We report systematic first-principles results of structural properties and compression behavior based on density functional theory (DFT) and an exchange-correlation functional for solids, of Al-bearing garnets of general compositions in the pyrope-almandine-grossular solid solution system. The combination of DFT and a simple solid solution model is able to produce a compositional dependence of the compression curve consistent with trends observed in experimental studies. Using end-member properties extrapolated from our computations and perturbing an extant thermodynamic model we observe only marginal effects on the bulk sound velocity of pyrolite and MORB along relevant geothermal paths. However, this could hide important effects on the elemental partitioning between garnet and other major phases which should be further investigated both experimentally and computationally. We also present simulations of the effect of combined Fe and Ca substitutions for Mg on the elastic tensor of Al-bearing garnets, our simplified modeling shows only partial agreement with the trends observed in experiments. Therefore, further computational investigations, especially of the effect of Fe-Mg substitution on the tensor, are needed.
{"title":"Effects of Fe-Ca-Mg substitutions on the equation-of-state of pyrope-rich garnet from ab initio modeling and experiments: Insights and implications for the upper mantle","authors":"Maribel Núñez-Valdez , Niccolò Satta , Sergio Speziale","doi":"10.1016/j.pepi.2024.107171","DOIUrl":"10.1016/j.pepi.2024.107171","url":null,"abstract":"<div><p>We report systematic first-principles results of structural properties and compression behavior based on density functional theory (DFT) and an exchange-correlation functional for solids, of Al-bearing garnets of general compositions in the pyrope-almandine-grossular solid solution system. The combination of DFT and a simple solid solution model is able to produce a compositional dependence of the compression curve consistent with trends observed in experimental studies. Using end-member properties extrapolated from our computations and perturbing an extant thermodynamic model we observe only marginal effects on the bulk sound velocity of pyrolite and MORB along relevant geothermal paths. However, this could hide important effects on the elemental partitioning between garnet and other major phases which should be further investigated both experimentally and computationally. We also present simulations of the effect of combined Fe and Ca substitutions for Mg on the elastic tensor of Al-bearing garnets, our simplified modeling shows only partial agreement with the trends observed in experiments. Therefore, further computational investigations, especially of the effect of Fe-Mg substitution on the tensor, are needed.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140181981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-13DOI: 10.1016/j.pepi.2024.107169
Arun K. Ojha , D.P. Monika Saini , Amar Agarwal , Ambrish K. Pandey
Singhbhum Craton (SC) hosted eight different dyke swarm events, which are collectively known as the Newer Dolerite Dykes. These have been correlated with different cratons and supercontinents based on age, geochemistry, and paleomagnetic data. However, our understanding of stress conditions during and after the dyke intrusions and the magma chamber dynamics is limited due to lack of information. In this study, we have investigated magma dynamics and crustal extension for different dyke swarm events in the SC to explore the magma chamber dynamics during the supercontinent breakup and at other cratons around the globe. Further, we have also quantified post-intrusion response to the far-field stress in different dyke swarms of the SC. For a comprehensive understanding of the magma dynamics and deformation history of the dyke swarms, we investigated dykes associated structures and estimated the magma pressure relative to the principal stresses. We used dyke wall attitude data to explore the paleostress conditions during the dyke intrusion, fault-slip data for post-emplacement deformation, and field structures with dyke thickness data to understand magma dynamics and crustal extension.
Paleostress analysis in four dyke swarms indicates relatively higher magma pressure in the Pipilia dyke swarm compared to Ghatgaon, Keonjhar, and Kaptipada dyke swarms. This is further supported by the fact that Pipilia dykes are thicker than the other three dyke swarms. Post-emplacement deformation is evident from the fault-slip observations, tectonic fractures, and veins cross-cutting dykes and host rock. Fault-slip observations suggest an extensional tectonic event followed by a compressive one. The extensional stress regime, active during the intrusion of Pipilia dyke swarm, overprints the Ghatgaon dyke swarm, while the far-field stress from the Singhbhum Shear Zone affects all the analyzed dykes and the host rock. These observations are in agreement with the thinned lithosphere of SC. We estimate that the Ghatgaon swarm caused the maximum average crustal extension/dilation of 9.65%, while the Keonjhar swarm led to the least average extension of 1.58%. We suggest that the Pipila dyke swarm event may have dilated a part of the Columbia supercontinent by ∼8.5% as the dilations for other regions in the supercontinents are not known.
