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Journal
Complex-valued adaptive-coefficient finite-difference frequency-domain method for wavefield modeling based on the diffusive-viscous wave equation
Zhao, Haixia (Xi’an Jiaotong University, National Engineering Research Center of Offshore Oil and Gas Exploration) | Wang, Shaoru (Xi’an Jiaotong University) | Xu, Wenhao (Hohai University) | Gao, Jinghuai (Xi’an Jiaotong University, National Engineering Research Center of Offshore Oil and Gas Exploration)
ABSTRACT The diffusive-viscous wave (DVW) equation is an effective model for analyzing seismic low-frequency anomalies and attenuation in porous media. To effectively simulate DVW wavefields, the finite-difference or finite-element method in the time domain is favored, but the time-domain approach proves less efficient with multiple shots or a few frequency components. The finite-difference frequency-domain (FDFD) method featuring optimal or adaptive coefficients is favored in seismic simulations due to its high efficiency. Initially, we develop a real-valued adaptive-coefficient (RVAC) FDFD method for the DVW equation, which ignores the numerical attenuation error and is a generalization of the acoustic adaptive-coefficient FDFD method. To reduce the numerical attenuation error of the RVAC FDFD method, we introduce a complex-valued adaptive-coefficient (CVAC) FDFD method for the DVW equation. The CVAC FDFD method is constructed by incorporating correction terms into the conventional second-order FDFD method. The adaptive coefficients are related to the spatial sampling ratio, number of spatial grid points per wavelength, and diffusive and viscous attenuation coefficients in the DVW equation. Numerical dispersion and attenuation analysis confirm that, with a maximum dispersion error of 1% and a maximum attenuation error of 10%, the CVAC FDFD method only necessitates 2.5 spatial grid points per wavelength. Compared with the RVAC FDFD method, the CVAC FDFD method exhibits enhanced capability in suppressing the numerical attenuation during anelastic wavefield modeling. To validate the accuracy of our method, we develop an analytical solution for the DVW equation in a homogeneous medium. Three numerical examples substantiate the high accuracy of the CVAC FDFD method when using a small number of spatial grid points per wavelength, and this method demands computational time and computer memory similar to those required by the conventional second-order FDFD method. A fluid-saturated model featuring various layer thicknesses is used to characterize the propagation characteristics of DVW.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.93)
- Geophysics > Seismic Surveying > Seismic Interpretation (0.93)
- Information Technology > Artificial Intelligence > Machine Learning (0.46)
- Information Technology > Hardware > Memory (0.34)
ABSTRACT The explicit finite-difference (EFD) method is widely used in numerical simulation of seismic wave propagation to approximate spatial derivatives. However, the traditional and optimized high-order EFD methods suffer from the saturation effect, which seriously restricts the improvement of numerical accuracy. In contrast, the implicit FD (IFD) method approximates the spatial derivatives in the form of rational functions and thus can obtain much higher numerical accuracy with relatively low orders; however, its computational cost is expensive due to the need to invert a multidiagonal matrix. We derive an explicit strategy for the IFD method to reduce the computational cost by constructing the IFD method with the discrete Fourier matrix; then, we transform the inversion of the multidiagonal matrix into an explicit matrix multiplication; next, we construct an objective function based on the norm to reduce approximation error of the IFD method. This explicit strategy of the IFD method can avoid inverting the multidiagonal matrix, thus improving the computational efficiency. This constant coefficient optimization method reduces the approximation error in the medium-wavenumber range at the cost of tolerable deviation (smaller than 0.0001) in the low-wavenumber range. For the 2D Marmousi model, the root-mean-square error of the numerical results obtained by this method is one-fifth that of the traditional IFD method with the same order (i.e., 5/3) and one-third that of the traditional EFD method with much higher orders (i.e., 72). The significant reduction of numerical error makes the developed method promising for numerical simulation in large-scale models, especially for long-time simulations.
