Abstract Shape analysis is of paramount importance in sedimentology. Particle morphology is a very useful texture parameter that provides information about particle history and is used to characterize and classify sedimentary material. Particle shape description has been both an important and a controversial subject. The most convincing description of shape defines particle shape by three hierarchical parameters: form, roundness, and surface texture (Barrett, 1980). Many different methods have been proposed to measure these parameters. Among them, Fourier shape analysis is particularly notable. Fourier analysis separates the three parameters into frequency ranges. The low frequency range is related to form, the middle frequency range to roundness and the high frequency to surface texture. However, determining where the boundaries lie between the different morphological classes is not an easy task and has been an unsolvable problem since the FSA method was first proposed. The same is true for the signal-to-noise limit. To date, this information has been obtained empirically and with great uncertainty. One of the most important contributions of this work has been to quantitatively constrain the harmonic ranges corresponding to the morphological ranges proposed by Barrett, and to determine the best possible approximation for the upper limit of the signal and the onset of noise. To estimate these ranges, we propose here two original methodologies based on analysis of the cumulative amplitude spectrum (CAS), and on simulating the effect of artificial noise acting on a well-known geometric figure. The CAS of 3664 volcaniclastic particles and of 106 artificially silhouette charts have been quadrisected into form, roundness, roughness and noise using an optimization process. The analysis indicates overall that the limits are well constrained into a narrow range of harmonics with a small variance. The results obtained are reliable and allow the range of harmonics that contains a useful signal to be extended up to harmonic 256. The method has been successfully applied to the standard figures of Krumbein (1941a) and of Powers (1953), efficiently separating the different classes of roundness. As an example, the methodology has been applied to a real-life case where there was doubt about the pristine nature of the materials from some outcrops related to the block-and-ash flow deposit of the July 17, 1999 eruption of the Colima volcano. The results obtained applying the method show promising results, indicating the potential of FSA information to solve this ambiguity. The powerful, user-friendly FSA software that we distribute freely (open code) can be very useful for characterizing volcano-sedimentary and sedimentary deposits. To date, there is no other software for FSA studies. Moreover, FSA can be useful in other fields of science and engineering where quantitative particle shape analysis is needed.

中文翻译：

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傅立叶形状分析，FSA：用于颗粒形态定量研究的免费软件

摘要 形态分析在沉积学中具有极其重要的意义。颗粒形态是一个非常有用的纹理参数，可提供有关颗粒历史的信息，并用于表征和分类沉积物质。粒子形状描述既是一个重要的话题，也是一个有争议的话题。最有说服力的形状描述通过三个层次参数来定义颗粒形状：形状、圆度和表面纹理 (Barrett, 1980)。已经提出了许多不同的方法来测量这些参数。其中，傅立叶形状分析尤为引人注目。傅里叶分析将三个参数分成频率范围。低频范围与形状有关，中频范围与圆度有关，高频范围与表面纹理有关。然而，确定不同形态类别之间的边界不是一件容易的事，并且自从首次提出 FSA 方法以来一直是一个无法解决的问题。信噪比限制也是如此。迄今为止，这些信息是凭经验获得的，并且具有很大的不确定性。这项工作最重要的贡献之一是定量约束与 Barrett 提出的形态范围相对应的谐波范围，并确定信号上限和噪声开始的最佳可能近似值。为了估计这些范围，我们在此提出了两种基于累积振幅谱 (CAS) 分析和模拟人工噪声对众所周知的几何图形的影响的原始方法。3664 个火山碎屑颗粒和 106 个人工轮廓图的 CAS 已使用优化过程四等分为形状、圆度、粗糙度和噪声。分析表明，总体而言，限制被很好地限制在具有小方差的狭窄谐波范围内。获得的结果是可靠的，并允许包含有用信号的谐波范围扩展到 256 次谐波。该方法已成功应用于 Krumbein (1941a) 和 Powers (1953) 的标准图形，有效地分离了不同的类圆度。例如，该方法已被应用于一个现实案例，该案例怀疑与 1999 年 7 月 17 日科利马火山喷发的块状灰流沉积物有关的一些露头材料的原始性质. 应用该方法获得的结果显示出有希望的结果，表明 FSA 信息具有解决这种歧义的潜力。我们免费分发的功能强大、用户友好的 FSA 软件（开放代码）对于表征火山沉积和沉积沉积非常有用。迄今为止，没有其他用于 FSA 研究的软件。此外，FSA 可用于需要定量颗粒形状分析的其他科学和工程领域。