular to the central ray, it has better illumination than the conventional ray-tracing method, and it could partially alleviate the problem of shadow zones. Finally, we use the band-limited beam propagator to develop a band-limited beam migration and analyze the angle gathers in complicated areas. Numerical examples on synthetic models indicate that the proposed band-limited beam propagator outperforms the conventional ray method in terms of illumination. Its applications in migration determine that it could enhance the imaging quality and produce better angle gathers in a complex area.

A new method of fluxgate signal extraction

2017 ◽  
Vol 2017 (45) ◽  
pp. 83-89
Author(s):  
A.A. Marusenkov ◽  
Keyword(s):  
High Frequency ◽  
Second Harmonic ◽  
Excitation Frequency ◽  
Low Noise ◽  
Measuring System ◽  
Signal Extraction ◽  
Fluxgate Magnetometer ◽  
New Approach ◽  
Average Value ◽  
The Time Domain

Using dedicated high-frequency measuring system the distribution of the Barkhausen jumps intensity along a reversal magnetization cycle was investigated for low noise fluxgate sensors of various core shapes. It is shown that Barkhausen (reversal magnetization) noise intensity is strongly inhomogeneous during an excitation cycle. In the traditional second harmonic fluxgate magnetometers the signals are extracted in the frequency domain, as a result, some average value of reversal magnetization noises is contributed to the output signals. In order to fit better the noise shape and minimize its transfer to the magnetometer output the new approach for demodulating signals of these sensors is proposed. The new demodulating method is based on information extraction in the time domain taking into account the statistical properties of cyclic reversal magnetization noises. This approach yields considerable reduction of the fluxgate magnetometer noise in comparison with demodulation of the signal filtered at the second harmonic of the excitation frequency.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals Improving the performance of a radio-frequency localization system in adverse outdoor applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Marcelo N. de Sousa ◽  
Ricardo Sant’Ana ◽  
Rigel P. Fernandes ◽  
Julio Cesar Duarte ◽  
José A. Apolinário ◽  
...  
Keyword(s):  
Random Forest ◽  
Ray Tracing ◽  
Real World ◽  
Practical Implication ◽  
Real Life ◽  
Simulated Data ◽  
Real Data ◽  
Gradient Boosting ◽  
Real World Data ◽  
Localization Accuracy

AbstractIn outdoor RF localization systems, particularly where line of sight can not be guaranteed or where multipath effects are severe, information about the terrain may improve the position estimate’s performance. Given the difficulties in obtaining real data, a ray-tracing fingerprint is a viable option. Nevertheless, although presenting good simulation results, the performance of systems trained with simulated features only suffer degradation when employed to process real-life data. This work intends to improve the localization accuracy when using ray-tracing fingerprints and a few field data obtained from an adverse environment where a large number of measurements is not an option. We employ a machine learning (ML) algorithm to explore the multipath information. We selected algorithms random forest and gradient boosting; both considered efficient tools in the literature. In a strict simulation scenario (simulated data for training, validating, and testing), we obtained the same good results found in the literature (error around 2 m). In a real-world system (simulated data for training, real data for validating and testing), both ML algorithms resulted in a mean positioning error around 100 ,m. We have also obtained experimental results for noisy (artificially added Gaussian noise) and mismatched (with a null subset of) features. From the simulations carried out in this work, our study revealed that enhancing the ML model with a few real-world data improves localization’s overall performance. From the machine ML algorithms employed herein, we also observed that, under noisy conditions, the random forest algorithm achieved a slightly better result than the gradient boosting algorithm. However, they achieved similar results in a mismatch experiment. This work’s practical implication is that multipath information, once rejected in old localization techniques, now represents a significant source of information whenever we have prior knowledge to train the ML algorithm.

scholarly journals Sparse Functional Linear Discriminant Analysis

Biometrika ◽  
2021 ◽  
Author(s):  
Juhyun Park ◽  
Jeongyoun Ahn ◽  
Yongho Jeon
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Real Data ◽  
New Approach ◽  
Linear Discriminant ◽  
Finite Samples ◽  
Regularization Problem ◽  
Bayes Error ◽  
Functional Setting ◽  
Regularized Solution

Abstract Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is a growing interest in interpretability of the analysis, which favors a simple and sparse solution. In this work, we propose a new approach that incorporates a type of sparsity that identifies nonzero sub-domains in the functional setting, offering a solution that is easier to interpret without compromising performance. With the need to embed additional constraints in the solution, we reformulate the functional linear discriminant analysis as a regularization problem with an appropriate penalty. Inspired by the success of ℓ1-type regularization at inducing zero coefficients for scalar variables, we develop a new regularization method for functional linear discriminant analysis that incorporates an L1-type penalty, ∫ |f|, to induce zero regions. We demonstrate that our formulation has a well-defined solution that contains zero regions, achieving a functional sparsity in the sense of domain selection. In addition, the misclassification probability of the regularized solution is shown to converge to the Bayes error if the data are Gaussian. Our method does not presume that the underlying function has zero regions in the domain, but produces a sparse estimator that consistently estimates the true function whether or not the latter is sparse. Numerical comparisons with existing methods demonstrate this property in finite samples with both simulated and real data examples.

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