DOI:10.1038/s43017-023-00497-8

Abstract

Anthropogenic operations involving underground fluid extraction or injection can cause unexpectedly large and even damaging earthquakes, despite operational and regulatory efforts. In this Review, we explore the physical mechanisms of induced seismicity and their fundamental applications to modelling, forecasting, monitoring and mitigating induced earthquakes. The primary mechanisms of injection-induced earthquakes considered important for creating stress perturbations include pore-pressure diffusion, poroelastic coupling, thermoelastic stresses, earthquake interactions and aseismic slip.

尽管在操作和监管方面做出了努力，但涉及地下流体提取或注入的人为操作可能会引发意想不到的大地震，甚至是破坏性地震。在本综述中，我们将探讨诱发地震的物理机制及其在模拟、预测、监测和减轻诱发地震方面的基本应用。注水诱发地震的主要机制被认为是产生应力扰动的重要因素，包括孔隙压力扩散、孔弹性耦合、热弹性应力、地震相互作用和无震滑移。

Extraction-induced earthquakes are triggered by differential compaction linked with poroelastic effects and reservoir creep. Secondary mechanisms include reducing the rock mass strength subject to stress corrosion, dynamic weakening and cohesion loss. However, constraining the maximum magnitude, $M_{\text{max}}$, of a potential earthquake on the basis of physical process understanding is still challenging.

开采引起的地震是由与孔弹性效应和储层蠕变有关的压实差异引发的。次要机制包括应力腐蚀、动态削弱和内聚力损失导致岩体强度降低。然而，根据对物理过程的理解来确定潜在地震的最大震级（$M_{\text{max}}$）仍然具有挑战性。

Common $M_{\text{max}}$ theories are based on injection volume as the single source of strain, which might not be efficient in seismically active regions. Alternative time-based $M_{\text{max}}$ models have the potential to explain why some induced earthquake events tap into tectonic strain and lead to runaway ruptures (in which the rupture front extends beyond the perturbed rock volume). Developments in physics-based forecasting and potential future success in mitigation of induced-seismic risk could help increase the acceptance of emerging energy technologies such as enhanced geothermal systems and underground gas storage during the sustainable transition.

常见的 $M_{\text{max}}$ 理论以注入量为单一应变源，这在地震活跃地区可能并不有效。另一种基于时间的 $M_{\text{max}}$ 模型有可能解释为什么一些诱发地震事件会利用构造应变并导致失控破裂（破裂前沿超出扰动岩石体积）。基于物理学的预测的发展以及未来在减轻诱发地震风险方面可能取得的成功，有助于在可持续转型期间提高对新兴能源技术（如增强型地热系统和地下天然气储存）的接受程度。

Key points

• Induced earthquakes are primarily triggered by stress perturbations that destabilize pre-existing critically stressed faults. However, industrial operations can also reactivate faults that were not initially critically stressed.

• 诱发地震主要是由应力扰动引发的，应力扰动破坏了原有的严重受压断层的稳定性。然而，工业生产也会重新激活最初并未严重受压的断层。

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• The major triggering mechanism of injection-induced seismicity is pore-pressure diffusion, which reduces the normal stress acting on fractures and fault planes. The main mechanism of extraction-induced seismicity is poroelasticity, which affects the stress field in the surrounding rock formations and can trigger earthquakes.

• 注入诱发地震的主要触发机制是孔隙压力扩散，它降低了作用在裂缝和断层面上的法向应力。开采诱发地震的主要机制是孔隙弹性，它会影响周围岩层的应力场，从而引发地震。

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• The occurrence of large-magnitude-induced earthquake events supports the hypothesis that the maximum earthquake magnitude is likely controlled by regional tectonics. Particularly, in seismically active regions, the tectonic source of strain often controls the extent of rupture on critically stressed faults.

• 大震级地震事件的发生支持了最大震级可能受区域构造控制的假设。特别是在地震活跃地区，构造应变源往往控制着严重受压断层的破裂范围。

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• Fluid injection volume is not the only controlling parameter of maximum earthquake magnitude, and other factors such as the time elapsed from beginning of fluid extraction or injection (the triggering time) might have a substantial role. Triggering time is likely related to the time required to perturb the stress or strength of pre-existing faults.

• 流体注入量并不是控制最大震级的唯一参数，其他因素，如从开始抽取或注入流体起 所经过的时间（触发时间），可能也有重要作用。触发时间可能与扰动原有断层的应力或强度所需的时间有关。

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• Accurate estimates of maximum magnitude can be aided when an inventory of pre-existing critically stressed faults, detailed in situ stress information and a physical understanding of the processes that control the rupture dynamics are available.

• 如果能够获得先前存在的严重受压断层的清单、详细的现场应力信息以及对控制断裂动态过程的物理理解，就可以帮助准确估算最大震级。

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• Experiments in in situ underground laboratories with extensive monitoring systems and well-characterized rock mass provide a unique opportunity to test the methodological advances in managing seismicity and the effectiveness of numerical models at resolving coupled processes.

在拥有广泛监测系统和特征明确岩体的原地地下实验室进行的实验，为检验地震管理方法的进步和数值模型在解决耦合过程方面的有效性提供了一个独特的机会。

Introduction

The occurrence of moderate-to-large-magnitude-induced earthquakes (magnitudes above 4) has created negative social, environmental and economic consequences. Such earthquakes can be felt by the public, damage surface infrastructures, cause casualties and lead to the suspension of the industrial projects. Potential causes include anthropogenic activities such as water impoundment behind dams, geothermal developments, hydraulic fracturing of unconventional hydrocarbon reservoirs, conventional hydrocarbon recovery, waste- water disposal (WWD), underground gas or CO2 storage (UGS) and mining operations (Fig. 1).

中、大震级地震（震级在 4 级以上）的发生对社会、环境和经济造成了负面影响。公众能感知到这种地震，地表基础设施会受到破坏，造成人员伤亡，并导致工业项目停工。潜在的原因包括人为活动，如大坝蓄水、地热开发、非常规碳氢化合物储层的水力压裂、常规碳氢化合物回收、废水处理（WWD）、地下天然气或二氧化碳储存（UGS）以及采矿作业（图 1）。

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Many documented induced earthquakes were explained by the seismogenic response of subsurface reservoirs to injection or extraction and the maximum magnitudes $M_\text{max}$ were comparable to that of natural ones (namely, magnitudes above 4). Hence, it is relevant to understand the physical processes governing these earthquakes and develop strategies that forecast, control and mitigate the seismic risk. Since 2015, some notable advances have improved the current understanding of induced seismicity. In situ experiments with extensive monitoring systems and well-characterized rock mass were performed in underground laboratories to bridge the gap between the small-scale laboratory and field-scale experiments.

许多记录在案的诱发地震是由地下储层对注入或开采的地震学响应引起的，其最大震级 $M_\text{max}$ 与天然地震相当（即震级超过 4 级）。因此，了解这些地震的物理过程并制定预报、控制和减轻地震风险的策略具有重要意义。自 2015 年以来，一些显著的进展增进了目前对诱发地震的了解。在地下实验室进行了具有广泛监测系统和表征良好岩体的原位实验，缩小了小规模实验室实验与现场规模实验之间的差距。

Methodological progress in small-scale experiments (both in laboratory and underground in situ experiments), large-scale operations and risk-informed traffic light protocols (TLPs) were achieved to reduce the seismicity and to enhance the current risk management capabilities. Also, theoretical developments in physical understanding of $M_\text{max}$ have explained the occurrence of large magnitude induced event such as in Pohang, South Korea 2017. Despite these advances, the occurrence of unexpectedly large (such as $M \geq 4$) induced events cannot be excluded.

在小规模实验（实验室实验和地下原位实验）、大规模作业和风险知情交通灯协议（TLPs）方面取得了方法上的进步，从而降低了地震发生率，增强了当前的风险管理能力。此外，对 $M_\text{max}$ 物理理解的理论发展也解释了大震级诱发事件的发生，如 2017 年韩国 Pohang 地震。尽管取得了这些进展，但仍不能排除意外大震级（如 $M \geq 4$）诱发事件的发生。

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Previous reviews have covered topics such as monitoring, modelling and controlling inducedseismicity. Other reviews cover the seismological or geological aspects with a particular focus on a single application such as hydraulic fracturing, hydrocarbon recovery, WWD, enhanced geothermal systems (EGS), mining and UGS. However, there is a need for a process-based and mechanistic review of induced earthquakes more generally, with a particular focus on available $M_{\text{max}}$ theories and the broad implications for monitoring, discrimination between natural and induced earthquakes, hazard and risk assessments and mitigation strategies.

以往的综述涉及监测、建模和控制诱发地震等主题。其他综述涉及地震学或地质学方面，尤其侧重于单一应用，如水力压裂、碳氢化合物回收、WWD、增强地热系统（EGS）、采矿和 UGS。然而，有必要对诱发地震进行更广泛的基于过程和机理的综述，尤其侧重于现有的 $M_{\text{max}}$ 理论以及对监测、区分天然地震和诱发地震、危害和风险评估以及减灾战略的广泛影响。

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In this Review, we provide a brief and comprehensive overview of the physical processes governing fluid-induced (by injection or extraction) earthquakes. We place a specific focus on the triggering mechanisms and discuss the $M_{\text{max}}$ models in relation to physical processes. Then, we outline the implications of physics-based approaches for monitoring, discrimination, seismic risk and hazard assessment and mitigation strategies. Finally, we highlight emerging research directions to shape future developments to improve the current understanding of induced earthquakes, minimize their negative consequences and increase the acceptance of innovative energy technologies.

在这篇综述中，我们简要而全面地概述了流体诱发（注入或抽取）地震的物理过程。我们特别关注触发机制，并讨论了与物理过程相关的 $M_{\text{max}}$ 模型。然后，我们概述了基于物理学的方法对监测、判别、地震风险和危害评估以及减灾战略的影响。最后，我们强调了新出现的研究方向，以塑造未来的发展，从而改善当前对诱发地震的理解，最大限度地减少其负面影响，并提高对创新能源技术的接受度。

Activities associated with induced earthquakes

Globally, more than $50\%$ of the industrial projects that were associated with anthropogenic earthquakes were directly linked to underground fluid injection or extraction. Among them, a notable number of cases have induced earthquakes exceeding M3 (Fig. 2). Here, we briefly discuss these activities and point out some of the largest events that occurred since 2010 (Table 1).

