以FT为基础的概率密度成像对欧勒解决方案的成像.
Shujin Cao1,2,3, Peng Chen1, Guangyin Lu2
1School of Earth Sciences and Spatial Information Engineering, Hunan University of Science and Technology, Xiangtan 411201, China.
Entropy (Basel, Switzerland)
|June 26, 2024
概括
一种新的B-spline概率密度 (BSS) 方法有效地分离欧勒解卷解决方案,克服了传统技术的局限性. 这种方法可以准确地识别异常源,即使在像 Bishop 5X.这样的复杂数据集中也是如此.
科学领域:
- 地质物理学 地质物理学
- 潜在场解释 潜在场解释
- 计算地震学计算地震学
背景情况:
- 传统的欧勒解卷努力区分真正的异常与虚假的欧勒尾巴,仅使用结构指数.
- 现有的方法需要手动干预或复杂的过来移除错位的欧勒溶液,影响效率和准确性.
- 规范化的B-spline概率密度 (BSS) 方法提供了一种数据驱动的方法,可以根据溶液相似性和密度对异常源进行集群和划分.
研究的目的:
- 引入BSS方法的计算效率高的算法,解决与大型数据集相关的内存和时间限制.
- 开发和验证基于快速里叶变换 (BSSFFT) 结合快速线性分类的多变量B线分线概率密度估计方法.
- 为了证明BSSFFT算法的有效性,在地理物理数据中分离和定位相邻的异常源.
主要方法:
- 一个快速的线性分类近似算法被集成到BSS中,以加速样本投射到估计网格上.
- 快速里叶变换 (FFT) 用于在网格和密度函数之间实现高效的离散卷积.
- 拟议的BSSFFT算法使用随机正常分布,合成模型和真实地质物理数据 (Bishop 5X) 进行了验证.
主要成果:
- BSS和BSSFFT算法准确地估计了概率密度函数,与真实的pdfs和高斯核光滑进行了验证.
- 使用BSS和BSSFFT对合成模型的分析产生了与理论值一致的欧勒解决方案,证实了算法的正确性.
- 对Bishop 5X数据的应用表明了BSSFFT通过3D概率密度分析有效分离和定位相邻异常源的能力.
结论:
- 结合快速线性分组和FFT的BSSFFT算法为欧勒解卷分析提供了强大而高效的解决方案.
- 这种方法显著提高了在地球物理数据集中区分和界定多个紧密相距的异常源的能力.
- BSSFFT算法表现出强大的适应性和实际实用性,用于解释复杂的潜在现场数据.
相关概念视频
Euler Equations of Motion
209
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
209
Euler's Formula for Pin-Ended Columns
304
In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
To calculate the critical load,...
To calculate the critical load,...
304
Euler's Equations of Motion
442
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
442
Euler's Formula to Columns: Problem Solving
225
Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
The system comprises two vertical rigid bars, AB and BC,...
The system comprises two vertical rigid bars, AB and BC,...
225
Exponential Fourier series
193
In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
Euler's identity...
193
Fast Fourier Transform
301
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
The computational efficiency of the FFT becomes...
301