{"title":"Tectonic development in Singhbhum Craton, NE India decrypted from dyke swarms: A window to understand magma dynamics in Archean-Proterozoic supercontinents","authors":"Arun K. Ojha , D.P. Monika Saini , Amar Agarwal , Ambrish K. Pandey","doi":"10.1016/j.pepi.2024.107169","DOIUrl":"https://doi.org/10.1016/j.pepi.2024.107169","url":null,"abstract":"<div><p>Singhbhum Craton (SC) hosted eight different dyke swarm events, which are collectively known as the Newer Dolerite Dykes. These have been correlated with different cratons and supercontinents based on age, geochemistry, and paleomagnetic data. However, our understanding of stress conditions during and after the dyke intrusions and the magma chamber dynamics is limited due to lack of information. In this study, we have investigated magma dynamics and crustal extension for different dyke swarm events in the SC to explore the magma chamber dynamics during the supercontinent breakup and at other cratons around the globe. Further, we have also quantified post-intrusion response to the far-field stress in different dyke swarms of the SC. For a comprehensive understanding of the magma dynamics and deformation history of the dyke swarms, we investigated dykes associated structures and estimated the magma pressure relative to the principal stresses. We used dyke wall attitude data to explore the paleostress conditions during the dyke intrusion, fault-slip data for post-emplacement deformation, and field structures with dyke thickness data to understand magma dynamics and crustal extension.</p><p>Paleostress analysis in four dyke swarms indicates relatively higher magma pressure in the Pipilia dyke swarm compared to Ghatgaon, Keonjhar, and Kaptipada dyke swarms. This is further supported by the fact that Pipilia dykes are thicker than the other three dyke swarms. Post-emplacement deformation is evident from the fault-slip observations, tectonic fractures, and veins cross-cutting dykes and host rock. Fault-slip observations suggest an extensional tectonic event followed by a compressive one. The extensional stress regime, active during the intrusion of Pipilia dyke swarm, overprints the Ghatgaon dyke swarm, while the far-field stress from the Singhbhum Shear Zone affects all the analyzed dykes and the host rock. These observations are in agreement with the thinned lithosphere of SC. We estimate that the Ghatgaon swarm caused the maximum average crustal extension/dilation of 9.65%, while the Keonjhar swarm led to the least average extension of 1.58%. We suggest that the Pipila dyke swarm event may have dilated a part of the Columbia supercontinent by ∼8.5% as the dilations for other regions in the supercontinents are not known.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140137843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The earthquake, which occurred in Yogyakarta, Indonesia, on May 26, 2006, at 22:53:58 UTC with Mw ∼6.4, was one of the most destructive earthquakes in Indonesia. The earthquake caused thousands of fatalities, tens of thousands of injuries, and hundreds of thousands of house damages in the Yogyakarta area and its surroundings at a loss of billions of dollars. Previous studies from seismic tomography and satellite radar imaging hypothesized that the earthquake was caused by activating a so far unknown fault east of the Opak Fault. Although, in the beginning, the Opak fault was suspected to be the source of the Yogyakarta earthquake in 2006. This assumption was made because the damage was maximum in the Bantul area west of the Opak Fault. This study demonstrates that our seismic tomography achieved a higher resolution than the previous study and could resolve a failed complex fault system. We utilized more aftershocks (2170 events) and smaller grid sizes for seismic tomography inversion. Four focal mechanisms from aftershocks for Mw ≥ 4.5 were also conducted to support structure interpretation in the study area. Our results successfully delineate the Opak Fault and the second fault, namely the Ngalang Fault, parallel to the eastern part of the fault at a depth of 9 km. Two faults could be indicated by the velocity contrast of Vp, Vp/Vs ratio, and Vs from a horizontal section tomogram. Our focal mechanisms also support seismic tomography, revealing two fault planes in our study area. The results show that the two faults are connected by the Oyo Fault, which is ruptured in the opposite direction compared to the two faults.