在全球范围内，$50\%$ 以上与人为地震相关的工业项目与地下流体注入或提取直接相关。其中，诱发超过 M3 级地震的案例不在少数（图 2）。在此，我们将简要讨论这些活动，并指出自 2010 年以来发生的一些最大事件（表 1）。

Enhanced geothermal systems

Geothermal energy aims to exploit the vast unexploited amount of heat stored in the crust that could be extracted by circulating fluids (such as water) between injection and extraction wells. Despite hydrothermal-type geothermal reservoirs, EGS technology aims to exploit the heat stored in high temperature formations with insufficient permeabilities. Such condition is typically met at the depths of $3–5\text{ km}$, where the host formation is composed of low-permeability crystalline basement rocks. High-pressure fluid injection, known as hydraulic stimulation, is often carried out to create a subsurface heat exchanger.

地热能源旨在利用地壳中储存的大量未开发热量，这些热量可以通过在注入井和提取井之间循环流体（如水）来提取。尽管存在热液型地热储层，但 EGS 技术旨在开采渗透率不足的高温地层中储存的热量。这种情况通常发生在 $3-5\text{km}$ 深的地层中，那里的主地层由渗透率低的结晶基底岩石组成。通常会注入高压流体，即水力刺激，以形成地下热交换器。

Hydraulic stimulation activates multiple physical processes that create a high-permeability connection between the input and output wells. However, hydraulic stimulation is often associated with induced seismicity. The $M_{w}$ 5.4 Pohang 2017, South Korea, was triggered by hydraulic stimulation of the close-by EGS project. Moreover, numerous small-to-moderate events (that is, $M > 3$) have been felt by public (Fig. 2), raising concern and threatening the social license to operate.

水力激发激活了多个物理过程，在输入井和输出井之间建立了高渗透性连接。然而，水力激发往往与诱发地震有关。韩国 Pohang 2017 年 5.4 级地震就是由附近的 EGS 项目水力刺激引发的。此外，许多中小规模事件（即 $M > 3$）已被公众感受到（图 2），引起了人们的关注，并威胁到社会运营许可。

想想罗宇煊师兄的热剪切实验, 有没有引入或者拓展的可能呢?

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The physical processes in EGS reservoirs are rather complex. If the temperature of the injected fluid and that of the reservoir are close (such as underground laboratories), one could anticipate that the dominant hydromechanical processes are not substantially influenced by the thermal component. The high temperature in such systems can exert over-closure of fractures and faults (namely, a better fit of the opposing walls causing an increase of frictional strength), which can be released by cooling, causing contraction effects. Fluid injection or circulation can also disturb the geochemical equilibrium, with fluidrock interactions potentially playing an important role in long-term operations. However, suchrock–fluid interactions might be negligible over short-term injection operations.

EGS 储层的物理过程相当复杂。如果注入流体的温度与储层的温度接近（如地下实验室），我们可以预计主要的水力机械过程不会受到热力成分的实质性影响。此类系统中的高温会造成裂缝和断层的过度闭合（即对立壁的更好贴合导致摩擦强度增加），冷却后又会释放出来，造成收缩效应。流体注入或循环也会扰乱地球化学平衡，流体与岩石的相互作用可能在长期作业中发挥重要作用。不过，在短期注入作业中，这种岩流相互作用可能可以忽略不计。

Hydraulic fracturing

Unconventional oil and gas reservoirs are often located in low-permeability formations such as shale. Extended reach horizontal wells, up to several kilometres in length, are hydraulically fractured at multiple intervals to create flow paths for oil and gas when the well is under production (namely, ‘flow-back’). Here, the objective is to generate a connected fracture network that facilitates hydrocarbon withdrawal. In such environments, hydromechanical processes influence both hydraulic fracture propagation and damage evolution, which controls the dimensions of hydraulic fracture and attendant seismicity.

非常规油气藏通常位于页岩等低渗透地层中。长达数公里的长距离水平井在生产时（即 “回流”），在多个间隔处进行水力压裂，为油气创造流动通道。这样做的目的是形成一个连通的裂缝网络，以促进碳氢化合物的抽取。在这种环境下，水力机械过程会影响水力裂缝的扩展和破坏演化，从而控制水力裂缝的尺寸和随之而来的地震。

Although it is widely observed that the generation of new fractures do not produce noticeable seismic magnitudes, pre-existing fractures and faults can be reactivated and cause felt events, even at relatively large distances. It is important to note that many shale plays did not encounter any M3+ events at all. At the basin scale in seismogenic shale plays, approximately $0.1–1\%$ of the hydraulic fracturing wells were associated with substantial induced earthquakes (namely, $M > 3$).

尽管人们普遍认为，新裂缝的产生不会产生明显的地震震级，但原有的裂缝和断层会被重新激活，甚至在相对较远的距离上也会引起有感地震。值得注意的是，许多页岩区根本没有发生任何 M3+ 事件。在成震页岩区的盆地范围内，约有 $0.1-1 \%$ 的水力压裂井与重大诱发地震有关（即 $M > 3 $）。

In Eastern Ohio USA, this percentage is approximately $10–33\%$ (ref. 37). Yet, these percentages can vary substantially by location within the shale play. For example, the Duvernay play in Canada had percentages up to $10\%$ in the most seismically active areas. However, the susceptibility of a location to encounter induced seismicity depends on many factors, including the geological conditions and the proximity to seismogenic and hydraulically active faults.

在美国俄亥俄州东部，这一比例约为 $10–33\%$（参考文献 37）。然而，在页岩区内，这些百分比会因地点不同而有很大差异。例如，在加拿大的 Duvernay 地区，在地震最活跃的地区，这一比例高达 $10\%$ 美元。然而，一个地点发生诱发地震的敏感性取决于许多因素，包括地质条件以及是否靠近地震活动断层和水力活动断层。

Two notable $M_{s}$ 6 and $M_{w}$ 5.7 earthquakes in Luxian 2021 and Sichuan Basin 2019, both in China, were speculated to be linked with hydraulic fracturing of unconventional resources. Also, the $M_{w}$ 4.6 earthquake in northwest of Fort St John, British Columbia 2015 was the largest induced event caused by hydraulic fracturing in Canada.

据推测，2021 年泸县和 2019 年四川盆地发生的两次显著的 $M_{s}$ 6 和 $M_{w}$ 5.7 地震都与非常规资源的水力压裂有关。此外，2015 年不列颠哥伦比亚省圣约翰堡西北部发生的 4.6 级地震是加拿大水力压裂引起的最大诱发事件。

Wastewater disposal

The exploitation of petroleum resources produces large volumes of wastewater, which are typically disposed of via subsurface injection. WWD usually targets porous rocks in sedimentary layers, to store large volumes that can exceed $10^{6}\text{ m}^3$. In the corresponding formations, temperature and composition of injected fluid could be variable and require considering coupled processes. Some large magnitude ($M \geq 5$) earthquakes were likely related to WWD injections. An $M_{w}$ 5.1 in Peace River, Alberta, Canada 2022 was likely related to the WWD of in situ bitumen recovery. The $M_{w}$ 5 earthquakes in the Permian Basin of West Texas 2020, USA were potentially induced by nearby WWD operations. Also, three earthquakes of $M_{w}$ 5.8, 5.1 and 5.7 occurred in Pawnee (2016), Fairview (2016) and Prague (2011) OK USA, respectively, were also caused by WWD associated with unconventional hydrocarbon production.

石油资源的开采会产生大量废水，这些废水通常通过地下注入的方式进行处理。WWD 通常以沉积层中的多孔岩石为目标，以储存可能超过 $10^{6}\text{ m}^3$ 的大量废水。在相应的地层中，注入流体的温度和成分可能是可变的，需要考虑耦合过程。一些大震级（$M \geq 5$）地震很可能与 WWD 注入有关。加拿大艾伯塔省和平河 2022 年发生的 5.1 级地震很可能与原地沥青回收的 WWD 有关。2020 年在美国西得克萨斯州二叠纪盆地发生的 5 级地震可能是由附近的 WWD 作业诱发的。此外，在美国 OK 州 Pawnee（2016 年）、Fairview（2016 年）和 Prague（2011 年）分别发生的 3 次 $M_{w}$ 5.8、5.1 和 5.7 级地震也是由与非常规碳氢化合物生产相关的 WWD 引起的。

回想一下 Jia 有关于干湿密堆积的 $Q$ 因子的论述, 以及半月板的形成相关内容

Increase in induced seismicity related to industrial operations. a, Global number of documented industrial projects associated with anthropogenic earthquakes compared with the number of fluid injection-induced or extraction-induced earthquakes. b, The number of reported induced earthquake events with $M_{\text{max}} \geq 3$ in industrial operations dealing with fluid injection or extraction (yellow bars, left axis). The largest reported $M_{\text{max}}$ for each of the corresponding industrial operations since 2010 (blue diamonds, right axis). EGS, enhanced geothermal systems; UGS, underground gas or CO2 storage; WWD, wastewater disposal. Data are from the Human-Induced Earthquake Database (HiQuake).

与工业活动有关的诱发地震增加 a, 全球有记录的与人为地震相关的工业项目数量与流体注入或开采引发的地震数量的比较。 b, 在涉及流体注入或提取的工业运行中，$M_{\text{max}} \geq 3$ 的已报告诱发地震事件的数量（黄色条形图，左轴）。自 2010 年以来，各相应工业活动中报告的最大 $M_{\text{max}}$（蓝色菱形，右轴）。EGS，增强型地热系统；UGS，地下气体或二氧化碳封存；WWD，废水处理。数据来自人类诱发地震数据库（HiQuake）。

Underground gas storage

Similar to WWD operations, UGS targets high-permeability porous rocks. High-permeability formations are typically selected to store large volumes (million tons) of gas or CO2 in the subsurface. In such systems, the hydraulic processes are controlled by the multiphase mixture of the fluid, where the overpressure dissipates by pressure gradients and buoyancy forces. In the case of CO2 storage, the fluid is typically injected in supercritical conditions and the transport occurs in a multiphase mixture. As CO2 can disturb the geochemical equilibrium, the fluid–rock interactions can restructure the pore space by mineral dissolution and precipitation. These interactions change the permeability, porosity and poroelastic properties of the host formation. The most remarkable case history is the Castor project in offshore Spain, which triggered three M 4.1 earthquakes in 2013. However, very few UGS projects reported induced seismicity.

