Collaborative Research: CMG --Quantifying Tectonic and Geomorphic Interpretations of Thermochronometer Data with Inverse Problem Theory

数千年来，雄伟的山脉地形一直吸引着诗人、艺术家和科学家的注意。数百万年来，造山的板块构造过程和地表过程造成的山脉侵蚀如何相互作用而产生地形，现在处于地球科学研究的前沿。研究山脉演化时产生的一个基本问题是：过去的山脉地形是什么样子的？事实证明，这个问题很难回答。在造山和侵蚀过程的计算机模拟方面的最新进展，以及在地球化学方面的进展，都在重建古地形方面取得了进展。新的地球化学技术和数学(反问题理论)的进步现在使人们能够用今天暴露在地球表面的岩石的地球化学(热时计)数据来测试计算机模型预测。这些数据记录了岩石被侵蚀和断层作用挖掘到地表时的冷却历史。这个跨学科的项目正在解决对山脉地形演化进行量化的基本问题和假设，包括：(1)如何从温度计时仪数据、计算机建模和数学的集成来改进对影响山脉地形的构造和地貌过程的地质意义的解释？(2)温度计时仪数据对不同的造山和侵蚀过程有多敏感？如何优化采样策略以提高解释？以及(3)通过温度计时数据的数学反演可以解决的地形变化的大小和速率是多少？为了解决这些问题，本项目研究了山区地形演化的正反问题，并建立了一个综合模型。除了考虑冰川、河流和山坡侵蚀过程的表面过程模型外，耦合的3D热、水文和运动学计算机模型正在开发中。耦合模型被用来探索温度计时数据对不同过程的敏感性，并对来自不列颠哥伦比亚省南部海岸山脉的新的和现有的温度计时样本的密集网络进行数学反演，以用于区域古地形。收集更多数据的实地工作正在进行中。几种新的数学技术也在开发中。特别是，低通滤波技术和正则化迭代方法被用来求解出臭名昭著的不适定的反向抛物型方程和大规模的非线性逆热传输方程。这些问题本质上是跨学科的，在预测和解释温度计时数据和山脉地形方面处于领先地位。

The grandeur of mountain topography has for millennia captured the attention of poets, artists, and scientists. How plate tectonic processes of mountain building and mountain erosion by surface processes interact to produce topography over millions of years is now at the forefront of Earth science research. A fundamental question that arises when studying the evolution of mountains is: what did the past topography of mountain ranges look like? This question has proven very difficult to answer. Recent developments in both computer modeling of mountain building and erosional processes, and developments in geochemistry have made progress in reconstructing paleotopography. Advances in new geochemical techniques and mathematics (inverse problem theory) now allow a means of testing computer model predictions with geochemical (thermochronometer) data from rocks exposed at the Earth's surface today. These data record the cooling history of rocks as they are exhumed to the surface by erosion and faulting. This interdisciplinary project is addressing questions and hypotheses that are fundamental to quantifying the evolution of mountain topography including: (1) How can geologically meaningful interpretations of tectonic and geomorphic processes influencing mountain topography be improved from an integration of thermochronometer data, computer modeling, and mathematics? (2) How sensitive are thermochronometer data to different mountain building and erosional processes and how can sampling strategies be optimized to improve interpretations? and (3) What is the magnitude and rate of topographic change that can be resolved from mathematical inversion of thermochronometer data? To address these questions, this project investigates the forward and inverse problems of mountain topographic evolution with a comprehensive model. Coupled 3D thermal, hydrologic, and kinematic computer models are under development in addition to a surface process model accounting for glacial, fluvial, and hillslope erosional processes. The coupled model is used to explore the sensitivity of thermochronometer data to different processes and mathematically invert a dense network of new and existing thermochronometer samples from the southern Coast Mountains, B.C., for the regional paleotopography. Field work is in progress for the collection of additional data. Several novel mathematical techniques are also under development. In particular, a low pass filter technique and a regularized iterative method are being used to solve the notoriously ill-posed backward parabolic equation and large scale, nonlinear inverse heat transport equation. These problems are by nature interdisciplinary and in the forefront of predicting and interpreting thermochronometer data and mountain topography.