{"id":258,"date":"2022-01-13T23:17:33","date_gmt":"2022-01-13T23:17:33","guid":{"rendered":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/induced-seismicity\/"},"modified":"2022-01-16T18:07:54","modified_gmt":"2022-01-16T18:07:54","slug":"induced-seismicity","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/induced-seismicity\/","title":{"raw":"5.2  Induced Seismicity","rendered":"5.2  Induced Seismicity"},"content":{"raw":"<div class=\"induced-seismicity\">\r\n<p class=\"import-Normal\">In recent years, concerns have been raised about the risk of inducing or triggering seismic activity as a consequence of pumping water from or injecting water into geologic formations (Ellsworth, 2013). Very recently, injection\u2011induced earthquakes have become a discussion topic and a focus for research in connection with (i) hydraulic fracturing of tight shale formations for hydrocarbon production; (ii) disposal of wastewaters; and (iii) enhanced geothermal systems. The activation of thrusts\/faults caused by groundwater withdrawal (as well as by fluid injection) may pose a serious hazard of anthropogenic seismicity. According to Ellsworth (2013), the mechanism responsible for inducing seismicity \"appears to be the well\u2011understood process of weakening a pre\u2011existing fault\" by changing the fault loading conditions. In essence, \"increasing the shear stress, reducing the normal stress and\/or elevating the pore pressure can bring the fault to failure triggering the nucleation of an earthquake\" (Figure\u00a033). The number of earthquakes with magnitude <em class=\"import-Cambria\">M<\/em>\u00a0\u2265\u00a03 <em class=\"import-Cambria\">r<\/em>ecorded annually in the USA midcontinent has grown significantly since 2001, with anthropogenic earthquakes suspected as being largely responsible for the increase. Magnitudes are usually determined from measurements of an earthquake's seismic waves as recorded on a seismogram. Notice that the <em class=\"import-Cambria\">M<\/em> scale is logarithmic, so that each unit represents a ten\u2011fold increase in the amplitude of the seismic waves. The value <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a03 characterizes \u201cminor\u201d events, i.e., events often felt by people, but very rarely causing damage. As the energy of a seismic wave is 10<sup>1.5<\/sup> times its amplitude, each unit of magnitude represents a nearly 32\u2011fold increase in the seismic energy (strength) of an earthquake. Earthquake initiation and propagation is site\u2011dependent, influenced by fault frictional properties and geometry, the pre\u2011seismic natural stress regime, stress changes induced by anthropogenic activity, and the volume of injected or pumped fluid.<\/p>\r\n<img class=\"alignnone wp-image-410 size-full\" src=\"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33.jpg\" alt=\"Sketch of the mechanisms inducing earthquakes\" width=\"937\" height=\"670\" \/>\r\n<p class=\"import-Normal\"><strong>Figure\u00a0<\/strong><strong>33<\/strong><strong>\u00a0<\/strong><strong>\u2011\u00a0<\/strong>Sketch of the mechanisms inducing earthquakes: (left) pore pressure increase or (right) change of the geostatic load in the vicinity of a fault. In the above cases, both the effective normal and tangential stresses acting on the fault change, causing fault reactivation (after Schultz et al., 2017).<\/p>\r\n<p class=\"import-Normal\">Several cases have been reported in which micro\u2011seismic events were correlated directly to hydraulic fracking. These cases are notable because of the public concern they raised, although the magnitudes are small, usually not creating appreciable damages. Extracting hydrocarbons from shale requires the generation of a network of open fractures connected to the producing boreholes. This is accomplished by way of a high\u2011pressure injection of water into the formation. Thus, fracking intentionally induces numerous micro\u2011seismic events, the vast majority of which are of <em class=\"import-Cambria\">M<\/em>\u00a0&lt;\u00a01. However, a number of cases have recently been experienced where earthquakes large enough to be felt correlated directly to hydraulic fracturing. Holland (2013) investigated a sequence of events in south\u2011central Oklahoma, with maximum <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a02.9, revealing a clear temporal correlation between fracking operations in a nearby well and seismic activity. On April 2011, the Blackpool area of northern England experienced seismicity of magnitude 2.3 shortly after the hydraulic fracturing of a well to develop a shale gas reservoir in the Bowland basin (The Royal Society and the Royal Academy of Engineering, 2012).