与 WWD 作业类似，UGS 以高渗透多孔岩为目标。高渗透地层通常是为了在地下储存大量（百万吨）天然气或二氧化碳。在这种系统中，水力过程由流体的多相混合物控制，超压通过压力梯度和浮力消散。在二氧化碳封存中，流体通常在超临界条件下注入，并在多相混合物中传输。由于二氧化碳会扰乱地球化学平衡，流体与岩石之间的相互作用会通过矿物溶解和沉淀重组孔隙空间。这些相互作用会改变主岩层的渗透性、孔隙度和孔弹性特性。最突出的案例是西班牙近海的 Castor 项目，该项目在 2013 年引发了三次 M 4.1 级地震。然而，只有极少数 UGS 项目报告了诱发地震。

Hydrocarbon recovery

Conventional hydrocarbon recovery from sedimentary rocks depressurizes the underground reservoirs. During the fluid extraction, the reservoir pressure drops and the elastic stresses become activated. One major challenge arises from the multiphase nature of fluids in geological systems (including oil, gas and water) and the chemical interactions among different phases. During fluid extraction, the temperature of the reservoir system is not disturbed by external sources, the thermal interaction between the rock and fluid might not be substantial. The $M_{w}$ 4.8 earthquake in the Eagle Ford Shale, TX, USA (2011) is one example of seismicity that was exclusively caused by hydro- carbon recovery. Also, prominent case histories of Groningen gas field, The Netherlands and Lacq gas field, France are examples of extraction-induced seismicity in seismically quiet regions.

从沉积岩中开采碳氢化合物的传统方法会降低地下储层的压力。在流体开采过程中，储层压力下降，弹性应力被激活。地质系统中流体（包括油、气和水）的多相性质以及不同相之间的化学作用是一大挑战。在流体开采过程中，储层系统的温度不受外界干扰，岩石与流体之间的热相互作用可能不大。美国德克萨斯州鹰福特页岩 4.8 级地震（2011 年）就是一个完全由碳氢化合物开采引起的地震实例。此外，荷兰 Groningen 气田和法国 Lacq 气田的突出案例也是在地震静区开采引发地震的例子。

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The maximum observed magnitude of induced earthquakes during underground fluid injection and extraction experiments varied between 4 and 6. Various operations target different geological formations and operational variants that control the magnitude of induced earthquakes.

在地下流体注入和提取实验中，观测到的最大诱发地震震级在 4 到 6 级之间。各种操作针对不同的地质构造和控制诱发地震幅度的操作变体。

Earthquake triggering mechanisms

The primary triggering mechanisms of induced earthquakes (Box 1) considered important for creating stress perturbations include pore-pressure diffusion, poroelastic coupling, thermoelastic stresses, earthquake interactions and aseismic slip. Fault-weakening processes via chemical and physical processes can also expedite fluid–rock interactions and/or promote further instabilities. However, unravelling the influence of a single mechanism is challenging, as multiple mechanisms likely contribute to a single seismic event.

诱发地震的主要触发机制（方框 1）被认为是产生应力扰动的重要因素，包括孔隙压力扩散、孔弹性耦合、热弹性应力、地震相互作用和地震滑动。通过化学和物理过程产生的断层弱化过程也会加速流体与岩石之间的相互作用和/或促进进一步的不稳定性。然而，要解开单一机制的影响是具有挑战性的，因为多种机制可能会对单一地震事件产生影响。

Stress perturbation

Pore-pressure changes. Pore-pressure changes and propagation are the primary mechanisms for inducing earthquakes. Often, the process of pore-pressure propagation is referred to as pressure diffusion as the equation governing such propagation can be approximated with a diffusion equation, assuming constant fluid density. When the fluid enters pre-exiting fractures and faults, the rise in pore pressure supports a fraction of the normal stress and the effective normal stress is reduced — bringing the fault closer to the failure. Pressure changes can be transmitted far beyond the injection zone, up to tens of kilometres in highly permeable formations.

孔隙压力变化。孔隙压力变化和传播是诱发地震的主要机制。通常情况下，孔隙压力的传播过程被称为压力扩散，因为假设流体密度不变，控制这种传播的方程可以用扩散方程来近似表示。当流体进入预先存在的裂缝和断层时，孔隙压力的上升会支撑一部分法向应力，有效法向应力会降低，从而使断层更接近于破坏。压力变化可远远传递到注入区之外，在高渗透地层中可达数十公里。

扩散方程再次出现在了地震学的研究中. 关注两者同时成立的共性所在

Pore-pressure diffusion has been identified as the primary mechanism for earthquakes induced by WWD, often many kilometres from the injection point, for which substantial seismicity can be delayed by months or longer. Earthquakes induced during EGS stimulations also primarily initiate in response to pore-pressure diffusion. During hydraulic fracturing, the pressure front outside the fractures is inhibited by the low permeability of the reservoir. Therefore, a hydrologic connection is required to transfer the pressure diffusion to critically stressed faults, on which dynamic rupture occurs.

孔隙压力扩散已被确定为 WWD 引发地震的主要机制，通常在距离注入点数公里以外的地方发生，其实质性地震可能会延迟数月或更长时间。在 EGS 激发过程中诱发的地震也主要是由孔隙压力扩散引起的。在水力压裂过程中，裂缝外的压力前沿受到储层低渗透性的抑制。因此，需要水文连接将压力扩散传递到受压严重的断层，在断层上发生动态破裂。

This connection is likely provided by pre-existing fracture corridors that allowed communication of fluid-pressure perturbations to larger faults, even in distances more than $1\text{ km}$ (ref. 67). Most case histories of hydraulic fracturing are ascribed by the pore-pressure diffusion and hydraulic connection to the nearby faults. Hence, the proximity to the deep basement is a substantial geological factor when faults in crystalline basement become involved. The hydraulic connection and pressure migration to deeper formations have also been observed in the cases of WWD and UGS. However, pressure diffusion can also reactivate the faults in shallower depths of the injection point.

这种联系很可能是由先前存在的断裂走廊提供的，这些断裂走廊可以将流体压力扰动传递到更大的断层，即使距离超过 $1\text{ km}$（参考文献67）。大多数水力压裂案例都是由于孔隙压力扩散和与附近断层的水力联系造成的。因此，当涉及到结晶基底中的断层时，靠近深层基底是一个重要的地质因素。在 WWD 和 UGS 案例中，也观察到水力联系和压力迁移到更深的地层。然而，压力扩散也会重新激活注入点较浅层的断层。

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Poroelastic coupling. Poroelastic stresses created by injection are also a triggering mechanism for either injection-induced or extraction-induced seismicity. During injection, seismicity is sometimes observed to outpace the pore-pressure front. Pressure diffusion cannot explain such seismicity unless high permeability fractures are present. Poroelastic stress transfer occurs at the speed of seismic waves and perturbs the strength balance on distant fractures and faults without any hydraulic communication. Poroelastic stress transfer results from overburden changes and pressurized expansion of the rock volume, which further trigger distant stress-induced pore-pressure changes.

挤塑耦合。注水产生的挤塑应力也是注水诱发或抽水诱发地震的一个触发机制。在注入过程中，有时会观察到地震超过孔隙压力前沿。除非存在高渗透率裂缝，否则压力扩散无法解释这种地震现象。褶皱弹性应力传递以地震波的速度发生，在没有任何水力交流的情况下扰动远处断裂和断层的强度平衡。褶皱应力传递源于覆盖层的变化和岩石体积的受压膨胀，这进一步引发了远处应力引起的孔隙压力变化。

Although the stress perturbation owing to poroelastic effects is relatively small and diminishes with distance, it can be sufficient to awaken critically stressed fractures and faults in offset locations. Investigations have revealed that shear stress changes as small as $0.01–0.1\text{ MPa}$ can trigger seismic events. However, some authors reported perturbations as small as a few kilopascals. This threshold of stress perturbation is likely bounded by the Earth tidal stresses that rarely induce natural earthquakes. The role of poroelastic stress transfer has been discussed during geothermal developments, hydraulic fracturing operations, WWD and UGS.

虽然孔弹性效应引起的应力扰动相对较小，并随距离的增加而减弱，但足以唤醒偏移位置的临界应力断裂和断层。调查显示，小到 $0.01–0.1\text{ MPa}$ 的剪应力变化都可能引发地震事件。然而，一些学者报告的扰动小到几千帕。应力扰动的这一阈值可能与地球潮汐应力有关，而潮汐应力很少诱发天然地震。在地热开发、水力压裂作业、WWD 和 UGS 过程中，都讨论过孔弹性应力传递的作用。.

Fluid extraction reduces the pore pressure, which causes reservoir depletion and/or compaction. In comparison to fluid injection, extraction-induced seismicity can seem counterintuitive as fluid extraction generates negative pressure change (and thus increases fault stability). However, this argument is incomplete. Reservoir depletion and/or compaction also create high-stress regions surrounding the extraction volume that might eventually fail and trigger earthquakes. As the reservoir formation cannot contract freely in response to the fluid extraction, horizontal contraction within the reservoir generates differential stresses.

流体抽取会降低孔隙压力，导致储层耗竭和/或压实。与注入流体相比，采出流体引起的地震似乎与直觉相反，因为采出流体会产生负压变化（从而增加断层的稳定性）。然而，这种说法并不全面。储层耗竭和/或压实也会在抽采区周围形成高应力区，最终可能失效并引发地震。由于储层不能随着流体的抽取而自由收缩，储层内的水平收缩会产生不同的应力。

The onset of compaction-induced seismicity in some cases can require a considerable pore-pressure drop of $\sim 10\text{ MPa}$ (refs. 51,85). Higher thresholds of stress perturbations support the viewpoint that the fluid production can reactivate faults that were not critically stressed before operation. Reservoir compaction also manifests itself as surface subsidence seen in deformation on the surface. Several prominent cases of extraction-induced seismicity were explained by the heterogeneously distributed strain.

在某些情况下，压实诱发地震的发生可能需要相当大的孔隙压力下降 $\sim 10\text{ MPa}$（参考文献 51,85）。较高的应力扰动阈值支持这样一种观点，即流体生产可以重新激活在运行前并不严重受压的断层。储层压实还表现为地表下沉，表现为地表变形。一些突出的开采诱发地震的案例可以用异质分布的应变来解释。

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Thermal stresses. When the temperature of injection fluid differs from the in situ temperature, thermal stresses can contribute to mechanical instability. Fluid injection into subsurface cools down the reservoir and generates contractional strain. The magnitude of thermal stress depends on the stiffness of the reservoir rock, becoming more important in stiffer formations. However, it is difficult to determine the contribution of thermal stresses during in situ injection experiments. The thermal drawdown front is often slower than that of pore pressure. Moreover, the thermal stresses can be transmitted beyond the cooled region and destabilize faults in distant locations. Therefore, thermal effects are likely more important at later times than at the start of injection, but could have a critical role in the long run. The triggering of induced seismicity by thermal stresses was explored in several case histories during EGS stimulations and CO2 storage.