{"title":"Detailed seismic structure beneath the earthquake zone of Yogyakarta 2006 (Mw ∼6.4), Indonesia, from local earthquake tomography","authors":"Virga Librian , Mohamad Ramdhan , Andri Dian Nugraha , Muhammad Maruf Mukti , Syuhada Syuhada , Birger-Gottfried Lühr , Sri Widiyantoro , Adityo Mursitantyo , Ade Anggraini , Zulfakriza Zulfakriza , Faiz Muttaqy , Yayan Mi'rojul Husni","doi":"10.1016/j.pepi.2024.107170","DOIUrl":"10.1016/j.pepi.2024.107170","url":null,"abstract":"<div><p>The earthquake, which occurred in Yogyakarta, Indonesia, on May 26, 2006, at 22:53:58 UTC with Mw ∼6.4, was one of the most destructive earthquakes in Indonesia. The earthquake caused thousands of fatalities, tens of thousands of injuries, and hundreds of thousands of house damages in the Yogyakarta area and its surroundings at a loss of billions of dollars. Previous studies from seismic tomography and satellite radar imaging hypothesized that the earthquake was caused by activating a so far unknown fault east of the Opak Fault. Although, in the beginning, the Opak fault was suspected to be the source of the Yogyakarta earthquake in 2006. This assumption was made because the damage was maximum in the Bantul area west of the Opak Fault. This study demonstrates that our seismic tomography achieved a higher resolution than the previous study and could resolve a failed complex fault system. We utilized more aftershocks (2170 events) and smaller grid sizes for seismic tomography inversion. Four focal mechanisms from aftershocks for Mw ≥ 4.5 were also conducted to support structure interpretation in the study area. Our results successfully delineate the Opak Fault and the second fault, namely the Ngalang Fault, parallel to the eastern part of the fault at a depth of 9 km. Two faults could be indicated by the velocity contrast of Vp, Vp/Vs ratio, and Vs from a horizontal section tomogram. Our focal mechanisms also support seismic tomography, revealing two fault planes in our study area. The results show that the two faults are connected by the Oyo Fault, which is ruptured in the opposite direction compared to the two faults.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140275562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-12DOI: 10.1016/j.pepi.2024.107168
Quentin Kriaa , Landeau Maylis , Le Bars Michael
At a late stage of its accretion, the Earth experienced high-energy planetary impacts. Following each collision, the metal core of the impactor sank into molten silicate magma oceans. The efficiency of chemical equilibration between these silicates and the metal core controlled the composition of the Earth interior and left a signature on geochemical and isotopic data. These data constrain the timing, pressure and temperature of Earth formation, but their interpretation strongly depends on the efficiency of metal-silicate mixing and equilibration. We investigate the role of planetary rotation on the dynamics of the sinking metal and on its chemical equilibration using laboratory experiments of particle clouds settling in a rotating fluid. Our clouds initially sink as spherical turbulent thermals, but after a critical depth, rotation becomes important and they transition to a vortical columnar flow aligned with the rotation axis. Applied to Earth formation, our results predict that rotation strongly affects the fall of metal in the magma ocean for impactors smaller than 459 km in radius on a proto-Earth that rotates twice faster than today. On a proto-Earth spinning 5 times faster than today, rotation is important for any impactor smaller than the Earth itself. In contrast with a thermal that grows in all directions, the vortical column grows vertically but keeps a constant horizontal extent. The slower dilution in vortical columns reduces chemical equilibration compared to previous estimates that neglect planetary rotation. We find that rotation significantly affects the degree of equilibration for highly siderophile elements with partition coefficients larger than . In this case, for a planet spinning twice faster than today, the degree of equilibration decreases by up to a factor 2 compared to previous estimates that neglect the effect of rotation. Finally, the ultimate fate of iron drops is to be detrained from the vortical column as an iron rain, reconciling the traditional iron rain scenario with the model of turbulent thermal.