<\/p>\r\n<p class=\"import-Normal\">Injection disposal wells appear to have triggered or induced several earthquake sequences in the mid\u2011western USA. Before 2011, the <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a04.8 event in 1967 near Denver, Colorado, USA, was the largest event widely accepted in the scientific community as having been induced by wastewater injection (Hermann and Park,1981). By that time, the earthquakes had migrated as far as 10\u00a0km from the injection point along an ancient fault system, tracing a critical pressure front of 3.2\u00a0MPa. Wastewater disposal appears to have induced over 109 small earthquakes (0.4\u00a0&lt;\u00a0<em class=\"import-Cambria\">M<\/em><em>\u00a0<\/em>&lt;\u00a03.9) from January 2011 to February 2012 in Youngstown, Ohio, USA, close to a deep fluid injection well. The main shocks occurred at depths between 3500 and 4000\u00a0m along a fault located in the Precambrian basement (Kim, 2013). A similar situation was observed in central Arkansas, USA (Horton, 2012).<\/p>\r\n<p class=\"import-Normal\">A number of studies have explored the response of water injection\u2011induced activity in enhanced geothermal systems. The most prominent example is an <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a03.4 event induced in 2006 by the stimulation of a geothermal reservoir below the city of Basel, Switzerland, at a depth of about 5000\u00a0m (H\u00e4ring et al., 2008). Thousands of smaller shocks were recorded afterward, leading insurance companies to claim over 7 million euros in damage. In 2003, at the geothermal site of Soultz\u2011sous\u2011Forts, France, stimulation of the 4800\u00a0m deep reservoir produced seismic events with magnitude of up to <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a02.9 in 2003 (Baisch et al., 2010). Epicenters align along a preexisting subvertical regional\u2011scale fault structure. A hot\u2011fractured\u2011rock project was launched at Cooper Basin, South Australia, in 2002 to exploit the Habanero granite reservoir at a depth of 4000\u20114500\u00a0m. Various stimulation experiments have been conducted which triggered earthquakes with moment magnitude between 1.7 and 3.1 with hypocentral distances between 2.4 and 7.8\u00a0km and depth between 3900 and 4500\u00a0m (Baisch et al., 2010). In these cases, injection caused significant changes in the effective stress regime due to both the pressure change of the formation fluid and the thermal drawdown of the rock, increasing the likelihood of fault reactivation and consequently, induced seismicity (Gan and Elsworth, 2014).<\/p>\r\n<p class=\"import-Normal\">As regards the possibility of inducing seismic events by groundwater pumping, the <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a05.1 earthquake that occurred in May 2011 in Lorca, southeast Spain, is a renowned case study. The earthquake struck the city of Lorca causing significant property damage, injuring hundreds of people and resulting in nine casualties. The hypocenter was located in a complex, active system of strike\u2011slip faults at a depth of 3\u00a0km. According to Gonzalez et al. (2012), the event may have been triggered by the significant crustal unloading caused by the 250\u00a0m decline in groundwater level occurring between 1960 and 2010 as a consequence of aquifer over\u2011draft. The decrease in total stress may have relaxed the effective normal stress acting on the fault plane, thus triggering its reactivation. However, we note that there exists no general consensus in regards to the relation between piezometric lowering and the 2011 event.<\/p>\r\n<p class=\"import-Normal\">When concern is raised about the possibility of inducing earthquakes, an area\u2011wide reconnaissance study aimed at identifying major geological discontinuities is of paramount importance. These data are best used as input to a modeling tool capable of predicting fault\/thrust activation resulting from the removal or injection of fluid (Ferronato et al., 2008; Gan and Elsworth, 2014; Jha and Juanes, 2014; and, Teatini et al., 2014). With the aid of an ad hoc model, we can estimate the sliding of the fault\/thrust, and hence predict the seismic moment. The seismic literature presents several empirical relationships enabling us to predict the possible magnitude <em class=\"import-Cambria\">M<\/em> induced by a fault\/thrust reactivation. Recently, Mazzoldi et al. (2012) have suggested an equation based on the seismicity theory that provides an estimate of the seismic moment <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub> of a possible seismic event induced or triggered by a fault\/thrust slip as expressed by Equation\u00a029.