Pressure and temperature estimates of rocks provide the fundamental data for the investigation of many geological processes such as subduction and exhumation, and yet their determination remains extremely challenging (Tajcmanova et al. 2020). A wide variety of methods are constantly being developed to tackle the ambitious objective of pinpointing the geological history of rocks through the many complex processes often interacting with one another at depth in our planet. Analytical advances are being pushed to the limit of conventional methods, allowing information preserved by mineral, fluid, and solid inclusions to be used for high spatial resolution determinations that can unravel a large variety of processes occurring at the micro-to the nano-scale. Among these, chemical geothermobarometry that is often challenging in many rock types due to alteration processes, chemical re-equilibration, diffusion, and kinetic limitations has been increasingly coupled with elastic geothermobarometry (e.g., Anzolini et al. 2019; Gonzalez et al. 2019). Elastic geothermobarometry of host-inclusion systems, in paper Mazzucchelli et al. 2021, this issue, is a new and complementary non-destructive method (see Fig. 1 for an example) to determine the pressures (P) and temperatures (T) of inclusion entrapment (i.e., the P-T conditions attained by rocks and minerals at depth in the Earth) from the remnant stress or strain measured in inclusions still trapped in their host mineral at room conditions (e.g., Nestola et al. 2011; Howell et al. 2012; Alvaro et al. 2020).This method underwent significant developments in the past decade aimed at overcoming several serious restrictions to previously available models and methodologies, which led to questions being raised about the general validity of the method. Most of the recent developments have been focused on enhancing the method to allow its application to a broader variety of scenarios, overcoming the three major assumptions (1) linear elasticity (Angel et al. 2014); (2) spherical shape (Campomenosi et al. 2018; Mazzucchelli et al. 2018); and (3) isotropic elastic properties for the host and the inclusion, allowing its application to an increasing number of host inclusion pairs with a variety of analytical techniques (e.g., micro-Raman spectroscopy, Murri et al. 2018) and calculation methods (e.g., nonlinear elasticity and numerical modeling, Anzolini et al. 2019; Mazzucchelli et al. 2019; Morganti et al. 2020).This first part of the development essentially concerned the calculation of the mutual elastic relaxation of the host and inclusion, for which initial estimates have relied on the assumption of linear elasticity theory. Angel et al. (2014) presented a new formulation of the problem that avoids this assumption and incorporates full nonlinear elastic behavior for the host and the inclusion and has been enhanced with the progressive implementation of carefully validated equations of state for several host and inclusion phases (e.g., Angel et al. 2017a, 2020; Mihailova et al. 2019; Milani et al. 2015, 2017; Murri et al. 2019; Zaffiro et al. 2019). This finally allowed analyses incorporating the accurate behavior of quartz inclusions in garnet over a large P and T interval (Angel et al. 2017a; Morana et al. 2020). The methods and the calculation algorithm have been included in the freely available EoSFit-Pinc software (Angel et al. 2017b). The availability of the new software and algorithm strongly promoted the use of this methodology, enabling several researchers to perform their measurements and calculations independently (Anzolini et al. 2019, 2018; Nestola et al. 2016, 2018a, 2018b; Nimis et al. 2016, 2019).The second part of the development