热应力。当注入流体的温度与原位温度不同时，热应力会导致机械不稳定。注入地下的流体会使储层冷却并产生收缩应变。热应力的大小取决于储层岩石的硬度，在硬度较高的地层中更为重要。然而，在原位注入实验中很难确定热应力的作用。热压降前沿通常比孔隙压力前沿慢。此外，热应力可能会传递到冷却区域之外，破坏远处断层的稳定性。因此，热效应在后期可能比在注入开始时更为重要，但从长远来看可能具有关键作用。在 EGS 激发和二氧化碳封存过程中，对热应力引发诱发地震的几个案例进行了探讨。

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Earthquake interactions. When an earthquake occurs, static stress along a fault changes near the rupture front, potentially advancing or retarding the generation of new earthquakes. This mechanism is known as earthquake interaction. Earthquakes also interact through the stress carried by the radiated waves, which are capable of triggering distant events — even in the stress shadow of the static field. Both static and dynamic mechanisms contribute to the occurrence of natural and induced earthquake sequences. According to rate-and-state theory, the time it takes for the system to evolve to failure after perturbation depends nonlinearly on the initial state, size of the perturbation and stressing rate.

地震相互作用。地震发生时，断层前沿附近的静应力会发生变化，有可能推动或延缓新地震的发生。这种机制被称为地震相互作用。地震还通过辐射波携带的应力发生相互作用，辐射波能够触发远处的事件–甚至在静态场的应力阴影中。静态和动态机制都有助于自然地震和诱发地震序列的发生。根据速率与状态理论，系统在受到扰动后演变为破坏所需的时间与初始状态、扰动大小和应力速率呈非线性关系。

*无懈可击的一段话(听君一席话, 如听一席话), *

Hence, failure can be nearly instantaneous or delayed by months or longer, giving rise to the spectrum of spatial and temporal clustering of seismicity seen in both natural and induced earthquakes. Therefore, it can be difficult to assign causality between an industrial action and a specific earthquake when there are multiple sources of perturbations. In addition to the stress transfer of earlier earthquakes, the tensile opening of fractures generates an extrastatic stress that can generate a sequence of events that control the spatial distribution of seismic events, specifically during hydraulic fracturing experiments. Many prominent case histories were explained by earthquake static stress transfer during EGS stimulations, hydraulic fracturing, WWD and UGS.

因此，破坏可能几乎是瞬时发生，也可能延迟数月或更长的时间，这就产生了在天然地震和诱发地震中都能看到的地震时-空聚类现象。因此，当存在多个扰动源时，很难确定工业活动与特定地震之间的因果关系。除了早期地震的应力传递之外，裂缝的拉伸张开也会产生外应力，这种外应力可以产生一系列事件，控制地震事件的空间分布，特别是在水力压裂试验期间。在 EGS 激励、水力压裂、WWD 和 UGS 期间发生的地震静应力传递解释了许多突出的案例。

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Aseismic slip or reservoir creep. Earthquakes are manifestations of unstable slip, requiring the resistance to sliding diminishes faster than the elastic unloading (creating a force imbalance). If this condition is not met, fault displacement is aseismic. Detecting aseismic slip is challenging and has rarely been seen, except in exceptional natural and induced earthquake circumstances. The observed fault displacement during in situ injection experiments on borehole televiewer can be substantially larger than the slip attributed to the largest induced event, implying that most of the fault displacement occurred aseismically. This has also been confirmed by small-scale injection experiments at relatively shallow depth in underground laboratories, in which seismo-hydromechanical responses of fault zones were precisely monitored.

地震滑移或储层蠕变。地震是不稳定滑动的表现，要求滑动阻力的减小速度快于弹性卸荷（产生力的不平衡）。如果不满足这一条件，断层位移就是非地震位移。检测无震滑动具有挑战性，除非在特殊的自然地震和诱发地震情况下，否则很少出现无震滑动。在井眼遥视仪上进行原位注水实验时，观测到的断层位移可能远远大于最大诱发事件引起的滑移，这意味着大部分断层位移是以非地震方式发生的。在地下实验室进行的深度相对较浅的小规模注水实验也证实了这一点，实验中精确监测了断层带的地震-水力学反应。

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On critically stressed faults, the aseismic slip front can outpace the pore-pressure front and extend beyond the characteristic length of pressure diffusion. The conditions over which the aseismic rupture front outpaces the pore-pressure front depend on the stress criticality of the pre-existing faults. The aseismic rupture front can be estimated by the product of the pore-pressure front and a correction factor that is a function of stress criticality. Several studies suggested that aseismic slip was a contributing mechanism to several prominent induced seismicity cases in EGS stimulation, hydraulic fracturing and UGS. This can explain the induced earthquakes at distant locations from the injection point.

在应力临界断层上，地震滑移前沿可能超过孔隙压力前沿，并延伸到压力扩散特征长度之外。地震破裂前沿超过孔隙压力前沿的条件取决于先存断层的应力临界程度。地震破裂前沿可通过孔隙压力前沿与应力临界值函数校正因子的乘积来估算。一些研究表明，地震滑动是 EGS 激励、水力压裂和 UGS 中几个突出诱发地震案例的促成机制。这可以解释距注入点较远位置的诱发地震。

Aseismic deformation during fluid extraction is typically referred as reservoir creep, which is the inelastic response of rocks. Reservoir creep or time-dependent viscous deformation is a potential mechanism to impose an additional stress perturbation within the hydrocarbon reservoirs driving further instability. This can be explained by the temporal variation of the differential stressing rate driven by fluid extraction. Reservoir creep explains the discrepancy between the observations and the anticipated deformation computed by poroelasticity theory. Moreover, the delay between the pressure depletion and subsidence is often related to time-dependent viscous deformation. These concepts have been proposed to explain the sharp decrease of seismicity rate after the production reductions in the Groningen gas field.

流体开采过程中的地震变形通常被称为储层蠕变，即岩石的非弹性反应。储层蠕变或随时间变化的粘性变形是在油气储层中施加额外应力扰动的一种潜在机制，会进一步加剧不稳定性。这可以用流体开采驱动的差异应力速率的时间变化来解释。储层蠕变解释了观测结果与孔弹性理论计算的预期变形之间的差异。此外，压力耗竭与下沉之间的延迟通常与时间相关的粘性变形有关。这些概念被用来解释格罗宁根气田减产后地震率急剧下降的原因。

Fault weakening

Stress corrosion and geochemical interactions. Fluid injection or extraction can change the geochemical equilibrium in the subsurface and expedite fluid–rock interactions. Geochemical processes result in dissolution and/or precipitation of minerals along pre-existing fracture planes and thereby modify the strength of the interface. Stress corrosion often reduces the friction and hence fault strength. In EGS reservoirs, secondary minerals such as clay are formed during hydrothermal alteration and markedly reduce the frictional strength of the rocks. Aseismic slip along such weak zones can substantially perturb the stress field during the injection operations and influence seismicity.

应力腐蚀和地球化学相互作用。流体注入或抽取会改变地下的地球化学平衡，加速流体与岩石之间的相互作用。地球化学过程会导致矿物质沿已存在的断裂面溶解和/或沉淀，从而改变界面的强度。应力腐蚀通常会降低摩擦力，从而降低断层强度。在 EGS 储层中，热液蚀变过程中会形成粘土等次生矿物，从而显著降低岩石的摩擦强度。在注水过程中，沿这些薄弱带的地震滑动会对应力场产生很大的扰动，并影响地震活动。

In CO2 storage, the geochemical processes can contribute to stress corrosion and generation of new cracks around faults125. However, fault weakening owing to geochemical processes requires longer timescales and could be insubstantial during short-term hydraulic fracturing injections. For instance, Westaway and Burnside proposed the stress corrosion as a potential triggering mechanism of $M_{w}$ 5.4 earthquake during hydraulic stimulation of Pohang EGS. They related the delay of 2–3 months between the injection and shock to the time needed for the fluid–rock interactions to take effect.

在二氧化碳封存过程中，地球化学过程可能会导致应力腐蚀，并在断层周围产生新的裂缝125。然而，地球化学过程导致的断层削弱需要更长的时间尺度，在短期水力压裂注入过程中可能并不显著。例如，Westaway 和 Burnside 提出，在 Pohang EGS 的水力压裂过程中，应力腐蚀是 5.4 $M_{w}$ 级地震的潜在触发机制。他们将注入与地震之间 2-3 个月的延迟与流体-岩石相互作用生效所需的时间联系起来。

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Dynamic weakening. Earthquakes are generally described as stick–slip phenomenon, in which the dynamic friction is lower than the static value. Slip hardening results in aseismic creep and occurs when the frictional resistance increases with slip. By contrast, slip weakening is the requirement for instability, in which the friction decreases with slip. Any reduction of the frictional strength promotes further instabilities, and frictional properties of faults have been investigated in many studies dealing with natural earthquakes. Note that the fault-weakening studies were mostly executed in the laboratory conditions. For a detailed review on the dynamic weakening mechanisms of faults, we refer to Di Toro et al..

动态减弱。地震一般被描述为粘滑现象，即动态摩擦力低于静态值。滑动硬化会导致地震蠕变，当摩擦阻力随滑动而增加时，就会发生滑动硬化。相比之下，滑动减弱是不稳定的必要条件，在这种情况下，摩擦力会随着滑动而减小。摩擦强度的任何减弱都会进一步加剧不稳定性，许多关于天然地震的研究都对断层的摩擦特性进行了调查。需要注意的是，断层削弱研究大多是在实验室条件下进行的。有关断层动态削弱机制的详细综述，请参阅 Di Toro 等人的研究报告。

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Cohesion loss. The strength of rock mass is composed of frictional and cohesive resistances. However, the cohesive strength of faults is commonly disregarded in crustal conditions, as it is small compared with frictional strength. Experiments and observations show that both friction and cohesion increase with time after fault slip. This restrengthening of inactive faults can be sufficiently high to influence the long-term strength. During the co-seismic slip, the cohesion is decreased and this cohesion loss can lead to higher stress drops creat- ing stronger static and dynamic interactions, triggering more events. Despite progress, the mechanisms of cohesion loss and its impact on fault rupture are not sufficiently explored yet.

内聚力损失。岩体强度由摩擦阻力和内聚阻力组成。然而，在地壳条件下，断层的内聚强度通常被忽视，因为与摩擦强度相比，内聚强度很小。实验和观测表明，断层滑动后，摩擦力和内聚力都会随着时间的推移而增加。不活动断层的这种重新加固足以影响长期强度。在共震滑动过程中，内聚力会降低，这种内聚力损失会导致应力下降，从而产生更强的静态和动态相互作用，引发更多事件。尽管取得了进展，但内聚力损失的机制及其对断层破裂的影响尚未得到充分探讨。

In general, all mechanisms discussed earlier can contribute to the triggering of seismicity, because induced earthquakes can be triggered by stress changes slightly higher than the stress perturba- tions caused by the tides of the Earth. However, unravelling the influence of a single mechanism is challenging. Multiphysical modelling of well-characterized injection and extraction locations shows that the relative significance of triggering mechanisms can vary from site to site depending on the physical rock properties, reservoir structure, operational parameters, fault geometry, seismotectonic conditions and distance from injection and extraction, among others. However, pore-pressure change is considered a primary mechanism for injection-induced seismicity, and poroelastic coupling is the major mechanism of extraction-induced seismicity.