{"title":"Influence of planetary rotation on metal-silicate mixing and equilibration in a magma ocean","authors":"Quentin Kriaa , Landeau Maylis , Le Bars Michael","doi":"10.1016/j.pepi.2024.107168","DOIUrl":"10.1016/j.pepi.2024.107168","url":null,"abstract":"<div><p>At a late stage of its accretion, the Earth experienced high-energy planetary impacts. Following each collision, the metal core of the impactor sank into molten silicate magma oceans. The efficiency of chemical equilibration between these silicates and the metal core controlled the composition of the Earth interior and left a signature on geochemical and isotopic data. These data constrain the timing, pressure and temperature of Earth formation, but their interpretation strongly depends on the efficiency of metal-silicate mixing and equilibration. We investigate the role of planetary rotation on the dynamics of the sinking metal and on its chemical equilibration using laboratory experiments of particle clouds settling in a rotating fluid. Our clouds initially sink as spherical turbulent thermals, but after a critical depth, rotation becomes important and they transition to a vortical columnar flow aligned with the rotation axis. Applied to Earth formation, our results predict that rotation strongly affects the fall of metal in the magma ocean for impactors smaller than 459 km in radius on a proto-Earth that rotates twice faster than today. On a proto-Earth spinning 5 times faster than today, rotation is important for any impactor smaller than the Earth itself. In contrast with a thermal that grows in all directions, the vortical column grows vertically but keeps a constant horizontal extent. The slower dilution in vortical columns reduces chemical equilibration compared to previous estimates that neglect planetary rotation. We find that rotation significantly affects the degree of equilibration for highly siderophile elements with partition coefficients larger than <span><math><msup><mn>10</mn><mn>3</mn></msup></math></span>. In this case, for a planet spinning twice faster than today, the degree of equilibration decreases by up to a factor 2 compared to previous estimates that neglect the effect of rotation. Finally, the ultimate fate of iron drops is to be detrained from the vortical column as an iron rain, reconciling the traditional iron rain scenario with the model of turbulent thermal.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The combination of ultrasonic technique with synchrotron X-ray diffraction and radiography in a multi-anvil apparatus was utilized to measure the elastic wave velocities of sodium aluminosilicate glass and melt with the partially depolymerized composition of Na3AlSi3O9 (NAS). The measurements were conducted at pressure and temperature of up to 7.3 GPa and at ambient temperature for glass and up to 4.3 GPa and 2120 K for melt, respectively. The compressional wave velocity (VP) of the NAS glass remained mostly constant up to 4 GPa; subsequently, it increased with increasing pressure. Additionally, the NAS glass exhibited a minimum shear wave velocity (VS) at 4–5 GPa. Alternatively, the VP of the NAS melt was smaller than that of the NAS glass, showing a velocity minimum at ∼2 GPa. The negative pressure dependence of VP of the NAS melt is completely different from the depolymerized diopside (Di) melt, which shows a monotonic increase in VP with pressure. The contrasting behavior of the NAS and Di melts is caused by the difference in their structure, characterized by their degree of polymerization. Natural magma found in the interior of the Earth, such as basalt, has a partially depolymerized composition. This study indicates that the magma can exhibit elastic properties with negative pressure dependence, similar to the NAS melt.
在一台多管仪器中,利用超声波技术与同步辐射 X 射线衍射和射线照相术的结合,测量了部分解聚成分为 NaAlSiO(NAS)的钠铝硅酸盐玻璃和熔体的弹性波速。玻璃的测量是在压力和温度分别高达 7.3 GPa 和环境温度下进行的,熔体的测量是在压力和温度分别高达 4.3 GPa 和 2120 K 下进行的。NAS 玻璃的压缩波速度()在 4 GPa 以下基本保持不变,随后随着压力的增加而增加。此外,NAS 玻璃在 4-5 GPa 时表现出最小剪切波速(V)。另外,NAS 熔体的剪切波速度小于 NAS 玻璃,在 ~2 GPa 处显示出速度最小值。NAS 熔体的负压依赖性完全不同于解聚的透辉石(Di)熔体,后者表现出随压力单调增加。NAS 和 Di 熔体的对比行为是由它们的结构差异造成的,其特点是它们的聚合度不同。地球内部的天然岩浆(如玄武岩)具有部分解聚成分。这项研究表明,岩浆可以表现出与负压相关的弹性特性,与 NAS 熔体类似。
{"title":"Elastic wave velocity measurements of sodium aluminosilicate glass and melt at high pressure and temperature","authors":"Naoki Takahashi , Tatsuya Sakamaki , Osamu Ikeda , Sho Kakizawa , Yuji Higo , Akio Suzuki","doi":"10.1016/j.pepi.2024.107167","DOIUrl":"10.1016/j.pepi.2024.107167","url":null,"abstract":"<div><p>The combination of ultrasonic technique with synchrotron X-ray diffraction and radiography in a multi-anvil apparatus was utilized to measure the elastic wave velocities of sodium aluminosilicate glass and melt with the partially depolymerized composition of Na<sub>3</sub>AlSi<sub>3</sub>O<sub>9</sub> (NAS). The measurements were conducted at pressure and temperature of up to 7.3 GPa and at ambient temperature for glass and up to 4.3 GPa and 2120 K for melt, respectively. The compressional wave velocity (<em>V</em><sub>P</sub>) of the NAS glass remained mostly constant up to 4 GPa; subsequently, it increased with increasing pressure. Additionally, the NAS glass exhibited a minimum shear wave velocity (<em>V</em><sub>S</sub>) at 4–5 GPa. Alternatively, the <em>V</em><sub>P</sub> of the NAS melt was smaller than that of the NAS glass, showing a velocity minimum at ∼2 GPa. The negative pressure dependence of <em>V</em><sub>P</sub> of the NAS melt is completely different from the depolymerized diopside (Di) melt, which shows a monotonic increase in <em>V</em><sub>P</sub> with pressure. The contrasting behavior of the NAS and Di melts is caused by the difference in their structure, characterized by their degree of polymerization. Natural magma found in the interior of the Earth, such as basalt, has a partially depolymerized composition. This study indicates that the magma can exhibit elastic properties with negative pressure dependence, similar to the NAS melt.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0031920124000256/pdfft?md5=5415ffd84d8ab5d465d2350f314ffe4c&pid=1-s2.0-S0031920124000256-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1016/j.pepi.2024.107157