has been focused on measurements and calculations of non-spherical inclusions in complex geometrical relationships with the host and/or other inclusions. Such issues have been addressed with several numerical models on a variety of shapes by Mazzucchelli et al. (2018), producing numerical correction factors to guide the readers toward estimating the uncertainties associated with shapes different from spheres, including the complex interplay of edges and corners for which only numerical solutions can be provided. In Mazzucchelli et al. (2018), the authors estimated the maximum discrepancies caused by geometry and shape and validated their estimations against simple experimental results obtained on mechanically polished host inclusion systems by Campomenosi et al. (2018).The most complex portion of development dealt with elastic anisotropy of inclusions as this is also the largest source of uncertainties that cannot be evaluated a priori simply by looking at the sample under the optical microscope or with more complex techniques (e.g., Scanning Electron Microscopy, X-ray micro-Tomography, inter alia). The importance of elastic anisotropy essentially arises from the fact that an inclusion trapped in a host of any symmetry exhumed to the lower P and T conditions at the Earth surface is subject to the strain imposed by the host. The simplest, and yet still extremely complex, case that can be envisaged is that of a cubic host (e.g., diamond) that we will consider nearly isotropic. In this case, after exhumation, the inclusion is subject to isotropic strains imposed by the host. An anisotropic inclusion subject to isotropic strains must develop non-hydro-static stresses (Angel et al. 2019; Murri et al. 2019, 2018). This observation is sufficient to demonstrate that whatever tentative interpretation of the measured state of stress for a non-isotropic inclusion in an isometric host using conventional equations of state (as currently determined under hydrostatic compression) is meaningless. However, several tentative steps have been made to try to estimate the effect of the elastic anisotropy on (1) the calculation of the residual strain, stress, and pressures; and (2) the calculation of the entrapment conditions. For the calculation of the residual pressure, the major issue arises from measurements performed via micro-Raman where most of the studies interpret the peak shift of Raman bands (∆ω) as a pressure effect using an empirical calibration that relates Raman shift with P (e.g., Morana et al. 2020; Schmidt and Ziemann 2000). As already shown by Grüneisen (1926) and later confirmed by Angel et al. (2019) and Murri et al. (2018, 2019), this is physically incorrect as the Raman band shift depends upon the applied strains through the Grüneisen tensor rather than the applied stress through a ∆ω vs. P calibration. This fact may appear to have small effects when dealing with cubic hosts, but as shown by Bonazzi et al. (2019), the effects become non-negligible at a few gigpascals of entrapment. There are several examples (Bonazzi et al. 2019; Gonzalez et al. 2019; Thomas and Spear 2018) of inclusions with 0 kbar of residual pressure calculated from the shift of the 464 cm–1 band that instead were apparently entrapped at several kilobars, if calculations are performed via the Grüneisen tensor approximation. These calculations from the Raman shift of multiple bands are now possible through the software “Strainman” (Angel et al. 2019). The second part of the elastic anisotropy contribution plays a crucial role in calculating the entrapment conditions starting from the strains determined either from the Raman shifts or from the lattice parameters measured via X-ray diffraction (e.g., Alvaro