一般来说，前面讨论的所有机制都可能有助于引发地震，因为诱发地震的应力变化可能略高于地球潮汐造成的应力扰动。然而，揭示单一机制的影响具有挑战性。对特征明确的注采地点进行的多重物理建模表明，触发机制的相对重要性因地而异，取决于岩石物理性质、储层结构、运行参数、断层几何形状、地震构造条件以及与注采地点的距离等等。不过，孔隙压力变化被认为是注水诱发地震的主要机制，而孔隙弹性耦合则是开采诱发地震的主要机制。

Maximum induced earthquake magnitude

Despite advances in physical understanding, forecasting the seismic response to industrial activities remains challenging. Frequent changes in operation (such as injection or extraction rates) result in pronounced time-dependent induced earthquake rates. Moreover, seismicity in some regions occurs at a problematic level, whereas other regions remain rela- tively quiet, even if injection or extraction volumes are comparable. The variability of the seismic response to industrial activity has been related to various natural factors including the regional tectonics, number, size and orientation of pre-existing fractures and faults, local stratigraphy and existence of hydraulic conduits.

尽管在物理理解方面取得了进步，但预测工业活动的地震响应仍然具有挑战性。频繁的操作变化（如注入率或开采率）会导致明显的时变诱发地震率。此外，有些地区的地震发生率很高，而另一些地区则相对平静，即使注入量或开采量相当。工业活动引起的地震反应的变化与各种自然因素有关，包括区域构造、原有断裂和断层的数量、大小和走向、当地地层以及水力导管的存在。

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Forecasting the number and magnitude of earthquakes that might be induced during the lifetime of a project has a critical role in the assessment of the seismic hazard and risk. Ultimately, the seismic risk associated with induced seismicity depends on whether a large magnitude earthquake is triggered. In some cases, damaging magnitude thresholds have been exceeded and substantial economic losses and even several fatalities have been reported. However, understanding and forecasting the maximum magnitude induced by industrial activity is problematic, because models for single events $M_{\text{max}}$ are inherently associated with large uncertainty. To date, it is unclear whether $M_{\text{max}}$ can be meaningfully forecasted on the basis of physical and statistical principles.

预测项目生命周期内可能诱发的地震次数和震级对于评估地震危害和风险至关重要。最终，与诱发地震相关的地震风险取决于是否会引发大震级地震。在某些情况下，破坏性震级阈值已被突破，据报道造成了巨大的经济损失，甚至有数人死亡。然而，理解和预测工业活动诱发的最大震级是个问题，因为单一事件的模型 $M_{\text{max}}$ 本身就具有很大的不确定性。迄今为止，尚不清楚是否可以根据物理和统计原理对 $M_{\text{max}}$ 进行有意义的预测。

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From a statistical view, maximum observed induced earthquake magnitude in many cases agrees with the modal value of $M_{\text{max}}$ expected from the Gutenberg–Richter relation:

$$ M_{\text{max}} = M_{c} + \frac{1}{b}\log{(N)},\tag{1} $$

in which $M_{c}$ is the magnitude of completeness, $N$ is the number of events larger than or equal to $M_{c}$ and $b$ is the $b$-value estimated from the observed earthquake magnitudes. Overall, reported $b$-values of induced earthquake sequences are close to $b = 1$, in agreement with $b$-values of tectonic earthquakes. However, $b$-values in the range of $0.5–3.0$ and time-dependent $b$-values have been discussed. Equation (1) implies that there is no upper limit to the maximum possible magnitude. The more earthquakes above $M_{c}$ that occur, the larger the $M_{\text{max}}$ is expected to be. Note that equation (1) is based on observations and cannot be directly used to forecast the expected maximum magnitude before or during operation. To allow forecasts of $M_{\text{max}}$, it should be combined with physics-based seismicity models estimating the expected number of events larger than or equal to $M_{c}$.

从统计角度看，在许多情况下，观测到的最大诱发震级与根据 Gutenberg–Richter 关系预期的 $M_{\text{max}}$ 模态值一致：

$$ M_{\text{max}} = M_{c} + \frac{1}{b}\log{(N)},\tag{1} $$

其中 $M_{c}$ 是完整震级，$N$ 是大于或等于 $M_{c}$ 的事件数，$b$ 是根据观测到的地震震级估计的 $b$ 值。总的来说，报道的诱发地震序列的 $b$ 值接近 $b = 1$，与构造地震的 $b$ 值一致。然而，讨论了 $b$ 值在 $0.5-3.0$ 范围内和时变 $b$ 值。方程（1）意味着最大可能震级没有上限。发生在 $M_{c}$ 以上的地震越多，预期的 $M_{\text{max}}$ 就越大。需要注意的是，方程（1）是基于观测的，不能直接用于预测运行前或运行期间预期的最大震级。为了允许对 $M_{\text{max}}$ 进行预测，它应与基于物理的地震模型相结合，估计大于或等于 $M_{c}$ 的事件数。

Volume-based theories

The seismogenic index theory, in which pore-pressure diffusion is the dominant triggering mechanism, incorporates the injected fluid volume to forecast the number of events $\geq M$ according to equation (2):

$$ \log{N_{M}(t)} = \Sigma + \log{V(t)} - bM,\tag{2} $$

in which $N_{M}(t)$ is the number of magnitudes larger than or equal to $M$, $b$ is the $b$-value, $V(t)$ is the cumulative injected fluid volume (in $\text{m}^3$) and $\Sigma$ is the seismogenic index. $\Sigma$ is a time-independent site-specific property describing the susceptibility to induced earthquakes. Reported $\Sigma$ values are between $−10$ and $1$ (ref. 141). The seismogenic index incorporates all unknown site-specific seismo-tectonic parameters and can be calibrated using observed magnitudes and reported injection volumes. Combination of equations (1) and (2) can be applied to estimate the expected maximum magnitude according to:

$$ M_{\text{max}} = \frac{1}{b}\left[\Sigma + \log{(V)}\right]. $$

成震指数理论认为孔隙压力扩散是主要的触发机制，该理论根据公式 (2) 结合注入流体体积来预测事件数量 $\geq M$:

$$ \log{N_{M}(t)} = \Sigma + \log{V(t)} - bM,\tag{2} $$

其中，$N_{M}(t)$ 是大于或等于 $M$ 的震级数，$b$ 是 $b$ 值，$V(t)$ 是累计注入流体体积（单位：$\text{m}^3$），$\Sigma$ 是致震指数。$\Sigma$是与时间无关的特定地点属性，描述了诱发地震的易感性。报告的 $\Sigma$ 值介于 $-10$ 和 $1$之间（参考文献 141）。成震指数包含了所有未知的特定地点地震构造参数，可使用观测到的震级和报告的注入量进行校准。结合公式 (1) 和 (2)，可根据以下公式估算预期最大震级:

$$ M_{\text{max}} = \frac{1}{b}\left[\Sigma + \log{(V)}\right]. $$

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The higher the seismogenic index, the larger the expected maximum magnitude for a given injection volume. The seismogenic index model was originally developed for EGS and hydraulic fracturing exper- iments with single injection boreholes, but has been extended to field-scale injection settings, to include a hydrogeological model, poroelastic effects, extraction-induced seismicity and arbitrary physical processes causing Coulomb stress perturbations.

成震指数越高，给定注入量下的预期最大震级就越大。成震指数模型最初是为单个注入井眼的 EGS 和水力压裂试验而开发的，现已扩展到野外规模的注入环境，包括水文地质模型、孔弹效应、抽取诱发地震以及引起 Coulomb 应力扰动的任意物理过程。

Generally, the validity of Gutenberg–Richter relation is accepted in all existing $M_{\text{max}}$ models. The main point of discussion is whether an overall or time-dependent limit to the maximum possible induced magnitude exists. When a critically stressed fault ruptures owing to a perturbation by fluid injection or production, it releases the stored tectonic strain energy. In this case, the rupture can extend beyond the pressure front and $M_{\text{max}}$ is largely controlled by the dimensions of the largest fault reactivated by anthropogenic activities. This viewpoint is supported by the focal mechanisms of larger magnitude events induced by hydraulic fracturing, WWDs and EGS stimulations, which correspond to failure of optimally oriented faults in the tectonic stress field.

一般来说，Gutenberg–Richter 关系的有效性在所有现有的 $M_{\text{max}}$ 模型中都得到了认可。讨论的重点是，最大可能诱导幅度是否存在一个总体限制或随时间变化的限制。当受力严重的断层由于流体注入或生产的扰动而断裂时，会释放出储存的构造应变能。在这种情况下，断裂会延伸到压力前沿之外，$M_{\text{max}}$ 在很大程度上受人为活动重新激活的最大断层的尺寸控制。这一观点得到了水力压裂、WWD 和 EGS 刺激所诱发的更大规模事件的焦点机制的支持，这些机制与构造应力场中最佳方向断层的破坏相对应。

In this direction, using a geometrical approach, injection-induced earthquakes mainly occur along faults located inside the stimulated rock volume. The finding suggested that the maximum possible magnitude gets larger with time as the perturbed rock volume grows. The main factor limiting the probability to induce a larger-magnitude event is the minimum principal axis of the fluid-stimulated rock volume. Shapiro et al. extended the geometrical approach to more complex perturbed rock volumes and faults only partially located inside the stimulated zone. A similar approach was also adopted to constrain the largest rupture plane in a cuboid perturbed volume using discrete fracture network models.

在这一方向上，利用几何方法，注入诱发的地震主要发生在位于激发岩体内部的断层上。研究结果表明，随着受扰动岩石体积的增大，最大可能震级也会随时间而增大。限制诱发更大震级事件概率的主要因素是流体激发岩体的最小主轴。Shapiro 等人将几何方法扩展到更复杂的扰动岩体和仅部分位于激发区内的断层。他们还采用了类似的方法，利用离散断裂网络模型来约束立方体扰动岩体中的最大破裂面。

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McGarr proposed an empirical relation between $M_{\text{max}}$ and injected volume, which defines an upper bound to the released seismic moment as in equation (4):

$$ M_{0} = GV,\tag{4} $$

in which $M_{0}$ is the cumulative seismic moment, $G$ is the shear modulus (approximately $30\text{ GPa}$) and $V$ is the cumulative injected volume. McGarr’s model can be used to estimate $M_{\text{max}}$ before injection operations. However, observations of large magnitude events of fluid injections exceeded $M_{\text{max}}$ of McGarr’s model. McGarr’s model was also reformulated by adding a term representing the initial stress state on a fault, which explained the $M_{\text{max}}$ in several case histories.

