Summary Significant compositional differences may exist in the lithospheric mantle and above the core-mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modeling. We investigated both the instabilities in lithospheric mantle (i.e., lithospheric instability) and the mantle above the CMB (i.e., plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e., two oscillatory convection modes and one layered convection regime) as that with no-slip boundary condition reported in Jaupart et al., (2007). However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modeling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.
{"title":"Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core-mantle boundary regions","authors":"Shunjie Han, Shijie Zhong","doi":"10.1093/gji/ggae340","DOIUrl":"https://doi.org/10.1093/gji/ggae340","url":null,"abstract":"Summary Significant compositional differences may exist in the lithospheric mantle and above the core-mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modeling. We investigated both the instabilities in lithospheric mantle (i.e., lithospheric instability) and the mantle above the CMB (i.e., plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e., two oscillatory convection modes and one layered convection regime) as that with no-slip boundary condition reported in Jaupart et al., (2007). However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modeling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"26 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255740","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}
Caifeng Zou, Kamyar Azizzadenesheli, Zachary E Ross, Robert W Clayton
Summary Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a Helmholtz neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.
{"title":"Deep neural helmholtz operators for 3D elastic wave propagation and inversion","authors":"Caifeng Zou, Kamyar Azizzadenesheli, Zachary E Ross, Robert W Clayton","doi":"10.1093/gji/ggae342","DOIUrl":"https://doi.org/10.1093/gji/ggae342","url":null,"abstract":"Summary Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a Helmholtz neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"16 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255741","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}
Han Bai, Xuan Feng, Xin Wang, Mengyan Ding, Xiaoshi Zheng
Summary The existence of pores, cracks, and cleavage in rocks results in significant non-linear elastic phenomena. One important non-linear elastic characteristic is the deviation of the stress-strain curve from the linear path predicted by Hooke's law. To provide a more accurate description of the non-linear elastic characteristics of rocks and to characterize the propagation of non-linear elastic waves, we introduce the Preisach-Mayergoyz space model. This model effectively captures the non-linear mesoscopic elasticity of rocks, allowing us to observe the stress-strain and modulus-stress relationships under different stress protocols. Additionally, we analyze the discrete memory characteristics of rocks subjected to cyclic loading. Based on the Preisach-Mayergoyz space model, we develop a new non-linear elastic constitutive relationship in the form of an exponential function. The new constitutive relationship is validated through copropagating acousto-elastic testing, and the experimental result is highly consistent with the data predicted by the theoretical non-linear elastic constitutive relationship. By combining the new non-linear elastic constitutive relationship with the strain-displacement formula and the differential equation of motion, we derive the non-linear elastic wave equation. We numerically solve the non-linear elastic wave equation with the finite difference method and observe two important deformations during the propagation of non-linear elastic waves: amplitude attenuation and dispersion. We also observe wavefront discontinuities and uneven energy distribution in the 2-D wavefield snapshot, which are different from those of linear elastic waves. We qualitatively explain these special manifestations of non-linear elastic wave propagation.
{"title":"Modelling of non-linear elastic constitutive relationship and numerical simulation of rocks based on the Preisach-Mayergoyz space model","authors":"Han Bai, Xuan Feng, Xin Wang, Mengyan Ding, Xiaoshi Zheng","doi":"10.1093/gji/ggae341","DOIUrl":"https://doi.org/10.1093/gji/ggae341","url":null,"abstract":"Summary The existence of pores, cracks, and cleavage in rocks results in significant non-linear elastic phenomena. One important non-linear elastic characteristic is the deviation of the stress-strain curve from the linear path predicted by Hooke's law. To provide a more accurate description of the non-linear elastic characteristics of rocks and to characterize the propagation of non-linear elastic waves, we introduce the Preisach-Mayergoyz space model. This model effectively captures the non-linear mesoscopic elasticity of rocks, allowing us to observe the stress-strain and modulus-stress relationships under different stress protocols. Additionally, we analyze the discrete memory characteristics of rocks subjected to cyclic loading. Based on the Preisach-Mayergoyz space model, we develop a new non-linear elastic constitutive relationship in the form of an exponential function. The new constitutive relationship is validated through copropagating acousto-elastic testing, and the experimental result is highly consistent with the data predicted by the theoretical non-linear elastic constitutive relationship. By combining the new non-linear elastic constitutive relationship with the strain-displacement formula and the differential equation of motion, we derive the non-linear elastic wave equation. We numerically solve the non-linear elastic wave equation with the finite difference method and observe two important deformations during the propagation of non-linear elastic waves: amplitude attenuation and dispersion. We also observe wavefront discontinuities and uneven energy distribution in the 2-D wavefield snapshot, which are different from those of linear elastic waves. We qualitatively explain these special manifestations of non-linear elastic wave propagation.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"15 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255435","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}
L Marconato, L Audin, M-P Doin, J-M Nocquet, P Jarrin, F Rolandone, N Harrichhausen, P Mothes, H Mora-Páez, D Cisneros
