SUMMARY The piezomagnetic effect is defined as a change in magnetization with applied stress. Changes in the geomagnetic field caused by the piezomagnetic effect, referred to as the piezomagnetic field, have been theoretically estimated and compared by previous studies to interpret observed variations in the geomagnetic field. However, the piezomagnetic field estimated in previous studies may not provide an accurate estimation because they ignored spatial variations in elasticity, leading to only a rough approximation of the properties of Earth's crust. In this paper, a semi-analytical procedure for calculating the piezomagnetic field arising from a point dislocation source embedded in a layered elastic medium is derived. Following a well-established method of the vector surface harmonic expansion, all of the governing equations written in partial differential equations in a real domain, together with the linear constitutive law of the piezomagnetic effect, are converted to a set of ordinary differential equations in a wavenumber domain. Equations in the wavenumber domain are solved analytically, and each component of the piezomagnetic field in the real domain is obtained after applying the Hankel transform. By using the derived procedure, the piezomagnetic and displacement fields due to a finite fault with strike-slip, dip-slip, and tensile-opening mechanisms are estimated for media with layered elasticity structures. Results for a finite fault are obtained by integrating the point source solution over the fault plane. The results of the numerical analysis allow the effect of heterogeneities in rigidity on the piezomagnetic effect to be examined and implications for the findings of previous investigations to be drawn. In cases where the moment-release at the dislocation source is fixed, the effect of the rigidity differences between upper and lower layers on the piezomagnetic field is minor even in the case where the Curie point depth is near the source of dislocation. This result is in contrast to a previous study that assumed the Mogi model and suggested that heterogeneities in the horizontal direction may be of importance when combined with layered rigidity structures. A contrast is seen between the piezomagnetic and displacement fields corresponding to models with layered rigidity structures: the piezomagnetic field is roughly proportional to the moment-release on a source fault, whereas the displacement field is proportional to slip or opening of the fault. Provided that the rigidity of the crust increases with increasing depth, the calculated piezomagnetic field is likely to have been underestimated in many earlier studies, which assumed uniform rigidity and a geodetically inverted size of slip.

中文翻译：

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层状弹性介质中与位错源相关的压电磁场

总结 压磁效应被定义为磁化强度随外加应力的变化。由压磁效应引起的地磁场变化（称为压磁场）已在理论上进行了估计，并通过先前的研究进行了比较，以解释观察到的地磁场变化。然而，先前研究中估计的压电磁场可能无法提供准确的估计，因为它们忽略了弹性的空间变化，导致只能粗略地近似地壳的性质。在本文中，推导了一种半解析程序，用于计算由嵌入层状弹性介质中的点位错源产生的压电磁场。遵循矢量表面谐波展开的成熟方法，所有在实域中用偏微分方程写成的控制方程，连同压磁效应的线性本构定律，都被转换为波数域中的一组常微分方程。对波数域的方程进行解析求解，应用汉克尔变换得到实域中压电磁场的各个分量。通过使用导出的程序，估计了具有走滑、倾滑和张开机制的有限断层引起的压磁和位移场，用于具有层状弹性结构的介质。通过在断层面上积分点源解来获得有限断层的结果。数值分析的结果允许检查刚性异质性对压磁效应的影响，并得出对先前研究结果的影响。在位错源处的力矩释放固定的情况下，即使居里点深度靠近位错源，上层和下层之间的刚度差异对压电磁场的影响也很小。该结果与之前假设 Mogi 模型的研究形成对比，该研究表明水平方向的异质性在与分层刚性结构结合时可能很重要。在对应于具有分层刚性结构的模型的压电磁场和位移场之间可以看到对比：压电磁场与源断层的力矩释放大致成正比，而位移场与断层的滑动或打开成正比。假设地壳的刚度随着深度的增加而增加，那么在许多早期的研究中，计算出的压电磁场很可能被低估了，这些研究假设了均匀的刚度和大地测量学上的滑动尺寸倒置。