McGarr 提出了 $M_{\text{max}}$ 与注入体积之间的经验关系，它定义了释放地震力矩的上限，如公式 (4) 所示:

$$ M_{0} = GV,\tag{4} $$

其中，$M_{0}$ 为累积地震力矩，$G$ 为剪切模量（约为 $30\text{GPa}$），$V$ 为累积注入体积。McGarr 模型可用于在注入操作前估算 $M_{\text{max}}$。然而，观测到的大规模流体注入事件超过了 McGarr 模型的 $M_{\text{max}}$。通过增加一个代表断层初始应力状态的项，McGarr 模型也被重新制定，这解释了几个案例中的 $M_{\text{max}}$。

More complex volume-based models were developed incorporating rupture physics. The model considered two rupture modes of self-arrested and runaway ruptures, and the transition between these modes is controlled by the area and the amplitude of the pressure front, friction parameters and the stress state. However, the nucleation and arrest of a dynamic slip could be linked to the injection rate ramp-up, with larger slip associated with slower injection ramp-up when the fault is not critically stressed.

结合破裂物理学，开发了更复杂的基于体积的模型。该模型考虑了两种断裂模式，即自停断裂和失控断裂，这两种模式之间的转换由压力前沿的面积和振幅、摩擦参数和应力状态控制。然而，动态滑移的成核和停止可能与注入速度的上升有关，当断层受力不严重时，较大的滑移与较慢的注入速度上升有关。

Time-based theory

The case histories of induced earthquakes were used to show that $M_{\text{max}}$ scales with the logarithm of nucleation time(that is, the elapsed time from the beginning of the fluid injection) (Fig. 3). They also argued that the earthquake triggering time better describes observed maximum magnitudes compared with scaling with injected volume and proposed the following:

$$ M_{\text{max}} = 2\xi\log{(T)} + \textit{const}.\tag{5} $$

in which $\xi$ accounts for the physical mechanism and $T$ is the triggering time ($\xi = 0.5$ in the case of pore-pressure diffusion). The proposed time-based $M_{\text{max}}$ model successfully explained the magnitude and nucleation time of runaway ruptures such as the 2017 Pohang earthquake. Runaway ruptures account for the case in which the triggering seismicity front outpaces the perturbed volume. However, current application of this model is limited to real-time monitoring of seismotectonic properties of the target reservoir such as seismogenic index. Langenbruch et al. further elaborated on the scaling of $M_{\text{max}}$ with time and discussed the increasing nucleation potential of larger magnitude earthquakes with time based on diffusion-controlled growth of pressure-perturbed fault sizes.

诱发地震的案例历史表明，$M_{\text{max}}$ 与成核时间（即从注入流体开始的时间）的对数成正比（图 3）。他们还认为，与随注入体积缩放相比，地震触发时间能更好地描述观测到的最大震级，并提出了以下建议:

$$ M_{\text{max}} = 2\xi\log{(T)} + \textit{const}.\tag{5} $$

其中，$\xi$表示物理机制，$T$为触发时间（在孔隙压力扩散的情况下，$\xi=0.5$）。所提出的基于时间的 $M_{\text{max}}$ 模型成功解释了失控破裂（如 2017 年 Pohang 地震）的震级和成核时间。失控破裂解释了触发地震前沿超过扰动体积的情况。然而，目前这一模型的应用仅限于实时监测目标储层的地震构造特性，如成震指数。Langenbruch 等人进一步阐述了 $M_{\text{max}}$ 随时间的缩放，并基于压力扰动断层尺寸的扩散控制增长，讨论了较大震级地震的成核潜力随时间的增加而增加。

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To date, there is no standard or best practice of how methods of the maximum possible induced earthquake magnitude are applied. Basically, the maximum possible induced magnitude should be estimated pre-operation based on an ensemble of existing methods. The range of estimated maximum magnitudes should be used to perform pre-operation scenario loss modelling to understand whether a planned project is within the local risk tolerance. In any case, uncertainty must be considered when assessing the maximum magnitude.

迄今为止，还没有关于如何应用最大可能诱发震级方法的标准或最佳做法。基本上，最大可能诱发震级应在运营前根据现有方法组合进行估算。最大震级的估算范围应用于进行运营前的损失模拟，以了解计划项目是否在当地的风险承受范围之内。无论如何，在评估最大震级时必须考虑不确定性。

The wide probability distribution of the maximum magnitude makes it impractical to base decisions about continuation, modification or termination of an energy project on the expected or observed maximum magnitude. The seismic risk posed by the occurrence of low‐probability, large‐magnitude events can be high but unidentified136. Forward-looking probabilistic approaches should be applied in real-time to update the assessments of the maximum induced earthquake magnitude, seismic hazard and risk.

最大震级的概率分布范围很广，因此根据预期或观测到的最大震级来决定是否继续、修改或终止能源项目是不切实际的。发生低概率、大震级事件所造成的地震风险可能很高，但却无法确定136。应实时采用前瞻性概率方法，更新对最大诱发震级、地震危害和风险的评估。

In general, the observed $M_{\text{max}}$ of documented past events revealed the absence of an upper deterministic limit. If a critically stressed fault is somewhat perturbed by fluid injection or production, the amount of tectonic strain energy controls the extent of rupture, which could be far beyond the pressure front. In such cases, the $M_{\text{max}}$ can be as large as that of natural earthquakes.

一般来说，过去记录的事件的观测值 $M_{\text{max}}$ 表明没有确定的上限。如果一个严重受压的断层受到流体注入或生产的一定扰动，构造应变能量的大小控制着断裂的范围，而断裂范围可能远远超出压力前沿。在这种情况下，$M_{\text{max}}$ 可能与天然地震一样大。

Monitoring, discrimination, risk, hazard and mitigation

The concepts of monitoring, discrimination, risk, hazard and mitigation are important to managing induced seismicity as they provide the means to quantify possible losses and to identify actions that can reduce the severity and frequency of these losses. In this section, these concepts are discussed with respect to the underlying physical mechanisms.

监测、判别、风险、危害和减灾的概念对于管理诱发地震非常重要，因为它们提供了量化可能的损失并确定可降低这些损失的严重性和频率的行动的手段。本节将结合基本物理机制讨论这些概念。

Monitoring and discrimination

Microseismic monitoring operations can have a crucial role to ensure the safety of underground industrial operations within real-time- induced seismicity risk management procedures. The optimal design of a microseismic monitoring network allows for improved detection and location performance for natural and induced microseismicity as well as the estimation of magnitudes and other source parameters. In this context, a better understanding of the physical mechanisms governing induced seismicity, hence an improved capability to simulate synthetic-induced seismicity catalogues, can greatly help to optimize network design before industrial operations begin. Pre-operational monitoring is essential to support the best risk mitigation strategies. The design of a seismic network is often performed following empirical, sometimes subjective, considerations without taking into account the type of industrial activity being monitored.

在实时诱发地震风险管理程序中，微震监测作业对确保地下工业作业的安全起着至关重要的作用。微震监测网络的优化设计可以提高对天然微震和诱发微震的探测和定位性能，并估算震级和其他震源参数。在这种情况下，更好地了解诱发地震的物理机制，从而提高模拟合成诱发地震目录的能力，将大大有助于在工业运行开始之前优化网络设计。运营前监测对于支持最佳风险缓解战略至关重要。地震台网的设计通常是根据经验（有时是主观因素）进行的，没有考虑到所监测的工业活动类型。

Thus, advanced physical models for the simulation of the stress perturbation caused by a particular industrial operation and the simulation of associated induced seismicity can be used to evaluate (at least as a first-order approximation) the extent of the area requiring monitoring and the characteristics (in terms of magnitude and spatial distribution) of the target seismicity. In other words, physical modelling of induced seismicity can provide information on the minimum magnitude that should be detected and on the required location accuracy that should be reached by the monitoring infrastructure, giving objective constraints on design parameters of different seismic networks such as the aperture of the network (that is, the spatial extension), the number and the location of the seismic stations.

因此，模拟由特定工业活动引起的应力扰动和模拟相关诱发地震的先进物理模型，可用于评估（至少是一阶近似值）需要监测的区域范围和目标地震的特征（在震级和空间 分布方面）。换句话说，诱发地震的物理建模可以提供应探测到的最小震级和监测基础设施应达到的所需定位精度方面的信息，从而对不同地震台网的设计参数，如台网的孔径（即空间扩展）、地震台站的数量和位置提供客观的限制。

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Physics-based models are also extremely important in the discrimination between natural and induced seismicity, a challenging problem that is not yet resolved. To date, no physical difference between the mechanism of natural and anthropogenic earthquakes has been found. It seems likely that they are not. Discrimination of induced seismicity is often performed, in a rather qualitative way, by considering the spatial and temporal ‘closeness’ (which is per se subjective) between the seismicity and the industrial operations. Although spatial and temporal correlation between human industrial operations and seismic events might represent a first-order approxima- tion to discriminate between natural and anthropogenic seismicity, a causal link can only be found using physical modelling approaches.

基于物理学的模型对于区分天然地震和诱发地震也极为重要，这是一个具有挑战性的问题，目前尚未解决。迄今为止，尚未发现天然地震和人为地震的机理之间存在物理差异。看来它们很可能没有区别。对诱发地震的判别通常是通过考虑地震与工业活动之间的时空 “接近性”（这本身是主观的），以一种相当定性的方式进行的。虽然人类工业活动与地震事件之间的时空相关性可能是区分天然地震和人为地震的一阶近似值，但只有使用物理建模方法才能找到因果联系。

Without a detailed study involving seismicity analysis, pore-pressure diffusion, poroelastic stress modelling and an assessment of the geological setting of the area, the discrimination between natural and induced seismicity is uncertain or even impossible. Physics-based models combined with seismicity models, such as rate-and-state seis- micity models, allow simulation of the evolution of seismicity in the space–time–magnitude domain. Furthermore, contemporaneous operations can each contribute to reactivating a fault, providing cases in which determining a single causal factor becomes complicated (or even impossible). By comparing simulated seismicity with the real one, it is, in principle, possible to answer the question regarding the origin and relative contributions of suspected cases of induced seismicity by directly investigating the physical processes governing such phenomenon (that is, stress perturbations caused by each of the industrial operations).