Summary In the Northern Andes, partitioning of oblique subduction of the Nazca plate beneath the South American continent induces a northeastward motion of the North Andean Sliver. The strain resulting from this motion is absorbed by crustal faults, which have produced magnitude 7 + earthquakes historically in the Andean Cordillera of Ecuador and southern Colombia. In order to quantify the strain in that area, we derive a high-resolution surface velocity map using InSAR time-series processing. We analyzed 6 to 8 years of Sentinel-1 data and combined different satellite line-of-sight directions to produce a reliable velocity map in the East direction. We use interpolated GNSS data to express the velocity map with respect to Stable South America and remove the long-wavelength pattern due to the post-seismic deformation following the 2016 Mw 7.8 Pedernales earthquake. The InSAR velocity map finds high E-W shortening strain rates along N-S trending structures within the Western Cordillera and the Interandean valley, with little deformation taking place east of them. This result strengthens the previous proposition of a ∼350 km long Quito-Latacunga tectonic block, forming a restraining bend in the overall right-lateral strike-slip fault system accommodating the northeastward escape motion of the North Andean Sliver. However, the high spatial resolution provided by InSAR indicates that previously proposed boundaries for this block need to be revised. In particular, InSAR results highlight high strain rate (>300 nstrain/yr) along undescribed active structures, south and west of the proposed limits for the Quito-Latacunga block, respectively in Peltetec and Ibarra regions. Interestingly, the two areas with the largest strain rates spatially correlate with the proposed areas of large historical earthquakes. Modeling of the InSAR and GNSS velocities in these areas suggests shallow coupling and high slip rates on structures which, previously, were not identified as active. We also demonstrate a slow-down of the shallow aseismic slip on the Quito fault after the Pedernales earthquake, suggesting that stress changes following large megathrust events might trigger transient slip behaviors on crustal faults. The high-resolution strain map provided by this work provides a new basis for future tectonic models in the Ecuadorian and southern Colombian Andes, and will contribute to the seismic hazard assessment in this highly populated area of the Andes.
{"title":"Internal deformation of the North Andean Sliver in Ecuador-southern Colombia observed by InSAR","authors":"L Marconato, L Audin, M-P Doin, J-M Nocquet, P Jarrin, F Rolandone, N Harrichhausen, P Mothes, H Mora-Páez, D Cisneros","doi":"10.1093/gji/ggae338","DOIUrl":"https://doi.org/10.1093/gji/ggae338","url":null,"abstract":"Summary In the Northern Andes, partitioning of oblique subduction of the Nazca plate beneath the South American continent induces a northeastward motion of the North Andean Sliver. The strain resulting from this motion is absorbed by crustal faults, which have produced magnitude 7 + earthquakes historically in the Andean Cordillera of Ecuador and southern Colombia. In order to quantify the strain in that area, we derive a high-resolution surface velocity map using InSAR time-series processing. We analyzed 6 to 8 years of Sentinel-1 data and combined different satellite line-of-sight directions to produce a reliable velocity map in the East direction. We use interpolated GNSS data to express the velocity map with respect to Stable South America and remove the long-wavelength pattern due to the post-seismic deformation following the 2016 Mw 7.8 Pedernales earthquake. The InSAR velocity map finds high E-W shortening strain rates along N-S trending structures within the Western Cordillera and the Interandean valley, with little deformation taking place east of them. This result strengthens the previous proposition of a ∼350 km long Quito-Latacunga tectonic block, forming a restraining bend in the overall right-lateral strike-slip fault system accommodating the northeastward escape motion of the North Andean Sliver. However, the high spatial resolution provided by InSAR indicates that previously proposed boundaries for this block need to be revised. In particular, InSAR results highlight high strain rate (>300 nstrain/yr) along undescribed active structures, south and west of the proposed limits for the Quito-Latacunga block, respectively in Peltetec and Ibarra regions. Interestingly, the two areas with the largest strain rates spatially correlate with the proposed areas of large historical earthquakes. Modeling of the InSAR and GNSS velocities in these areas suggests shallow coupling and high slip rates on structures which, previously, were not identified as active. We also demonstrate a slow-down of the shallow aseismic slip on the Quito fault after the Pedernales earthquake, suggesting that stress changes following large megathrust events might trigger transient slip behaviors on crustal faults. The high-resolution strain map provided by this work provides a new basis for future tectonic models in the Ecuadorian and southern Colombian Andes, and will contribute to the seismic hazard assessment in this highly populated area of the Andes.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"18 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255742","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}
Summary The grid search method is a common approach to estimate the three spatial coordinates of event hypocenters. However, locating events in large search spaces with small grid spacings is computationally prohibitive. This study accelerates the grid searches over large search spaces using a quadratic interpolation technique. We start with the coarse-grid-estimated location, where we have the minimum value of the difference in the traveltimes between S- and P-waves summed over all receivers. Then, we select the neighbouring grid points and build a 3D quadratic function. The unknown coefficients of the 3D quadratic function are computed by solving a system of linear equations. After that, we interpolate the location by solving partial derivatives of the quadratic function. The quadratic interpolation technique performs well on both synthetic and real microseismic data examples, typically leading to similar event locations as those obtained using 10 times smaller grid spacings in all three directions, at a minor additional computational expense, and without the need to generate traveltimes at new spatial positions.
