Mathematical Sciences: Presidential Young Investigator Award

这项研究涉及反问题，即从间接和扭曲的数据中推断世界。 具体例子包括：利用卫星和观测站的磁场测量来研究地核-地幔边界处的地球发电机和地球磁场。 利用地震后地面运动的观测研究地球的三维地震速度结构。 在勘探地震学、光谱学中“去模糊”图像并恢复宽带信号中缺失的频率。 反演理论的进步需要新的方法来测量给定非线性物理约束和非线性数据关系的不确定性。 将开发新技术并应用于利用非线性先验信息对非线性问题进行严格推理。

This research is concerned with Inverse Problems, that is, making inferences about the world from indirect and distorted data. Particular examples include: study of the geodynamo and earth's magnetic field at the core-mantle boundary using satellite and observatory mearurements of the magnetic field. study of the three-dimensional seismic velocity structure of Earth using observations of ground motion after earthquakes. "deblurring" images and recovery of missing frequencies in wideband signals in exploration seismology, spectroscopy. Progress in inverse theory requires new methods for measuring the uncertainty given nonlinear physical constraints, and nonlinear data relations. New techniques will be developed and applied to rigorous inference of nonlinear problems with nonlinear prior information.