如果不进行详细的研究，包括地震分析、孔隙压力扩散、孔弹性应力建模以及对该地区地质环境的评估，就无法确定甚至不可能区分天然地震和诱发地震。基于物理学的模型与地震模型（如速率-状态地震模型）相结合，可以模拟地震在空间-时间-震级域的演变。此外，同时发生的地震活动都可能导致断层的重新激活，从而使确定单一因果关系变得复杂（甚至不可能）。通过将模拟地震与实际地震进行比较，原则上可以通过直接研究诱发地震的物理过程（即每项工业活动造成的应力扰动）来回答有关诱发地震疑似案例的起源和相对贡献的问题。

Seismic hazard and risk assessment

Within the scope of natural tectonic seismicity, the use of probabilistic seismic hazard analysis (PSHA) is the de facto approach to understanding hazards from earthquake ground shaking. For example, PSHA-derived hazard curves inform building design codes, insurance policies and earthquake disaster reaction policies. The PSHA workflow constitutes three components: source modelling, ground motion characterization and hazard curve estimation — these procedures are inherently statistical, owing to the unpredictable nature of earthquakes.

在天然构造地震范围内，使用概率地震灾害分析（PSHA）是了解地震地震动危害的实际方法。例如，PSHA 得出的危害曲线为建筑设计规范、保险政策和地震灾害应对政策提供了依据。PSHA 工作流程由三个部分组成：震源建模、地动特征描述和危险曲线估算–由于地震的不可预测性，这些程序本质上都是统计性的。

Unfortunately, the nature of induced seismicity poses additional problems for the traditional PSHA source modelling assumptions, as induced seismicity rates are not stationary on human or construction time frames. Initial attempts to characterize induced earthquake hazards sidestepped this stationarity problem by instead producing a series of short-time assessments. Thus, future efforts that enable forecasting would allow for more complete hazard assessments, in which physics-based models can provide alternatives to statistics-based approaches.

不幸的是，诱发地震的性质给传统的 PSHA 震源建模假设带来了额外的问题，因为诱发地震率在人类或建筑时间框架内并不是静止的。最初对诱发地震危害进行定性的尝试避开了这一静止性问题，而是进行了一系列短时评估。因此，未来能够进行预测的工作将允许进行更全面的危害评估，其中基于物理的模型可提供基于统计的方法的替代方案。

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Currently used $M_{\text{max}}$ theories made simplifying assumptions in characterizing earthquake sources, owing to the difficulty and variability in observing relevant in situ properties; for example, by considering injected volume as a proxy variable to anticipate seismic response (such as event counts or seismic moment). These models have provided suggestions towards potential magnitude upper bounds and the seismogenic potential of reservoirs. The simplicity of these models has hampered their ability to account for delayed seismic responses, trailing seismicity (earthquakes that continue to occur after well shut-in), the Kaiser effect (a hysteresis in which events often occur only after exceeding previous stress extremums), or non-direct pore-pressure effects (such as poroelastic stress changes).

目前使用的 $M_{\text{max}}$ 理论在描述震源特征时进行了简化假设，原因是观测相关原位属性存在困难和可变性；例如，将注入体积视为预测地震响应的替代变量（如事件计数或地震力矩）。这些模型为潜在震级上限和储层的致震潜力提供了建议。这些模型的简单性妨碍了它们解释延迟地震反应、拖震（油井关闭后继续发生的地震）、Kaiser 效应（一种滞后现象，通常在超过之前的应力极值后才会发生地震）或非直接孔隙压力效应（如孔弹性应力变化）的能力。

Because of these limitations, modifications have been suggested that consider new maximums in Coulomb stress changes, addition of exponential tails following shut-in or convolution with Omori-like rate decay functions. More physically motivated models have also been suggested that are based on empirical frictional relations and stress rate changes that can account for stress-delayed seismic response and trailing seismicity. More sophisticated, still hydromechanical models have been used to model seismic rates at secondary oil fields and gas fields.

由于这些局限性，有人提出了一些修改建议，如考虑库仑应力变化的新的最大值，在关闭后增加指数尾，或与类似于 Omori 的速率衰减函数卷积。此外，还提出了基于经验摩擦关系和应力速率变化的更多物理模型，这些模型可以解释应力延迟地震响应和拖尾地震。更复杂的水力机械模型已被用于模拟二级油田和气田的地震速率。

In some cases, hybrid statistical–geomechanical approaches have been used for spatiotemporal seismic forecasting. Also, machine-learning approaches have attempted improved forecasting, especially given the success in the laboratory settings. In some studies, machine-learning techniques have been used towards better understanding of the relative importance of input variables for the forecasting of seismic response. The proliferation of these forecast models has also raised questions about discerning the suitability of approaches; here, ensembles of models can be aggregated on the basis of their relative data fit, with composite forecasts often outperforming any individual model.

在某些情况下，统计-地质力学混合方法被用于时空地震预报。此外，机器学习方法也尝试改进预报，尤其是在实验室环境中取得了成功。在一些研究中，机器学习技术被用于更好地理解地震反应预报中输入变量的相对重要性。这些预报模型的激增也提出了如何辨别各种方法的适用性的问题；在此，可根据模型的相对数据拟合度对模型集合进行汇总，综合预报往往优于任何单个模型。

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To manage induced earthquake risks, a TLP is often adopted. A TLP typically defines the green light as the threshold that allows unrestricted operations to proceed, the yellow light as the threshold to initiate mitigation strategies and the red light as the point requiring a regulatory intervention (including a cessation of the causal operation). Work has also begun to tie the design of TLPs to risk-based metrics including nuisance, building damage and chance of fatality as well as to adapt them to real-time information. Characterizing the events that can trail the end of an operation will be particularly important, as they are the most influential parameters under typical risk management.

为了管理诱发地震风险，通常采用 TLP。TLP 通常将绿灯定义为允许无限制的操作继续进行的阈值，将黄灯定义为启动缓解策略的阈值，将红灯定义为需要监管干预的点（包括停止因果操作）。工作也已经开始将 TLP 的设计与基于风险的指标联系起来，包括麻烦、建筑损坏和死亡几率，并将其调整为实时信息。特别重要的是，对结束操作后可能发生的事件进行表征，因为它们是典型风险管理中最有影响力的参数。

However, these approaches rely on a statistical estimation of the events that trail the end of an operation. The use of physics-based models has a potential role in modelling and forecasting the expected seismicity, to anticipate future hazard and risk and feedback information for operational adjustments or mitigation (Fig. 4).

然而，这些方法依赖于对结束操作后可能发生的事件的统计估计。基于物理模型的使用在模拟和预测预期的地震活动中具有潜在作用，以预测未来的危害和风险，并为操作调整或减灾提供反馈信息（图 4）。

Mitigation strategies

In the context of a TLP, the success of an operator strongly depends on the efficacy of mitigation strategies applied at the yellow-light level. In an ideal case, mitigation strategies would effectively reduce seismic risks and hazards, to ultimately avoid the operation-ending red-light scenario. Here, mitigation strategies are broadly defined as approaches that aim to decrease the hazards of induced seismicity. Mitigation strategies involve either reactionary approaches or longer-term avoidance or planning approaches. Traditionally, the reactionary strategies have entailed approaches including rate, pressure and/or volume reduction, operation pausing, skipping and even abandonment as a last resort. Avoidance or planning approaches entail monitoring, stress measurement, geophysical hazard pre-assessments and injection or production design. In this sense, physics-based models could provide notable improvements via suggesting and testing approaches to mitigation.

在 TLP 的背景下，操作者的成功与在黄灯级别采用的缓解策略的有效性密切相关。在理想情况下，缓解策略将有效降低地震风险和危害，最终避免操作结束的红灯情景。在这里，缓解策略被广泛定义为旨在减少诱发地震危害的方法。缓解策略包括反应性方法或长期避免或规划方法。传统上，反应性策略包括速率、压力和/或体积减少、操作暂停、跳过甚至放弃作为最后手段。避免或规划方法包括监测、应力测量、地球物理危害预评估和注入或生产设计。在这个意义上，基于物理模型可以通过建议和测试缓解方法来提供显著的改进。

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Physics-based principles have suggested several mitigation strategies throughout the history of induced seismicity. For example, one physically informed mitigation strategy is the slow change of injection or production rates to their targets (rather than sudden, step-like changes). This idea is rooted in concepts derived from both friction laws (that anticipate dynamic slip conditions from sudden rate changes) and water hammer effects (dynamic pressure pulses from suddenly driving a rate change). Empirically, this rate-change effect has often been sporadically supported through anecdotal examples at the field scale and in the laboratory.

在诱发地震的整个历史过程中，基于物理学原理提出了几种缓解策略。例如，一种基于物理原理的减震策略是缓慢改变注入率或生产率，使其达到目标（而不是突然的、阶梯式的变化）。这一想法源于摩擦定律（预测速率突然变化产生的动态滑移条件）和水锤效应（突然驱动速率变化产生的动态压力脉冲）。从经验上看，这种速率变化效应往往通过现场和实验室中的实例得到零星支持。

In another example, the observation-driven compaction model at Groningen led the re-prioritization of gas production: focusing the greatest extraction from wells at the margins of the field (where compaction was less pronounced) to relieve compaction from central wells (where seismic response was greatest). Although this rational is conceptually sound, these changes were unfortunately unable to prevent the abandonment of this gas field. Additionally, physics-based principles have suggested strategies such as fracture caging, cyclic stimulation, injection schemes that promote aseismic slip and even injection schemes that attempt to control and stabilize fault slip. The continued suggestion and evaluation of mitigation strategies from physical principles will allow for their refinement.

在另一个例子中，Groningen 的观测驱动压实模型导致了天然气生产优先次序的调整：将最大开采量集中在气田边缘（压实不太明显）的油井，以缓解中心油井（地震反应最大）的压实。虽然这一理念是合理的，但遗憾的是，这些改变未能阻止该气田的废弃。此外，基于物理学原理的策略还包括压裂笼、循环刺激、促进无震滑移的注水方案，甚至是试图控制和稳定断层滑移的注水方案。继续根据物理原理建议和评估缓解战略，将有助于完善这些战略。

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However, evaluating the effectiveness of mitigation strategies has largely been restricted by the availability of data. Field-scale data sets required to better understand the underlying processes include high-resolution earthquake catalogues along with injection time-series data, for a wide variety of cases, operations and settings. Building upon this, either in situ strain measurements or geodetic observations can be particularly helpful for partitioning aseismic and seismic fault moment release.

然而，评估减灾战略的有效性在很大程度上受到数据可用性的限制。要更好地了解基本过程，所需的现场尺度数据集包括高分辨率地震目录以及针对各种情况、操作和环境的注入时间序列数据。在此基础上，现场应变测量或大地测量观测对于划分地震和地震断层力矩释放特别有帮助。

To date, progress on mitigation during the active stages of injection has been restricted to inference from laboratory analogues or via decametre-scale experiments within tunnels or mines. There have been some cases in which field-scale physical models have been developed. Given the paramount importance of mitigation strategies for reducing seismic hazards and risks, high-resolution data sets and experiments will be required to validate their efficacy and build best practices at the field scale.

