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

数千年来，壮丽的山脉吸引了诗人、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对山的侵蚀如何相互作用形成地形，目前是地球科学研究的前沿。在研究山脉的演变时，一个基本的问题是：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。近年来，造山和侵蚀过程计算机模拟的发展以及地球化学的发展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）的进步现在允许用地球化学（温度计）数据来测试计算机模型预测，这些数据来自今天暴露在地球表面的岩石。这些数据记录了岩石因侵蚀和断层作用被挖掘到地表时的冷却历史。这个跨学科的项目正在解决的问题和假设是量化山地地形演变的基础，包括：(1)如何通过整合温度计数据、计算机建模和数学来改进对影响山地地形的构造和地貌过程的有意义的地质解释？(2)温度表数据对不同造山和侵蚀过程的敏感性如何？如何优化采样策略以改善解释？(3)从温度表数据的数学反演中可以解决的地形变化的幅度和速率是多少？为了解决这些问题，本项目利用综合模型研究了山地地形演变的正、逆问题。除了考虑冰川、河流和山坡侵蚀过程的地表过程模型外，还在开发耦合的三维热、水文和运动学计算机模型。利用该耦合模型探讨了测温仪数据对不同过程的敏感性，并用数学方法反演了bc省南部海岸山脉的新测温仪和现有测温仪样本的密集网络，用于区域古地形。正在进行实地工作，以收集更多的数据。一些新的数学技术也在发展中。特别是，低通滤波技术和正则化迭代方法被用于解决众所周知的病态反抛物方程和大规模非线性逆热传递方程。这些问题本质上是跨学科的，处于预测和解释温度计数据和山地地形的前沿。

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.