Pejvak Javaheri , Julian P. Lowman , Paul J. Tackley
The rock and rock-ice mixtures of the core-enveloping spherical shells comprising terrestrial body interiors have thermally determined viscosities well described by an Arrhenius dependence. Accordingly, the implied viscosity contrasts determined from the activation energies (E) characterizing such bodies can reach values exceeding , for a temperature range that spans the conditions found from the lower mantle to the surface. In this study, we first explore the impact of implementing a cut-off to limit viscosity magnitude in cold regions. Using a spherical annulus geometry, we investigate the influence of core radius, surface temperature, and convective vigour on stagnant lid formation resulting from the extreme thermally induced viscosity contrasts. We demonstrate that the cut-off viscosity must be increased with decreasing curvature factor, (, where and are the inner and outer radii of the annulus, respectively), if the solutions are to be not only computationally manageable but physically valid. We find that for statistically-steady systems, the mean temperature decreases with core size, and that a viscosity contrast of at least is required for stagnant lid formation as decreases below 0.5. Inverting the results from over 80 calculations featuring stagnant lids (from a total of approximately 180 calculations), we apply an energy balance model for heat flow across the thermal boundary layers and find that the non-dimensionalized temperature in the Approximately Isothermal Layer (AIL) in the convecting region under a stagnant lid is well predicted by where is a function of E and , and is the non-dimensionalized surface temperature. Moreover, the normalized (i.e., non-dimensional) thickness of the stagnant lid, , can be obtained from a measurement of the non-dimensional surface heat flux once <
{"title":"Spherical geometry convection in a fluid with an Arrhenius thermal viscosity dependence: The impact of core size and surface temperature on the scaling of stagnant-lid thickness and internal temperature","authors":"Pejvak Javaheri , Julian P. Lowman , Paul J. Tackley","doi":"10.1016/j.pepi.2024.107157","DOIUrl":"10.1016/j.pepi.2024.107157","url":null,"abstract":"<div><p>The rock and rock-ice mixtures of the core-enveloping spherical shells comprising terrestrial body interiors have thermally determined viscosities well described by an Arrhenius dependence. Accordingly, the implied viscosity contrasts determined from the activation energies (E) characterizing such bodies can reach values exceeding <span><math><msup><mn>10</mn><mn>40</mn></msup></math></span>, for a temperature range that spans the conditions found from the lower mantle to the surface. In this study, we first explore the impact of implementing a cut-off to limit viscosity magnitude in cold regions. Using a spherical annulus geometry, we investigate the influence of core radius, surface temperature, and convective vigour on stagnant lid formation resulting from the extreme thermally induced viscosity contrasts. We demonstrate that the cut-off viscosity must be increased with decreasing curvature factor, <span><math><mi>f</mi></math></span> (<span><math><mo>=</mo><msub><mi>r</mi><mtext>in</mtext></msub><mo>/</mo><msub><mi>r</mi><mtext>out</mtext></msub></math></span>, where <span><math><msub><mi>r</mi><mtext>in</mtext></msub></math></span> and <span><math><msub><mi>r</mi><mtext>out</mtext></msub></math></span> are the inner and outer radii of the annulus, respectively), if the solutions are to be not only computationally manageable but physically valid. We find that for statistically-steady systems, the mean temperature decreases with core size, and that a viscosity contrast of at least <span><math><msup><mn>10</mn><mn>7</mn></msup></math></span> is required for stagnant lid formation as <span><math><mi>f</mi></math></span> decreases below 0.5. Inverting the results from over 80 calculations featuring stagnant lids (from a total of approximately 180 calculations), we apply an energy balance model for heat flow across the thermal boundary layers and find that the non-dimensionalized temperature in the Approximately Isothermal Layer (AIL) in the convecting region under a stagnant lid is well predicted by <span><math><msubsup><mi>T</mi><mi>AIL</mi><mo>′</mo></msubsup><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><mo>−</mo><mfenced><mrow><mn>2</mn><msubsup><mi>T</mi><mtext>out</mtext><mo>′</mo></msubsup><mo>+</mo><mi>γ</mi></mrow></mfenced><mo>+</mo><msqrt><mrow><msup><mi>γ</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>γ</mi><mfenced><mrow><mn>1</mn><mo>+</mo><msubsup><mi>T</mi><mtext>out</mtext><mo>′</mo></msubsup></mrow></mfenced></mrow></msqrt></mrow></mfenced></math></span> where <span><math><mi>γ</mi></math></span> is a function of E and <span><math><mi>f</mi></math></span>, and <span><math><msubsup><mi>T</mi><mtext>out</mtext><mo>′</mo></msubsup></math></span> is the non-dimensionalized surface temperature. Moreover, the normalized (i.e., non-dimensional) thickness of the stagnant lid, <span><math><msup><mi>L</mi><mo>′</mo></msup></math></span>, can be obtained from a measurement of the non-dimensional surface heat flux once <","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0031920124000153/pdfft?md5=12d6c0f103726e2f43e8d3d47da8ce61&pid=1-s2.0-S0031920124000153-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140057312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1016/j.pepi.2024.107160