摘要 网格搜索法是估算事件次中心三个空间坐标的常用方法。然而，在网格间距较小的大型搜索空间中定位事件在计算上是非常困难的。本研究利用二次插值技术加速了在大型搜索空间中的网格搜索。我们从粗网格估计的位置开始，在这个位置上，我们有所有接收器的 S 波和 P 波的传播时间之差的最小值。然后，我们选择相邻的网格点，建立三维二次函数。三维二次函数的未知系数是通过求解线性方程组计算得出的。然后，我们通过求解二次函数的部分导数对位置进行插值。二次插值技术在合成和真实微地震数据实例中都表现良好，通常能得到与在所有三个方向上使用小 10 倍的网格间距所得到的事件位置相似的位置，只需少量额外的计算费用，而且无需在新的空间位置上生成遍历时间。
{"title":"Event locations: Speeding up grid searches using quadratic interpolation","authors":"Hanh Bui, Mirko van der Baan","doi":"10.1093/gji/ggae339","DOIUrl":"https://doi.org/10.1093/gji/ggae339","url":null,"abstract":"Summary The grid search method is a common approach to estimate the three spatial coordinates of event hypocenters. However, locating events in large search spaces with small grid spacings is computationally prohibitive. This study accelerates the grid searches over large search spaces using a quadratic interpolation technique. We start with the coarse-grid-estimated location, where we have the minimum value of the difference in the traveltimes between S- and P-waves summed over all receivers. Then, we select the neighbouring grid points and build a 3D quadratic function. The unknown coefficients of the 3D quadratic function are computed by solving a system of linear equations. After that, we interpolate the location by solving partial derivatives of the quadratic function. The quadratic interpolation technique performs well on both synthetic and real microseismic data examples, typically leading to similar event locations as those obtained using 10 times smaller grid spacings in all three directions, at a minor additional computational expense, and without the need to generate traveltimes at new spatial positions.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"16 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255436","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}
Longlong Wang, Daniel Zhengyu Huang, Yun Chen, Youshan Liu, Nanqiao Du, Wei Li
Summary Joint inversion, such as the combination of receiver function and surface wave dispersion, can significantly improve subsurface imaging by exploiting their complementary sensitivities. Bayesian methods have been demonstrated to be effective in this field. However, there are practical challenges associated with this approach. Notably, most Bayesian methods, such as the Markov Chain Monte Carlo (MCMC) method, are computationally intensive. Additionally, accurately determining the data noise across different data sets to ensure effective inversion is often a complex task. This study explores the unscented Kalman inversion (UKI) as a potential alternative. Through a data-driven approach to adjust estimated noise levels, we can achieve a balance between actual noise and the weights assigned to different data sets, enhancing the effectiveness of the inversion process. Synthetic tests of joint inversion of receiver function and surface wave dispersions indicate that the UKI can provide robust solutions across a range of data noise levels. Furthermore, we apply the UKI to real data from seismic arrays in Pamir and evaluate the accuracy of the joint inversion through posterior Gaussian distribution. Our results demonstrate that the UKI presents a promising supplement to conventional Bayesian methods in the joint inversion of geophysical data sets with superior computational efficiency.