et al. 2020). This part has been addressed by the recent publication of numerical and analytical solutions for non-isotropic, host-inclusion pairs presented in Mazzucchelli et al. (2019) and Morganti et al. (2020).The new EntraPT web application, published by Mazzucchelli et al. (2021) in American Mineralogist, provides a platform for elastic geobarometry that includes these recent advances. Thanks to this application, the user can interpret the residual strain of anisotropic inclusions in an intuitive and consistent manner. Moreover, EntraPT, that is built on the underlying code of Eosfit7c, provides the tools to perform calculations of the residual pressure and of the entrapment pressure and temperature of isotropic and anisotropic systems using a self-consistent set of thermoelastic properties (e.g., Alvaro et al. 2020; Gonzalez et al. 2019).

中文翻译：

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如何在地质学中应用弹性地压法

岩石的压力和温度估计值为研究许多地质过程（例如俯冲和掘出）提供了基础数据，但其确定仍然极具挑战性（Tajcmanova等，2020）。不断开发出各种各样的方法来解决这个雄心勃勃的目标，即通过我们地球深处经常相互作用的许多复杂过程来查明岩石的地质历史。分析的进展被推到了常规方法的极限，从而允许将矿物，流体和固体夹杂物保存的信息用于高空间分辨率测定，从而可以揭示从微观到纳米尺度的各种过程。在这些当中，化学地热气压法由于变化过程，化学再平衡，扩散和动力学局限性而在许多岩石类型中通常具有挑战性，因此越来越多地与弹性地热气压法结合使用（例如Anzolini等人2019; Gonzalez等人2019）。Mazzucchelli等人在论文中对宿主-包裹体系统的弹性地热大气压力法进行了研究。2021年这个问题是一种新的互补性非破坏性方法（例如，见图1），用于确定夹杂物夹带的压力（P）和温度（T）（即，岩石和矿物在PT达到的PT条件）。残余应力或应变的测量结果，这些残余应力或应变是在室温下仍被困在其宿主矿物中的夹杂物所测得的（例如，Nestola等人2011； Howell等人2012； Alvaro等人2020）。在过去的十年中，该方法经历了重大发展，旨在克服对先前可用的模型和方法的若干严重限制，从而导致对该方法的一般有效性提出了疑问。克服了三个主要假设（1）线性弹性（Angel等人，2014）；大多数最新进展都集中在增强该方法，以使其可应用于更广泛的场景中。（2）球形（Campomenosi等人2018; Mazzucchelli等人2018）; （3）主体和包裹体的各向同性弹性特性，使其能够通过各种分析技术（例如，显微拉曼光谱法，Murri等人，2018）和计算方法（例如， ，非线性弹性和数值建模，Anzolini等。2019; Mazzucchelli等。2019; Morganti等。2020年）。开发的第一部分主要涉及主体与夹杂物的相互弹性松弛的计算，对此的初步估计依赖于线性弹性理论的假设。安吉尔（Angel）等。（2014年）提出了一个新的问题表述，它避免了这种假设，并为主体和包含物引入了完全非线性的弹性行为，并随着逐步实施了针对几个主体和包含物阶段的状态方程的仔细验证而得到了增强（例如，Angel等人2017a，2020; Mihailova等人2019; Milani等人2015，2017; Murri等人2019; Zaffiro等人2019）。这最终允许进行分析，并在较大的P和T区间内纳入石榴石中石英夹杂物的准确行为（Angel等人2017a; Morana等。2020）。这些方法和计算算法已包含在免费提供的EoSFit-Pinc软件中（Angel等人2017b）。新软件和算法的可用性极大地促进了这种方法的使用，使一些研究人员能够独立进行测量和计算（Anzolini等人2019，2018; Nestola等人2016，2018a，2018b; Nimis等人2016 ，2019）。开发的第二部分重点在于与主体和/或其他夹杂物具有复杂几何关系的非球形夹杂物的测量和计算。Mazzucchelli等人已经通过各种形状的几个数值模型解决了这些问题。（2018），产生数值校正因子以指导读者估计与不同于球体的形状相关的不确定性，包括边缘和拐角的复杂相互作用，为此只能提供数值解。在Mazzucchelli等人中。（2018），作者估计了由几何形状和形状引起的最大差异，并根据Campomenosi等人在机械抛光的宿主夹杂物系统上获得的简单实验结果验证了他们的估计。（2018）。发展中最复杂的部分涉及夹杂物的弹性各向异性，因为这也是不确定性的最大来源，无法简单地通过光学显微镜或更复杂的技术（例如扫描）观察样本就无法进行先验评估电子显微镜，X射线显微断层摄影术等）。弹性各向异性的重要性主要源于以下事实：捕获在地球表面较低的P和T条件下的任何对称主体中所捕获的夹杂物，都会受到主体施加的应变。可以设想的最简单但仍然极其复杂的情况是立方主体（例如钻石）的情况，我们将其视为近似各向同性的。在这种情况下，发掘后，夹杂物受到宿主施加的各向同性应变。受各向同性应变作用的各向异性夹杂物必须产生非静水应力（Angel等人2019; Murri等人2019，2018）。该观察结果足以证明，使用常规的状态方程式（目前在静水压下确定），对等轴测主体中非各向同性夹杂物的应力测量状态的任何初步解释都是没有意义的。但是，已经采取了一些试验性步骤来尝试估计弹性各向异性对（1）残余应变，应力和压力的计算的影响；（2）诱捕条件的计算。对于残余压力的计算，主要问题来自通过微型拉曼进行的测量，其中大多数研究使用经验性校准将拉曼带的峰移（Δω）解释为压力效应，该经验校准将拉曼移与P（例如Morana等，2020； Schmidt和Ziemann，2000）。如Grüneisen（1926）所示，后来由Angel等证实。（2019）和Murri等人。（2018，2019），这在物理上是不正确的，因为拉曼带移取决于通过Grüneisen张量施加的应变，而不是通过Δωvs.P校准施加的应力。当处理立方宿主时，这一事实似乎影响很小，但正如Bonazzi等人所表明的那样。（2019），这种影响在几千兆帕斯卡内的滞留下变得不可忽略。有几个例子（Bonazzi等，2019年； Gonzalez等，2019年； Thomas和Spear，2018年），通过464 cm-1谱带的移动计算出的残余压力为0 kbar，显然包裹在几千kbar的夹杂物，如果通过Grüneisen张量逼近执行计算。现在可以通过软件“ Strainman”（Angel等人，2019）从多个波段的拉曼位移进行这些计算。弹性各向异性的第二部分在计算包裹条件时起着至关重要的作用，该包裹条件从拉曼位移或通过X射线衍射测量的晶格参数确定的应变开始（例如，Alvaro等人，2020年）。Mazzucchelli等人最近发表的有关非各向同性，主体-夹杂物对的数值和分析解决方案的出版物解决了这一部分的问题。（2019）和Morganti等人。（2020）。新的EntraPT网络应用程序，由Mazzucchelli等发布。American Mineralogist等人（2021年）提供了一个弹性地压法平台，其中包括这些最新进展。多亏了这个应用程序，用户可以直观，一致的方式解释各向异性夹杂物的残余应变。此外，基于Eosfit7c的基础代码构建的EntraPT提供了使用一组自洽的热弹性特性（例如Alvaro等）来计算各向同性和各向异性系统的残余压力以及包封压力和温度的工具。等人，2020年；冈萨雷斯等人，2019年）。