Tongzhang Qu , Ian Jackson , Ulrich H. Faul , Emmanuel C. David
Micromechanical models suggest that the onset of anelastic relaxation in polycrystalline olivine, critical to interpretation of the seismic wave attenuation and dispersion in the upper mantle, should be a mild dissipation peak caused by elastically accommodated grain-boundary sliding. Such behavior has been tentatively invoked to explain both a short-period shear modulus deficit and a dissipation plateau poorly resolved at 900–700 °C in previous forced-oscillation experiments on fine-grained dunite tested within mild-steel jackets. However, these observations may have been complicated by the austenite to ferrite plus cementite phase transition in the jacket material, compliance associated with interfacial Ni70Fe30 foils, and modeling of the mechanical properties of polycrystalline alumina as control specimen. To investigate the influence of these complications within the experimental setup and provide forced-oscillation data of better quality especially at moderate temperatures, we have conducted further forced-oscillation tests for which we removed the interfacial foils, employed single-crystal sapphire as reference sample, and used alternative jacket materials (stainless steel or copper) which experience no phase transition during the staged cooling. The newly acquired forced-oscillation data, although broadly consistent with the previous results, differ significantly especially in temperature sensitivity, and allow refinement of an appropriate Burgers creep-function model. A mild dissipation peak superimposed on monotonic dissipation background during the onset of anelastic relaxation in dry, melt-free and fine-grained dunite has now been consistently observed at temperatures of ∼950–1050 °C and seismic periods of 1–1000 s. Such a dissipation peak with relaxation strength 0.02 ± 0.01 is attributed to elastically accommodated grain-boundary sliding. The high activation energy (> 600 kJ/mol) of viscoelastic behavior involving both dissipation and related dispersion suggests that grain-boundary diffusion may be limited by interfacial reaction within grain boundaries. The reduced relaxation strength makes it difficult to attribute the oceanic lithosphere-asthenosphere boundary to water-mediated elastically accommodated grain-boundary sliding.
微观力学模型表明,多晶橄榄石中弹性松弛的起始点应该是一个由弹性容纳的晶界滑动引起的轻度耗散峰,这对解释上地幔中的地震波衰减和频散至关重要。在以前对置于软钢夹套中的细粒白云石进行的强制振荡实验中,这种行为被初步用来解释短周期剪切模量不足和在 900-700 °C时难以解析的耗散高原。然而,夹套材料中从奥氏体到铁素体加雪明体的相变、与界面镍铁箔相关的顺应性以及作为对照试样的多晶氧化铝的力学性能建模,都可能使这些观察结果变得复杂。为了研究实验装置中这些复杂因素的影响,并提供更高质量的强制振荡数据(尤其是在中等温度下),我们进行了进一步的强制振荡测试,去除了界面箔,使用单晶蓝宝石作为参考样品,并使用了在分段冷却过程中不会发生相变的其他夹套材料(不锈钢或铜)。新获得的强迫振荡数据虽然与之前的结果基本一致,但尤其在温度敏感性方面存在显著差异,因此可以完善适当的布尔格斯蠕变函数模型。在温度约为 950-1050 °C、地震周期为 1-1000 s 的干燥、无熔体和细粒度白云石中,在弹性松弛开始时,单调松弛背景上叠加了一个温和的耗散峰。同时涉及耗散和相关分散的粘弹性行为的高活化能(> 600 kJ/mol)表明,晶界扩散可能受到晶界内界面反应的限制。
{"title":"The onset of anelastic behavior in fine-grained synthetic dunite","authors":"Tongzhang Qu , Ian Jackson , Ulrich H. Faul , Emmanuel C. David","doi":"10.1016/j.pepi.2024.107160","DOIUrl":"10.1016/j.pepi.2024.107160","url":null,"abstract":"<div><p>Micromechanical models suggest that the onset of anelastic relaxation in polycrystalline olivine, critical to interpretation of the seismic wave attenuation and dispersion in the upper mantle, should be a mild dissipation peak caused by elastically accommodated grain-boundary sliding. Such behavior has been tentatively invoked to explain both a short-period shear modulus deficit and a dissipation plateau poorly resolved at 900–700 °C in previous forced-oscillation experiments on fine-grained dunite tested within mild-steel jackets. However, these observations may have been complicated by the austenite to ferrite plus cementite phase transition in the jacket material, compliance associated with interfacial Ni<sub>70</sub>Fe<sub>30</sub> foils, and modeling of the mechanical properties of polycrystalline alumina as control specimen. To investigate the influence of these complications within the experimental setup and provide forced-oscillation data of better quality especially at moderate temperatures, we have conducted further forced-oscillation tests for which we removed the interfacial foils, employed single-crystal sapphire as reference sample, and used alternative jacket materials (stainless steel or copper) which experience no phase transition during the staged cooling. The newly acquired forced-oscillation