{"title":"Joint inversion of receiver function and surface wave dispersion based on the unscented Kalman inversion","authors":"Longlong Wang, Daniel Zhengyu Huang, Yun Chen, Youshan Liu, Nanqiao Du, Wei Li","doi":"10.1093/gji/ggae332","DOIUrl":"https://doi.org/10.1093/gji/ggae332","url":null,"abstract":"Summary Joint inversion, such as the combination of receiver function and surface wave dispersion, can significantly improve subsurface imaging by exploiting their complementary sensitivities. Bayesian methods have been demonstrated to be effective in this field. However, there are practical challenges associated with this approach. Notably, most Bayesian methods, such as the Markov Chain Monte Carlo (MCMC) method, are computationally intensive. Additionally, accurately determining the data noise across different data sets to ensure effective inversion is often a complex task. This study explores the unscented Kalman inversion (UKI) as a potential alternative. Through a data-driven approach to adjust estimated noise levels, we can achieve a balance between actual noise and the weights assigned to different data sets, enhancing the effectiveness of the inversion process. Synthetic tests of joint inversion of receiver function and surface wave dispersions indicate that the UKI can provide robust solutions across a range of data noise levels. Furthermore, we apply the UKI to real data from seismic arrays in Pamir and evaluate the accuracy of the joint inversion through posterior Gaussian distribution. Our results demonstrate that the UKI presents a promising supplement to conventional Bayesian methods in the joint inversion of geophysical data sets with superior computational efficiency.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"70 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255437","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}
Jonathan Carrillo, Marco A Pérez-Flores, Marco Calò
Summary We present a method to jointly invert surface wave dispersion data and gravity measurements for three-dimensional shear wave velocity and density models. We implemented a petrophysical approach to combine the kernels of both methodologies in a single process. The synthetic experiments show that jointly inverted models recover shear wave velocity and density better than separate inversions. In particular, density models benefit from the good vertical resolution of surface wave dispersion data, while shear velocity models benefit from the good lateral resolution of gravity data. We also proposed two methods to stabilize the solution when using high-grade polynomials. We applied the methodology to the Los Humeros Geothermal area to demonstrate its applicability in a complex geological scenario. Compared with separate inversion, the joint inversion contributes to enhancing key aspects of the geothermal system by i) delimitating better the geometry of the caldera deposits in the first 0-2.8 km deep by increasing the vertical resolution in density, ii) delimitating better the lateral borders of low-Vs bodies at different depths interpreted as a part of a complex magmatic chamber system, and iii) estimating the local shear wave velocity-density relationship that conforms to other known relationships for sedimentary and igneous rocks but with some differences that bring us additional information.
摘要 我们提出了一种联合反演面波频散数据和重力测量数据的方法，用于建立三维剪切波速度和密度模型。我们采用了一种岩石物理方法，将两种方法的内核结合在一个过程中。合成实验表明，联合反演模型比单独反演能更好地恢复剪切波速度和密度。特别是，密度模型得益于面波频散数据良好的垂直分辨率，而剪切速度模型则得益于重力数据良好的横向分辨率。我们还提出了两种在使用高等级多项式时稳定解法的方法。我们将该方法应用于 Los Humeros 地热区，以证明其在复杂地质情况下的适用性。与单独反演相比，联合反演有助于通过以下方式增强地热系统的关键方面：i) 通过提高密度的垂直分辨率，更好地划定深度为 0-2.8 千米的火山口沉积的几何形状；ii) 更好地划定不同深度的低 Vs 体的横向边界，这些低 Vs 体被解释为复杂岩浆腔系统的一部分；iii) 估算当地剪切波速度-密度关系，该关系符合沉积岩和火成岩的其他已知关系，但存在一些差异，为我们带来了更多信息。
{"title":"Three-dimensional joint inversion of surface wave dispersion and gravity data using a petrophysical approach: an application to Los Humeros Geothermal Field.","authors":"Jonathan Carrillo, Marco A Pérez-Flores, Marco Calò","doi":"10.1093/gji/ggae333","DOIUrl":"https://doi.org/10.1093/gji/ggae333","url":null,"abstract":"Summary We present a method to jointly invert surface wave dispersion data and gravity measurements for three-dimensional shear wave velocity and density models. We implemented a petrophysical approach to combine the kernels of both methodologies in a single process. The synthetic experiments show that jointly inverted models recover shear wave velocity and density better than separate inversions. In particular, density models benefit from the good vertical resolution of surface wave dispersion data, while shear velocity models benefit from the good lateral resolution of gravity data. We also proposed two methods to stabilize the solution when using high-grade polynomials. We applied the methodology to the Los Humeros Geothermal area to demonstrate its applicability in a complex geological scenario. Compared with separate inversion, the joint inversion contributes to enhancing key aspects of the geothermal system by i) delimitating better the geometry of the caldera deposits in the first 0-2.8 km deep by increasing the vertical resolution in density, ii) delimitating better the lateral borders of low-Vs bodies at different depths interpreted as a part of a complex magmatic chamber system, and iii) estimating the local shear wave velocity-density relationship that conforms to other known relationships for sedimentary and igneous rocks but with some differences that bring us additional information.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"4 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255440","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}