<a id=\"eq_29\"><\/a><\/p>\r\n\r\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 10%;\"><\/td>\r\n<td style=\"width: 80%; text-align: center;\"><em>M<\/em><sub>0<\/sub> = <em>G<\/em> \u0394<em>L<\/em> \u0394<em>Z<\/em><sub><em>a<\/em><\/sub> s<sub><em>a<\/em><\/sub><\/td>\r\n<td style=\"width: 10%; text-align: right;\">(29)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 15%; text-align: right; vertical-align: top;\">\u0394<em>L<\/em><\/td>\r\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\r\n<td style=\"width: 83%; vertical-align: top;\">horizontal length of the activated portion of the fault\/thrust (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 15%; text-align: right; vertical-align: top;\">\u0394<em>Z<\/em><sub><em>a<\/em><\/sub><\/td>\r\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\r\n<td style=\"width: 83%; vertical-align: top;\">height of the activated portion of the fault\/thrust (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>s<\/em><sub><em>a<\/em><\/sub><\/td>\r\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\r\n<td style=\"width: 83%; vertical-align: top;\">average slip of the fault\/thrust surfaces (L)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>G<\/em><\/td>\r\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\r\n<td style=\"width: 83%; vertical-align: top;\">shear modulus of the formation incorporating the reactivated fault\/thrust (ML<sup>\u22121<\/sup>T<sup>\u22122<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p class=\"import-Normal\"><em class=\"import-Cambria\">G<\/em> is related to soil compressibility through the relationship shown in Equation\u00a030.<a id=\"eq_30\"><\/a><\/p>\r\n\r\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 10%;\"><\/td>\r\n<td style=\"width: 80%; text-align: center;\">[latex]\\displaystyle G=\\frac{1}{2c_{b}}\\frac{1-2\\nu }{1-\\nu }[\/latex]<\/td>\r\n<td style=\"width: 10%; text-align: right;\">(30)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>\u03bd<\/em><\/td>\r\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\r\n<td style=\"width: 83%; vertical-align: top;\">Poisson\u2019s ratio (ratio of transverse strain to axial strain in simple uni-axial compression)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p class=\"import-Normal\">The seismic moment <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub> obtained from Equation\u00a029 may be converted into a moment magnitude <em class=\"import-Cambria\">M<\/em> used to measure the strength of the seismic event. The <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub>\u00a0\u2011\u00a0<em class=\"import-Cambria\">M<\/em> relationship was defined by (Kanamori and Anderson, 1975) as shown in Equation\u00a031.<a id=\"eq_31\"><\/a><\/p>\r\n\r\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 10%;\"><\/td>\r\n<td style=\"width: 80%; text-align: center;\">[latex]M=\\frac{2}{3}\\left ( \\textup{log}_{10}M_{0}-9.1 \\right )[\/latex]<\/td>\r\n<td style=\"width: 10%; text-align: right;\">(31)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p class=\"import-Normal\"><em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\"><em>0<\/em><\/sub> is expressed in Newton\u2011meters (Nm). As far as <em class=\"import-Cambria\">G<\/em> is concerned, in Equation\u00a030 we have to use the value of <em>c<\/em><sub><em>b<\/em><\/sub> in the first loading cycle if the aquifer is pumped, and in the second unloading\/reloading phase if the aquifer is recharged\/repressurized. As a matter of fact, seismicity during reservoir production typically occurs when the pore pressure depletion has achieved relatively high values, that is, with a stress state never experienced previously by the reservoir formation. The Groningen reservoir in The Netherlands is an example where this occurred (van Thienen\u2011Visser and Breunese, 2015.)<\/p>\r\n\r\n<\/div>","rendered":"<div class=\"induced-seismicity\">\n<p class=\"import-Normal\">In recent years, concerns have been raised about the risk of inducing or triggering seismic activity as a consequence of pumping water from or injecting water into geologic formations (Ellsworth, 2013). Very recently, injection\u2011induced earthquakes have become a discussion topic and a focus for research in connection with (i) hydraulic fracturing of tight shale formations for hydrocarbon production; (ii) disposal of wastewaters; and (iii) enhanced geothermal systems. The activation of thrusts\/faults caused by groundwater withdrawal (as well as by fluid injection) may pose a serious hazard of anthropogenic seismicity. According to Ellsworth (2013), the mechanism responsible for inducing seismicity &#8220;appears to be the well\u2011understood process of weakening a pre\u2011existing fault&#8221; by changing the fault loading conditions. In essence, &#8220;increasing the shear stress, reducing the normal