data, although broadly consistent with the previous results, differ significantly especially in temperature sensitivity, and allow refinement of an appropriate Burgers creep-function model. A mild dissipation peak superimposed on monotonic dissipation background during the onset of anelastic relaxation in dry, melt-free and fine-grained dunite has now been consistently observed at temperatures of ∼950–1050 °C and seismic periods of 1–1000 s. Such a dissipation peak with relaxation strength 0.02 ± 0.01 is attributed to elastically accommodated grain-boundary sliding. The high activation energy (> 600 kJ/mol) of viscoelastic behavior involving both dissipation and related dispersion suggests that grain-boundary diffusion may be limited by interfacial reaction within grain boundaries. The reduced relaxation strength makes it difficult to attribute the oceanic lithosphere-asthenosphere boundary to water-mediated elastically accommodated grain-boundary sliding.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0031920124000189/pdfft?md5=c802be94068b4d599547a8d3330418ae&pid=1-s2.0-S0031920124000189-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140057192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01DOI: 10.1016/j.pepi.2024.107159
František Hrouda , Josef Ježek , Martin Chadima
The precision of the measurement of the anisotropy of magnetic susceptibility (AMS) depends, in addition to other factors like accuracy of measurement of directional susceptibility and number of measuring directions, also on the orientation of the measuring design with respect to the specimen's anisotropy. The last factor can be characterized by rotatability coefficient of the measuring design. We investigated through mathematical modelling of measuring process the effect of the rotatability coefficient on the error in the determination of degree of AMS, shape factor and principal directions. The effect is conspicuous in strongly non-rotatable designs with low number of measuring directions. It decreases with increasing rotatability and with increasing number of measuring directions. In designs with high number of directions this effect is small, virtually negligible from the practical point of view.
{"title":"The effect of rotatability of measuring directions design on the precision of the determination of the anisotropy of magnetic susceptibility: Mathematical model study","authors":"František Hrouda , Josef Ježek , Martin Chadima","doi":"10.1016/j.pepi.2024.107159","DOIUrl":"10.1016/j.pepi.2024.107159","url":null,"abstract":"<div><p>The precision of the measurement of the anisotropy of magnetic susceptibility (AMS) depends, in addition to other factors like accuracy of measurement of directional susceptibility and number of measuring directions, also on the orientation of the measuring design with respect to the specimen's anisotropy. The last factor can be characterized by rotatability coefficient of the measuring design. We investigated through mathematical modelling of measuring process the effect of the rotatability coefficient on the error in the determination of degree of AMS, shape factor and principal directions. The effect is conspicuous in strongly non-rotatable designs with low number of measuring directions. It decreases with increasing rotatability and with increasing number of measuring directions. In designs with high number of directions this effect is small, virtually negligible from the practical point of view.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140057181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-24DOI: 10.1016/j.pepi.2024.107158
Zeqiu Guo , Hao Dong , Keke Zhang
The regularization approach has been successfully applied to remove spurious solutions in the magnetotelluric (MT) forward problems of isotropic Earth media. However, spurious modes are more likely to occur in numerical solutions of anisotropic media, as electrical anisotropy introduces many more complications to electromagnetic (EM) induction in such media. This study focuses on developing the regularization approach to 3D MT forward problems of anisotropic media, especially those of nontrivial anisotropy. The governing equation is now derived with a conductivity tensor, and an accordingly adapted form of a scaled grad-div term is augmented to regularize the solutions and constrain the divergence-free condition. A new scaling scheme is proposed to cope with the complicated distribution of current densities in nontrivial anisotropy media, and an effective conductivity is approximated by the diagonal elements of the conductivity tensor to formulate the scaling factor. Numerical tests show that, for various models of electrical anisotropy, the regularization approach can effectively enforce the divergence condition and successfully suppress spurious solutions. Therefore, for nontrivial anisotropy media, this approach can also improve the efficiency of the iterative solvers while retaining the accuracy of the solutions. The derivation of the governing equation is based on the MT method. However, this strategy should be generally applicable to other frequency-domain EM methods.