迄今为止，在注入活跃阶段的缓解方面所取得的进展仅限于从实验室模拟或通过隧道或矿井内的十米尺度实验进行推断。在某些情况下，还开发了一些实地规模的物理模型。鉴于减灾战略对减少地震危害和风险的极端重要性，需要高分辨率的数据集和实验来验证其有效性，并在实地尺度上建立最佳做法。

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As an example, seismicity induced by WWD presents additional challenges, as the connection between the source (injection wells) and the response cannot be determined in many cases owing to the large number of wells, the large distances between them and the fabric, such as faults and fractures in the injection strata, which can exert strong directional control on the induced earthquakes. It can also lag injection by many months. This time lag makes physical sense and corresponds to the time the pressure and stress changes need to propagate from the injection wells to the pre-existing critically stressed faults. It is controlled by factors such as the distance between injection intervals and pre-existing faults, hydrogeological conditions, as well as the stress changes needed for fault reactivation. Examples in Alberta, Canada, suggest that seismicity can lag the operation of WWD by years or even decades.

例如，WWD 引发的地震带来了额外的挑战，因为在许多情况下无法确定震源（注水井）与地震反应之间的联系，原因是注水井数量众多，井与井之间距离遥远，而且注水地层中的断层和裂缝等构造会对诱发地震产生强烈的方向控制。这也会使注水滞后数月。这一滞后具有物理意义，相当于压力和应力变化从注入井传播到预先存在的严重应力断层所需的时间。它受多种因素控制，如注入区间与原有断层之间的距离、水文地质条件以及断层重新激活所需的应力变化。加拿大 Alberta 省的例子表明，地震活动可能会比世界水坝排水系统的运行滞后数年甚至数十年。

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The time lag was particularly evident during the seismic crisis in Oklahomacase (Box 2) in 2014–2016 when the state government acted to substantially reduce WWD volumes in mid-2016. By reducing, but not stopping disposal, seismicity has stabilized, although it remains elevated relative to the tectonic background rate. Similar steps have been taken in TX, USA in response to elevated seismicity near the cities of Midland and Odessa since 2022. Time will tell whether these reductions prove sufficient or whether other measures must be taken. Geomechanical approaches for managing WWD over the long term appear promising, based on the understanding gained from induced seismicity in the Oklahoma case.

在 2014-2016 年俄克拉荷马州的地震危机期间（方框 2），州政府在 2016 年年中采取行动大幅减少了 WWD 的数量，这一时间滞后尤为明显。通过减少而非停止弃置，地震活动已趋于稳定，尽管相对于构造背景速率而言，地震活动仍然较高。自 2022 年以来，美国德克萨斯州也采取了类似措施，以应对米德兰市和敖德萨市附近的地震活动。时间将证明这些减少措施是否足够，或者是否必须采取其他措施。根据对俄克拉荷马州诱发地震的了解，长期管理 WWD 的地质力学方法似乎大有可为。

In summary, physics-based approaches can enhance the current seismic monitoring, hazard and risk assessments and mitigation strategies. However, even the state-of-the-art cannot anticipate and prevent the occurrence of moderate-to-large magnitude earthquakes, namely, exceeding M4.

总之，基于物理学的方法可以加强当前的地震监测、灾害和风险评估以及减灾战略。然而，即使是最先进的方法也无法预测和预防中-大震级地震的发生，即超过 M4 的地震。

The operation and induced seismicity feedback loop. Operations are planned to avoid and minimize the impacts of induced seismicity. Seismic and geophysical monitoring provide data for models that can forecast earthquakes. Earthquake catalogues and source models can be used in hazard and risk assessments. Finally, risk and hazard assessments can be used to inform the design of a traffic light protocol (TLP), which acts as a real-time decision module for the operation. Each panel shows the categories of input information (blue boxes) and output products (orange boxes).

运行和诱发地震反馈回路。规划运行以避免和尽量减少诱发地震的影响。地震和地球物理监测为地震预报模型提供数据。地震目录和震源模型可用于灾害和风险评估。最后，风险和危害评估可用于交通信号灯协议（TLP）的设计，该协议可作为运行的实时决策模块。每个面板显示输入信息（蓝色方框）和输出产品（橙色方框）的类别。

Summary and future directions

Underground fluid injection and extraction activate complex physical processes that destabilize pre-existing faults. Fluid-induced earthquakes are mainly triggered by in situ stress perturbations on critically stressed faults. However, human activities might reactivate faults that were not critically stressed before the start of operation. The major triggering mechanisms of injection-induced and extraction-induced seismicity are pore-pressure diffusion and poroelastic coupling, respectively. During injection, pore-pressure elevation reduces the effective normal stress acting on fault planes leading to failure.

地下流体注入和抽取会激活复杂的物理过程，破坏原有断层的稳定性。流体诱发地震主要是由严重受压断层上的原位应力扰动引发的。然而，人类活动可能会重新激活在开始运行之前并未严重受压的断层。注入诱发地震和开采诱发地震的主要触发机制分别是孔隙压力扩散和孔弹性耦合。在注入过程中，孔隙压力升高降低了作用在断层面上的有效法向应力，导致断层破坏。

Also, poroelastic coupling can lead to reservoir compaction and perturb the stress field in the surrounding rock formations during fluid extraction and trigger earthquakes. These mechanisms often explain most seismic swarms around injection or extraction sites. However, other mechanisms such as aseismic deformation and earthquake interactions explain the stress transfer to distant locations.

此外，孔弹性耦合会导致储层压实，并在流体抽取过程中扰动周围岩层的应力场，引发地震。这些机制通常可以解释注水或抽采场周围的大多数地震群。然而，其他机制，如地震变形和地震相互作用，也能解释应力向远处传递的原因。

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Multiphysical modelling studies at well-characterized locations show that the relative importance of different triggering mechanisms can vary from site to site. An important aspect is the complex interaction among different industrial activities specifically when the earthquakes occur in an area where both hydraulic fracturing and WWD are occurring. One important question is to determine the dominating mechanisms and the main activity that is responsible to generate each seismicity cluster. Apparently, the amount of stress perturbation caused by different activities can be highly nonlinear and depends on many physical factors such as the distance to each well, the amount of injected volume, the operational time windows and the corresponding geological and hydrological characteristics.

在特征明显的地点进行的多物理模型研究表明，不同触发机制的相对重要性因地而异。一个重要的方面是不同工业活动之间复杂的相互作用，特别是当地震发生在同时进行水力压裂和 WWD 的地区时。一个重要的问题是确定产生每个地震群的主导机制和主要活动。显然，不同活动引起的应力扰动量可能是高度非线性的，并取决于许多物理因素，如与每口井的距离、注入量、作业时间窗口以及相应的地质和水文特征。

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Also, debates on the triggering mechanism or hypocentral depth of induced earthquakes are typically related to poor monitoring infrastruc- ture such as in offshore operations. Hence, physics-based design of microseismic monitoring network at each site might aid inferring the controlling mechanisms of induced seismicity. As an alternative, distributed acoustic sensing technology, which utilizes an optical fibre cable as the sensing element, can be sensitive enough to record microseismic events and provide reliable depth estimations. However, further research is necessary to elucidate the complementary opportunities and inherent limitations of distributed acoustic sensing technology.

此外，关于诱发地震的触发机制或次中心深度的争论通常与监测基础设施薄弱有关，如近海作业。因此，在每个地点设计基于物理学的微震监测网络可能有助于推断诱发地震的控制机制。作为替代方案，分布式声学传感技术利用光纤电缆作为传感元件，其灵敏度足以记录微震事件并提供可靠的深度估计。不过，有必要开展进一步研究，以阐明分布式声学传感技术的互补机会和固有局限。

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The current physical understanding is often inferred from largescale in situ experiments, in which the limited access and exposure of the target rock mass at great depth hinders precise measurements of THMC changes in the rock mass. As an alternative, in situ experiments at underground laboratories (decametre-to-hectometre scale) are evolving as an alternative to bridge the gap between the observations in the laboratory and field-scale operations. The major advantage of small-scale experiments is the possibility to precisely characterize the rock mass and in situ condition with full control over operational variants.

目前对物理的理解往往是通过大规模的现场实验推断出来的，在这些实验中，由于进入和暴露目标岩体的深度有限，无法精确测量岩体中 THMC 的变化。作为一种替代方法，在地下实验室进行的原位实验（分米级到八分米级）正在不断发展，以弥补实验室观测与实地操作之间的差距。小规模实验的主要优点是可以精确地描述岩体和原地条件的特征，并完全控制操作变数。

Extensive instrumentation provides high-resolution data sets that determine the physical processes controlling the seismicity and test the effectiveness of methodological advances that mitigate the seismic risk. In addition, such experiments can benchmark the numerical models that resolve the coupled processes at in situ conditions. However, numerical modelling of coupled processes demands anintensivecomputationaleffort.Hence, the developments in high-performance and efficient computing tools such as physics-based machine learning open a new door to resolve the 3D multiphysics problems and to quantify the uncertainty of the model parameters.

广泛的仪器可提供高分辨率的数据集，从而确定控制地震的物理过程，并检验减轻地震风险的先进方法的有效性。此外，这些实验还能为解决现场条件下耦合过程的数值模型提供基准。因此，高性能和高效计算工具（如基于物理的机器学习）的发展为解决三维多物理场问题和量化模型参数的不确定性打开了一扇新的大门。

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Ideally, the evaluation of induced seismicity hazard should be conducted with a deterministic approach, with high-resolution char- acterization of pre-existing fractures and faults, detailed 3D stress information, a fundamental understanding of physical mechanisms and transparent injection plans. In reality, these priors are barely available and constraining the magnitude and triggering time of induced earthquakes is challenging, just like natural earthquakes. Therefore, at the current stage, induced seismicity hazard has to be estimated statistically and only a few physical factors are integrated into physics-based models. From this aspect, our Review elucidates the importance of physics-based models that capture the multiphysical processes that control the rupture nucleation, propagation and arrest across multiple regions and scales.

理想情况下，对诱发地震危险性的评估应采用确定性方法，对已存在的断裂和断层进行高分辨率的特征描述，提供详细的三维应力信息，从根本上了解物理机制，并制定透明的注入计划。在现实中，这些先验条件几乎都不存在，要制约诱发地震的震级和触发时间与天然地震一样具有挑战性。因此，在现阶段，诱发地震的危害必须通过统计来估计，只有少数物理因素被纳入基于物理的模型。从这个角度来看，我们的综述阐明了基于物理的模型的重要性，这些模型能够捕捉控制多区域和多尺度破裂成核、传播和停顿的多重物理过程。