Summary Cracks are a common rock microstructure and have a large effect on elastic properties during wave propagation. The fluid flow between a crack and its adjacent pore space can cause wave attenuation and dispersion. In this work, we introduce a crack connectivity parameter which is meant to improve the expression of local flow by weighting the contributions of fully connected and isolated cracks. We then update the analytical expression for frequency-dependent moduli by modifying the boundary conditions of the linearized Navier-Stokes equation and mass conservation equation. The proposed model contains the effect of cracks and stiff pores, in which the attenuation and dispersion are determined by squirt-flow and stiff-pore relaxations. The resulting model shows the squirt-flow relaxation frequency depends on not only the crack aspect ratio but also the crack connectivity. However, their contributions are different. The crack connectivity has little effect on the attenuation amplitude of shear modulus, but affects the attenuation amplitude of bulk modulus when multiple sets of cracks exist in the rock. The attenuation frequency band is also affected by the crack connectivity. As the crack connectivity deteriorates, the attenuation peak moves to low frequencies. In addition, by comparing the crack connectivity with the fluid viscosity coefficient, it is observed that the crack connectivity only affects the attenuation frequency band of cracks, whereas the fluid viscosity coefficient affects the attenuation frequency bands of cracks and stiff pores simultaneously. Thus, the introduction of crack connectivity is a supplement to the theoretical model of cracked fluid-saturated rocks. It helps understand the local fluid flow induced by seismic waves and provides a reasonable variation analysis of moduli and attenuation, especially for tight reservoirs.
{"title":"Theoretical model for the elastic properties of cracked fluid-saturated rocks considering the crack connectivity","authors":"Pu Wang, Yi-an Cui, Jingye Li, Jianxin Liu","doi":"10.1093/gji/ggae330","DOIUrl":"https://doi.org/10.1093/gji/ggae330","url":null,"abstract":"Summary Cracks are a common rock microstructure and have a large effect on elastic properties during wave propagation. The fluid flow between a crack and its adjacent pore space can cause wave attenuation and dispersion. In this work, we introduce a crack connectivity parameter which is meant to improve the expression of local flow by weighting the contributions of fully connected and isolated cracks. We then update the analytical expression for frequency-dependent moduli by modifying the boundary conditions of the linearized Navier-Stokes equation and mass conservation equation. The proposed model contains the effect of cracks and stiff pores, in which the attenuation and dispersion are determined by squirt-flow and stiff-pore relaxations. The resulting model shows the squirt-flow relaxation frequency depends on not only the crack aspect ratio but also the crack connectivity. However, their contributions are different. The crack connectivity has little effect on the attenuation amplitude of shear modulus, but affects the attenuation amplitude of bulk modulus when multiple sets of cracks exist in the rock. The attenuation frequency band is also affected by the crack connectivity. As the crack connectivity deteriorates, the attenuation peak moves to low frequencies. In addition, by comparing the crack connectivity with the fluid viscosity coefficient, it is observed that the crack connectivity only affects the attenuation frequency band of cracks, whereas the fluid viscosity coefficient affects the attenuation frequency bands of cracks and stiff pores simultaneously. Thus, the introduction of crack connectivity is a supplement to the theoretical model of cracked fluid-saturated rocks. It helps understand the local fluid flow induced by seismic waves and provides a reasonable variation analysis of moduli and attenuation, especially for tight reservoirs.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"28 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255441","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}
Summary Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters probabilistically by calculating the posterior probability distribution function. Prior information is often described by a prior probability distribution. Situations arise in which we wish to change prior information during the course of a scientific project. However, estimating the solution to any single Bayesian inference problem is often computationally costly, as it typically requires many model samples to be drawn, and the data set that would have been recorded if each sample was true must be simulated. Recalculating the Bayesian inference solution every time prior information changes can therefore be extremely expensive. We develop a mathematical formulation that allows the prior information that is embedded within a solution, to be changed using variational methods, without recalculating the original Bayesian inference. In this method, existing prior information is removed from a previously obtained posterior distribution and is replaced by new prior information. We therefore call the methodology variational prior replacement (VPR). We demonstrate VPR using a 2D seismic full waveform inversion example, in which VPR provides similar posterior solutions to those obtained by solving independent inference problems using different prior distributions. The former can be completed within minutes on a laptop computer, whereas the latter requires days of computations using high-performance computing resources. We demonstrate the value of the method by comparing the posterior solutions obtained using three different types of prior information: uniform, smoothing and geological prior distributions.