{"title":"Three-dimensional magnetotelluric modeling with nontrivial anisotropy by a regularization approach","authors":"Zeqiu Guo , Hao Dong , Keke Zhang","doi":"10.1016/j.pepi.2024.107158","DOIUrl":"https://doi.org/10.1016/j.pepi.2024.107158","url":null,"abstract":"<div><p>The regularization approach has been successfully applied to remove spurious solutions in the magnetotelluric (MT) forward problems of isotropic Earth media. However, spurious modes are more likely to occur in numerical solutions of anisotropic media, as electrical anisotropy introduces many more complications to electromagnetic (EM) induction in such media. This study focuses on developing the regularization approach to 3D MT forward problems of anisotropic media, especially those of nontrivial anisotropy. The governing equation is now derived with a conductivity tensor, and an accordingly adapted form of a scaled grad-div term is augmented to regularize the solutions and constrain the divergence-free condition. A new scaling scheme is proposed to cope with the complicated distribution of current densities in nontrivial anisotropy media, and an effective conductivity is approximated by the diagonal elements of the conductivity tensor to formulate the scaling factor. Numerical tests show that, for various models of electrical anisotropy, the regularization approach can effectively enforce the divergence condition and successfully suppress spurious solutions. Therefore, for nontrivial anisotropy media, this approach can also improve the efficiency of the iterative solvers while retaining the accuracy of the solutions. The derivation of the governing equation is based on the MT method. However, this strategy should be generally applicable to other frequency-domain EM methods.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139986976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-15DOI: 10.1016/j.pepi.2024.107154
Cesar Jimenez , Yuchen Wang
The earthquake of Chimbote occurred on February 21, 1996 in the northern region of Peru. Despite its relatively small magnitude, it generated a tsunami of 2–3 m height in Chimbote, taking the lives of 12 people. We conducted the signal processing of 31 broadband teleseismic stations, and waveform inversion to obtain the slip distribution and source time function, which indicated a multiple rupture process. The rupture process had a duration of 70 s, a rather high value for a relatively small earthquake. The calculated scalar seismic moment was Nm, corresponding to a moment magnitude of Mw 7.5. The slip distribution was heterogeneous, with a maximum slip of 8.9 m around the main asperity concentrated in an area of , for an constrained rigidity of . We also calculated the vertical coseismic deformation for 45 subfaults, which was used as an initial condition for the tsunami propagation modelling. Simulated tsunami waveforms were calculated for Salaverry ( m), Santa ( m) and Chimbote ( m) tidal stations.
{"title":"Numerical modelling of the 1996 Chimbote-Peru tsunami earthquake (Mw 7.5)","authors":"Cesar Jimenez , Yuchen Wang","doi":"10.1016/j.pepi.2024.107154","DOIUrl":"10.1016/j.pepi.2024.107154","url":null,"abstract":"<div><p>The earthquake of Chimbote occurred on February 21, 1996 in the northern region of Peru. Despite its relatively small magnitude, it generated a tsunami of 2–3 m height in Chimbote, taking the lives of 12 people. We conducted the signal processing of 31 broadband teleseismic stations, and waveform inversion to obtain the slip distribution and source time function, which indicated a multiple rupture process. The rupture process had a duration of 70 s, a rather high value for a relatively small earthquake. The calculated scalar seismic moment was <span><math><mn>2.19</mn><mo>×</mo><msup><mn>10</mn><mn>20</mn></msup></math></span> Nm, corresponding to a moment magnitude of Mw 7.5. The slip distribution was heterogeneous, with a maximum slip of 8.9 m around the main asperity concentrated in an area of <span><math><mn>30</mn><mo>×</mo><mn>30</mn><mspace></mspace><msup><mi>km</mi><mn>2</mn></msup></math></span>, for an constrained rigidity of <span><math><mn>1.46</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mspace></mspace><mi>N</mi><mo>/</mo><msup><mi>m</mi><mn>2</mn></msup></math></span>. We also calculated the vertical coseismic deformation for 45 subfaults, which was used as an initial condition for the tsunami propagation modelling. Simulated tsunami waveforms were calculated for Salaverry (<span><math><msub><mi>H</mi><mi>max</mi></msub><mo>=</mo><mn>0.81</mn></math></span> m), Santa (<span><math><msub><mi>H</mi><mi>max</mi></msub><mo>=</mo><mn>4.62</mn></math></span> m) and Chimbote (<span><math><msub><mi>H</mi><mi>max</mi></msub><mo>=</mo><mn>2.67</mn></math></span> m) tidal stations.</p></div>","PeriodicalId":54614,"journal":{"name":"Physics of the Earth and Planetary Interiors","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139881810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}