stress and\/or elevating the pore pressure can bring the fault to failure triggering the nucleation of an earthquake&#8221; (Figure\u00a033). The number of earthquakes with magnitude <em class=\"import-Cambria\">M<\/em>\u00a0\u2265\u00a03 <em class=\"import-Cambria\">r<\/em>ecorded annually in the USA midcontinent has grown significantly since 2001, with anthropogenic earthquakes suspected as being largely responsible for the increase. Magnitudes are usually determined from measurements of an earthquake&#8217;s seismic waves as recorded on a seismogram. Notice that the <em class=\"import-Cambria\">M<\/em> scale is logarithmic, so that each unit represents a ten\u2011fold increase in the amplitude of the seismic waves. The value <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a03 characterizes \u201cminor\u201d events, i.e., events often felt by people, but very rarely causing damage. As the energy of a seismic wave is 10<sup>1.5<\/sup> times its amplitude, each unit of magnitude represents a nearly 32\u2011fold increase in the seismic energy (strength) of an earthquake. Earthquake initiation and propagation is site\u2011dependent, influenced by fault frictional properties and geometry, the pre\u2011seismic natural stress regime, stress changes induced by anthropogenic activity, and the volume of injected or pumped fluid.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-410 size-full\" src=\"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33.jpg\" alt=\"Sketch of the mechanisms inducing earthquakes\" width=\"937\" height=\"670\" srcset=\"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33.jpg 937w, https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33-300x215.jpg 300w, https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33-768x549.jpg 768w, https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33-65x46.jpg 65w, https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33-225x161.jpg 225w, https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/uploads\/sites\/20\/2022\/01\/figure33-350x250.jpg 350w\" sizes=\"auto, (max-width: 937px) 100vw, 937px\" \/><\/p>\n<p class=\"import-Normal\"><strong>Figure\u00a0<\/strong><strong>33<\/strong><strong>\u00a0<\/strong><strong>\u2011\u00a0<\/strong>Sketch of the mechanisms inducing earthquakes: (left) pore pressure increase or (right) change of the geostatic load in the vicinity of a fault. In the above cases, both the effective normal and tangential stresses acting on the fault change, causing fault reactivation (after Schultz et al., 2017).<\/p>\n<p class=\"import-Normal\">Several cases have been reported in which micro\u2011seismic events were correlated directly to hydraulic fracking. These cases are notable because of the public concern they raised, although the magnitudes are small, usually not creating appreciable damages. Extracting hydrocarbons from shale requires the generation of a network of open fractures connected to the producing boreholes. This is accomplished by way of a high\u2011pressure injection of water into the formation. Thus, fracking intentionally induces numerous micro\u2011seismic events, the vast majority of which are of <em class=\"import-Cambria\">M<\/em>\u00a0&lt;\u00a01. However, a number of cases have recently been experienced where earthquakes large enough to be felt correlated directly to hydraulic fracturing. Holland (2013) investigated a sequence of events in south\u2011central Oklahoma, with maximum <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a02.9, revealing a clear temporal correlation between fracking operations in a nearby well and seismic activity. On April 2011, the Blackpool area of northern England experienced seismicity of magnitude 2.3 shortly after the hydraulic fracturing of a well to develop a shale gas reservoir in the Bowland basin (The Royal Society and the Royal Academy of Engineering, 2012).<\/p>\n<p class=\"import-Normal\">Injection disposal wells appear to have triggered or induced several earthquake sequences in the mid\u2011western USA. Before 2011, the <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a04.8 event in 1967 near Denver, Colorado, USA, was the largest event widely accepted in the scientific community as having been induced by wastewater injection (Hermann and Park,1981). By that time, the earthquakes had migrated as far as 10\u00a0km from the injection point along an ancient fault system, tracing a critical pressure front of 3.2\u00a0MPa. Wastewater disposal appears to have induced over 109 small earthquakes (0.4\u00a0&lt;\u00a0<em class=\"import-Cambria\">M<\/em><em>\u00a0<\/em>&lt;\u00a03.9) from January 2011 to February 2012 in Youngstown, Ohio, USA, close to a deep fluid injection well. The main shocks occurred at depths between 3500 and 4000\u00a0m along a fault located in the Precambrian basement (Kim, 2013). A similar situation was observed in central Arkansas, USA (Horton, 2012).