CMG: Improved Seismic Inference via Better Spectrum Estimation

CMG RESEARCH：通过更好的频谱估计改进地震推断知识优点：地震学中的许多推断，从正常模式研究到断层机制分析，都依赖于对频谱的可靠估计，可能更重要的是，对其不确定性的可靠估计。该提案中数学和地球物理学之间的合作努力是由地震学领域的高动态范围宽带传感器网络的开发和部署所驱动的，这需要开发和实施复杂的数据分析工具，以更好地了解震源和地球结构。瞬态弹体波（P波和S波）的谱提供了震源性质和物理的基本信息和约束条件。目前，地震物理研究的最新进展是震源参数的估计，通常是从瞬态地震波的频谱中估计出来的。随着复杂技术的发展，光谱分析最近经历了一场革命，在这种技术中，数据依次乘以一组旨在最大化分辨率和最小化偏差的圆锥。除了在保持给定分辨率的同时最小化偏置之外，多锥度方法还允许估计功率谱中特征的统计显著性。发展二次逆理论，不仅利用频谱估计器，而且利用频谱的时间和频率导数，产生更高分辨率的光谱。本课题将该理论从单变量理论扩展到广义多元理论。虽然这里讨论的应用是地震，但很明显，还有其他地球物理、科学和工程应用将从拟议的研究中受益。显而易见的候选者是气候研究（包括古代和现代）和空间物理学。更广泛的影响：促进发现和理解，同时促进教学，培训和学习。通过少数民族学生的参与和以英语和西班牙语提供项目相关网页，扩大代表性不足群体的参与。结果的广泛传播将通过会议报告、期刊文章和网络报告来完成。

CMG RESEARCH: Improved Seismic Inference via Better SpectrumEstimationIntellectual Merits: Much of the inference in seismology, from normal--mode studies toanalysis of faulting mechanisms, depends on having reliable estimates of spectra and, possiblymore important, reliable estimates of their uncertainties. The collaborative effort betweenmathematics and geophysics in this proposal is being driven by the development and deploymentof high dynamic range broadband sensors networks in the field of seismology that require thedevelopment and implementation of sophisticated data analysis tools to create a betterunderstanding of the earthquake source and Earth structure.The spectra of the transient elastic body waves (P and S waves) provide fundamentalinformation and constraints on earthquake source properties and physics. Currently the state-of-the-art for the study of the physics of earthquakes is the estimation of source parameters, usuallyestimated from the spectra of the transient seismic waves.Spectral analysis has recently undergone a revolution with the development ofsophisticated techniques in which the data are multiplied in turn by a set of tapers that aredesigned to maximize resolution and minimize bias. In addition to minimizing the bias whilemaintaining a given resolution, the multi-taper approach allows an estimate of the statisticalsignificance of features in the power spectrum. Developing quadratic inverse theory that utilizesnot only the spectral estimators, but the time and frequency derivatives of the spectrum, togenerate a much higher resolution spectra. This project will extend this theory from a univariatetheory to generalized multivariate theory. While the applications discussed here are seismic, it isclear that there are other geophysical, scientific, and engineering applications that will benefitfrom the proposed studies. Obvious candidates are climate studies (both paleo and modern), andspace physics.Broader Impacts: Advancing discovery and understanding while promoting teaching, training,and learning. Broaden participation of underrepresented groups by participation of minoritystudents and by presenting project related web pages in English and Spanish. Broaddissemination of results will be accomplished through conference presentations, journal articles,and web presentations.