{"title":"Variational Prior Replacement in Bayesian inference and inversion","authors":"Xuebin Zhao, Andrew Curtis","doi":"10.1093/gji/ggae334","DOIUrl":"https://doi.org/10.1093/gji/ggae334","url":null,"abstract":"Summary Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters probabilistically by calculating the posterior probability distribution function. Prior information is often described by a prior probability distribution. Situations arise in which we wish to change prior information during the course of a scientific project. However, estimating the solution to any single Bayesian inference problem is often computationally costly, as it typically requires many model samples to be drawn, and the data set that would have been recorded if each sample was true must be simulated. Recalculating the Bayesian inference solution every time prior information changes can therefore be extremely expensive. We develop a mathematical formulation that allows the prior information that is embedded within a solution, to be changed using variational methods, without recalculating the original Bayesian inference. In this method, existing prior information is removed from a previously obtained posterior distribution and is replaced by new prior information. We therefore call the methodology variational prior replacement (VPR). We demonstrate VPR using a 2D seismic full waveform inversion example, in which VPR provides similar posterior solutions to those obtained by solving independent inference problems using different prior distributions. The former can be completed within minutes on a laptop computer, whereas the latter requires days of computations using high-performance computing resources. We demonstrate the value of the method by comparing the posterior solutions obtained using three different types of prior information: uniform, smoothing and geological prior distributions.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"10 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255443","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}
Summary Fault geometry is a key factor in controling the mechanics of faulting. However, there is currently limited theoretical knowledge regarding the effect of non-planar fault geometry on earthquake mechanics. Here, we address this gap by introducing an expansion of the relation between fault traction and slip, up to second order, relative to the deviation from a planar fault geometry. This expansion enables the separation of the effects of non-planarities from those of planar faults. This expansion is realised in the boundary integral equation, assuming a small fault slope. It provides an interpretation for the effect of complex fault geometry on fault traction, for any fault geometry and any slip distribution. Hence the results are also independent of the friction that applies on the fault. The findings confirm that fault geometry has a strong influence on in-plane faulting (mode II) by altering the normal traction on the fault and making it more resistant to slipping for any fault geometry. On the contrary, for out-of-plane faulting (mode III), fault geometry has a much smaller influence. Additionally, we analyse some singularities that arise for specific fault geometries often used in earthquake simulations and provide guidelines for their elimination. To conclude this study, we discuss the limits of the infinitesimal strain theory when non-planar faults are considered.
{"title":"The mechanics of static non-planar faults in infinitesimal strain theory","authors":"Pierre ROMANET, Tatsuhiko SAITO, Eiichi FUKUYAMA","doi":"10.1093/gji/ggae337","DOIUrl":"https://doi.org/10.1093/gji/ggae337","url":null,"abstract":"Summary Fault geometry is a key factor in controling the mechanics of faulting. However, there is currently limited theoretical knowledge regarding the effect of non-planar fault geometry on earthquake mechanics. Here, we address this gap by introducing an expansion of the relation between fault traction and slip, up to second order, relative to the deviation from a planar fault geometry. This expansion enables the separation of the effects of non-planarities from those of planar faults. This expansion is realised in the boundary integral equation, assuming a small fault slope. It provides an interpretation for the effect of complex fault geometry on fault traction, for any fault geometry and any slip distribution. Hence the results are also independent of the friction that applies on the fault. The findings confirm that fault geometry has a strong influence on in-plane faulting (mode II) by altering the normal traction on the fault and making it more resistant to slipping for any fault geometry. On the contrary, for out-of-plane faulting (mode III), fault geometry has a much smaller influence. Additionally, we analyse some singularities that arise for specific fault geometries often used in earthquake simulations and provide guidelines for their elimination. To conclude this study, we discuss the limits of the infinitesimal strain theory when non-planar faults are considered.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":"12 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255438","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}
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