This paper presents the computational basis for the study of Walzer and Hendel (2022), who consider the relationships between continental growth, sedimentary geology, natural climate change, and ice ages. Here we solve the full set of balance equations for mass, energy, momentum, and angular momentum for a 3D spherical-shell mantle. The assumed radial distribution of viscosity is given in Appendix B. Furthermore, the modeled viscosity depends on temperature and water concentration. The modeled mantle is internally heated by the radioactive decay of ²³⁸U, ²³⁵U, ²³²Th, and ⁴⁰K. The heat-producing elements are redistributed by chemical differentiation in spatial regions due to partial melting. Thus, in a simplified way, continental material is formed, which accumulates at the surface of a sphere, moves sideways in a non-prescribed way due to flow, and accretes to form continents. The growth curve of the total mass of continental crust resembles that of realistic geological models. We present in Appendix B the Grüneisen parameter, adiabatic temperature, thermal expansivity, and specific heat as a function of depth. The temporal distribution of juvenile additions to the continents, as obtained using our model, has a marked resemblance to global detrital zircon ages published by Puetz and Condie (2019, 2022). The results indicate the continental crust grew in an episodic manner rather than by steady state.

本文介绍了 Walzer 和 Hendel (2022) 研究的计算基础，他们考虑了大陆生长、沉积地质、自然气候变化和冰河时代之间的关系。在这里，我们求解了 3D 球壳地幔的质量、能量、动量和角动量的全套平衡方程。假定的粘度径向分布在附录 B 中给出。此外，模型粘度取决于温度和水浓度。模拟的地幔内部被²³⁸ U、²³⁵ U、²³² Th 和^{40的放射性衰变加热}K. 由于部分熔化，产热元素通过空间区域中的化学差异重新分布。因此，以一种简化的方式，大陆物质形成，它在球体表面积累，由于流动以非规定的方式侧向移动，并积聚形成大陆。大陆地壳总质量的增长曲线类似于现实地质模型。我们在附录 B 中介绍了 Grüneisen 参数、绝热温度、热膨胀率和作为深度函数的比热。使用我们的模型获得的大陆青少年添加物的时间分布与 Puetz 和 Condie（2019 年、2022 年）发表的全球碎屑锆石年龄显着相似。结果表明，大陆地壳以间歇方式而不是稳态方式生长。