<\/p>\n<p class=\"import-Normal\">A number of studies have explored the response of water injection\u2011induced activity in enhanced geothermal systems. The most prominent example is an <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a03.4 event induced in 2006 by the stimulation of a geothermal reservoir below the city of Basel, Switzerland, at a depth of about 5000\u00a0m (H\u00e4ring et al., 2008). Thousands of smaller shocks were recorded afterward, leading insurance companies to claim over 7 million euros in damage. In 2003, at the geothermal site of Soultz\u2011sous\u2011Forts, France, stimulation of the 4800\u00a0m deep reservoir produced seismic events with magnitude of up to <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a02.9 in 2003 (Baisch et al., 2010). Epicenters align along a preexisting subvertical regional\u2011scale fault structure. A hot\u2011fractured\u2011rock project was launched at Cooper Basin, South Australia, in 2002 to exploit the Habanero granite reservoir at a depth of 4000\u20114500\u00a0m. Various stimulation experiments have been conducted which triggered earthquakes with moment magnitude between 1.7 and 3.1 with hypocentral distances between 2.4 and 7.8\u00a0km and depth between 3900 and 4500\u00a0m (Baisch et al., 2010). In these cases, injection caused significant changes in the effective stress regime due to both the pressure change of the formation fluid and the thermal drawdown of the rock, increasing the likelihood of fault reactivation and consequently, induced seismicity (Gan and Elsworth, 2014).<\/p>\n<p class=\"import-Normal\">As regards the possibility of inducing seismic events by groundwater pumping, the <em class=\"import-Cambria\">M<\/em>\u00a0=\u00a05.1 earthquake that occurred in May 2011 in Lorca, southeast Spain, is a renowned case study. The earthquake struck the city of Lorca causing significant property damage, injuring hundreds of people and resulting in nine casualties. The hypocenter was located in a complex, active system of strike\u2011slip faults at a depth of 3\u00a0km. According to Gonzalez et al. (2012), the event may have been triggered by the significant crustal unloading caused by the 250\u00a0m decline in groundwater level occurring between 1960 and 2010 as a consequence of aquifer over\u2011draft. The decrease in total stress may have relaxed the effective normal stress acting on the fault plane, thus triggering its reactivation. However, we note that there exists no general consensus in regards to the relation between piezometric lowering and the 2011 event.<\/p>\n<p class=\"import-Normal\">When concern is raised about the possibility of inducing earthquakes, an area\u2011wide reconnaissance study aimed at identifying major geological discontinuities is of paramount importance. These data are best used as input to a modeling tool capable of predicting fault\/thrust activation resulting from the removal or injection of fluid (Ferronato et al., 2008; Gan and Elsworth, 2014; Jha and Juanes, 2014; and, Teatini et al., 2014). With the aid of an ad hoc model, we can estimate the sliding of the fault\/thrust, and hence predict the seismic moment. The seismic literature presents several empirical relationships enabling us to predict the possible magnitude <em class=\"import-Cambria\">M<\/em> induced by a fault\/thrust reactivation. Recently, Mazzoldi et al. (2012) have suggested an equation based on the seismicity theory that provides an estimate of the seismic moment <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub> of a possible seismic event induced or triggered by a fault\/thrust slip as expressed by Equation\u00a029.<a id=\"eq_29\"><\/a><\/p>\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 10%;\"><\/td>\n<td style=\"width: 80%; text-align: center;\"><em>M<\/em><sub>0<\/sub> = <em>G<\/em> \u0394<em>L<\/em> \u0394<em>Z<\/em><sub><em>a<\/em><\/sub> s<sub><em>a<\/em><\/sub><\/td>\n<td style=\"width: 10%; text-align: right;\">(29)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>where:<\/p>\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 15%; text-align: right; vertical-align: top;\">\u0394<em>L<\/em><\/td>\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\n<td style=\"width: 83%; vertical-align: top;\">horizontal length of the activated portion of the fault\/thrust (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 15%; text-align: right; vertical-align: top;\">\u0394<em>Z<\/em><sub><em>a<\/em><\/sub><\/td>\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\n<td style=\"width: 83%; vertical-align: top;\">height of the