Purpose

This paper aims to provide a method for obtaining physically sound temperature fields to be used in geophysical inversions in the presence of immersed essential conditions.

Design/methodology/approach

The method produces a thermal field in agreement with a given location of the interface between the Lithosphere and Asthenosphere. It leverages the known location of the interface to enforce the location of a given isotherm while relaxing other constraints known with less precision. The method splits the domain: in the Lithosphere the solution is immediately obtained by standard procedures, while in the Asthenosphere a minimization problem is solved to fulfill continuity of temperatures (strongly imposed) and fluxes at the interface (weakly imposed).

Findings

The numerical methodology, based on the relaxation of the bottom fluxes, correctly recovers the thermal field in the complete domain. To obtain bottom fluxes following geophysical expected values, a constrained minimization strategy is required. The sensitivity of the method could be improved by relaxing other quantities such as lateral fluxes or mantle velocities.

Originality/value

A statement of the energy balance problem in terms of a known immersed condition is presented. A novel numerical procedure based on a domain-splitting strategy allows the solution of the problem. The procedure is tailored to be used within geophysical inversions and provides physically sound solutions.

中文翻译：

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基于等温线参数化位置的地球物理反演的物理一致温度场

 目的

本文旨在提供一种获得物理健全温度场的方法，用于在存在浸没必要条件的情况下进行地球物理反演。

设计/方法论/途径

该方法产生与岩石圈和软流圈之间界面的给定位置一致的热场。它利用已知的界面位置来强制指定给定等温线的位置，同时放宽其他已知精度较低的约束。该方法分割了域：在岩石圈中，通过标准程序立即获得解决方案，而在软流圈中，解决最小化问题以满足界面处温度（强施加）和通量（弱施加）的连续性。

 发现

基于底部通量松弛的数值方法可以正确地恢复整个域中的热场。为了获得符合地球物理预期值的底部通量，需要采用约束最小化策略。该方法的灵敏度可以通过放宽其他量（例如横向通量或地幔速度）来提高。

 原创性/价值

给出了已知浸入条件下的能量平衡问题的陈述。基于域分割策略的新颖数值过程可以解决该问题。该程序专为在地球物理反演中使用而定制，并提供物理上合理的解决方案。