activated portion of the fault\/thrust (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>s<\/em><sub><em>a<\/em><\/sub><\/td>\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\n<td style=\"width: 83%; vertical-align: top;\">average slip of the fault\/thrust surfaces (L)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>G<\/em><\/td>\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\n<td style=\"width: 83%; vertical-align: top;\">shear modulus of the formation incorporating the reactivated fault\/thrust (ML<sup>\u22121<\/sup>T<sup>\u22122<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"import-Normal\"><em class=\"import-Cambria\">G<\/em> is related to soil compressibility through the relationship shown in Equation\u00a030.<a id=\"eq_30\"><\/a><\/p>\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 10%;\"><\/td>\n<td style=\"width: 80%; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/ql-cache\/quicklatex.com-74c3db0a84db3d75a30787b68f4fcaeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#71;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#99;&#95;&#123;&#98;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#45;&#50;&#92;&#110;&#117;&#32;&#125;&#123;&#49;&#45;&#92;&#110;&#117;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"117\" style=\"vertical-align: -15px;\" \/><\/td>\n<td style=\"width: 10%; text-align: right;\">(30)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>where:<\/p>\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 15%; text-align: right; vertical-align: top;\"><em>\u03bd<\/em><\/td>\n<td style=\"width: 2%; text-align: center; vertical-align: top;\">=<\/td>\n<td style=\"width: 83%; vertical-align: top;\">Poisson\u2019s ratio (ratio of transverse strain to axial strain in simple uni-axial compression)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"import-Normal\">The seismic moment <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub> obtained from Equation\u00a029 may be converted into a moment magnitude <em class=\"import-Cambria\">M<\/em> used to measure the strength of the seismic event. The <em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\">0<\/sub>\u00a0\u2011\u00a0<em class=\"import-Cambria\">M<\/em> relationship was defined by (Kanamori and Anderson, 1975) as shown in Equation\u00a031.<a id=\"eq_31\"><\/a><\/p>\n<table style=\"border: none; border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 10%;\"><\/td>\n<td style=\"width: 80%; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-content\/ql-cache\/quicklatex.com-1a6238f2b1d53f845621ef90ef806508_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#77;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#32;&#92;&#116;&#101;&#120;&#116;&#117;&#112;&#123;&#108;&#111;&#103;&#125;&#95;&#123;&#49;&#48;&#125;&#77;&#95;&#123;&#48;&#125;&#45;&#57;&#46;&#49;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"176\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 10%; text-align: right;\">(31)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"import-Normal\"><em class=\"import-Cambria\">M<\/em><sub class=\"import-Cambria\"><em>0<\/em><\/sub> is expressed in Newton\u2011meters (Nm). As far as <em class=\"import-Cambria\">G<\/em> is concerned, in Equation\u00a030 we have to use the value of <em>c<\/em><sub><em>b<\/em><\/sub> in the first loading cycle if the aquifer is pumped, and in the second unloading\/reloading phase if the aquifer is recharged\/repressurized. As a matter of fact, seismicity during reservoir production typically occurs when the pore pressure depletion has achieved relatively high values, that is, with a stress state never experienced previously by the reservoir formation. The Groningen reservoir in The Netherlands is an example where this occurred (van Thienen\u2011Visser and Breunese, 2015.)<\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":22,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-258","chapter","type-chapter","status-publish","hentry"],"part":147,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/258","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":4,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/258\/revisions"}],"predecessor-version":[{"id":415,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/258\/revisions\/415"}],"part":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/parts\/147"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/258\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/media?parent=258"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapter-type?post=258"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/contributor?post=258"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/license?post=258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}