ABSTRACT We compare microseismic observations against pumping information, landing heights, and various well logs. The data were acquired during cyclic-steam injection between September 2002 and December 2005. Ninety-five percent of the microseismicity occurred during injection and in the overburden; 70% of the events happened during the first cycle. Microseismicity in the overburden is likely caused by a greater brittleness than in the reservoir and a cluster of microseismic events in regions with a smaller landing height, thereby facilitating dry cracking due to the volumetric expansion of the reservoir. Yet, other areas with equally shallow landing heights displayed little to no microseismicity, pointing to an inhomogeneous steam front. Furthermore, recorded microseismicity is subject to the Kaiser effect in that event rates are low in subsequent cycles until the current injection pressure exceeds the previous maximum, explaining why 70% of the events occurred during the first cycle and possibly why microseismicity during production accounted for only 5%. Microseismicity in brittle formations can be caused by pore-pressure variations (wet cracking) and/or changes in the total stresses (dry cracking). Identification of pore-pressure variations in the overburden is important because it may indicate containment challenges. Analysis of the growth rate of the microseismic cloud combined with the shallow landing height indicated dry cracking to be more likely than wet cracking but analysis of additional data is required to strengthen this conclusion.
- North America > Canada > Alberta (1.00)
- Europe (0.93)
- North America > Canada > British Columbia (0.68)
- Geology > Sedimentary Geology (1.00)
- Geology > Petroleum Play Type > Unconventional Play > Heavy Oil Play (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (0.46)
- North America > United States > Texas > Fort Worth Basin > Barnett Shale Formation (0.99)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Greater Peace River High Basin > Debolt Formation (0.99)
- North America > Canada > British Columbia > Peace River Field (0.99)
- (3 more...)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Thermal methods (1.00)
Complex-valued adaptive-coefficient finite-difference frequency-domain method for wavefield modeling based on the diffusive-viscous wave equation
Zhao, Haixia (Xi’an Jiaotong University, National Engineering Research Center of Offshore Oil and Gas Exploration) | Wang, Shaoru (Xi’an Jiaotong University) | Xu, Wenhao (Hohai University) | Gao, Jinghuai (Xi’an Jiaotong University, National Engineering Research Center of Offshore Oil and Gas Exploration)
ABSTRACT The diffusive-viscous wave (DVW) equation is an effective model for analyzing seismic low-frequency anomalies and attenuation in porous media. To effectively simulate DVW wavefields, the finite-difference or finite-element method in the time domain is favored, but the time-domain approach proves less efficient with multiple shots or a few frequency components. The finite-difference frequency-domain (FDFD) method featuring optimal or adaptive coefficients is favored in seismic simulations due to its high efficiency. Initially, we develop a real-valued adaptive-coefficient (RVAC) FDFD method for the DVW equation, which ignores the numerical attenuation error and is a generalization of the acoustic adaptive-coefficient FDFD method. To reduce the numerical attenuation error of the RVAC FDFD method, we introduce a complex-valued adaptive-coefficient (CVAC) FDFD method for the DVW equation. The CVAC FDFD method is constructed by incorporating correction terms into the conventional second-order FDFD method. The adaptive coefficients are related to the spatial sampling ratio, number of spatial grid points per wavelength, and diffusive and viscous attenuation coefficients in the DVW equation. Numerical dispersion and attenuation analysis confirm that, with a maximum dispersion error of 1% and a maximum attenuation error of 10%, the CVAC FDFD method only necessitates 2.5 spatial grid points per wavelength. Compared with the RVAC FDFD method, the CVAC FDFD method exhibits enhanced capability in suppressing the numerical attenuation during anelastic wavefield modeling. To validate the accuracy of our method, we develop an analytical solution for the DVW equation in a homogeneous medium. Three numerical examples substantiate the high accuracy of the CVAC FDFD method when using a small number of spatial grid points per wavelength, and this method demands computational time and computer memory similar to those required by the conventional second-order FDFD method. A fluid-saturated model featuring various layer thicknesses is used to characterize the propagation characteristics of DVW.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.93)
- Geophysics > Seismic Surveying > Seismic Interpretation (0.93)
- Information Technology > Artificial Intelligence > Machine Learning (0.46)
- Information Technology > Hardware > Memory (0.34)
Fourier domain vertical derivative of the nonpotential squared analytical signal of dike and step magnetic anomalies: A case of serendipity
de Souza, Jeferson (Paraná State Secretary of Education) | Oliveira, Saulo Pomponet (Federal University of Paraná) | Szameitat, Luizemara Soares Alves (Universidade Do Estado Do Rio de Janeiro — UERJ) | de Souza Filho, Oderson Antônio (Geological Survey of Brazil (CGA/SGB)) | Ferreira, Francisco José Fonseca (Federal University of Paraná)
ABSTRACT Vertical derivatives of nonpotential fields are, intentionally or not, often performed in the Fourier domain producing nonphysical but interpretable results. Using the dike model, we prove that the vertical derivative of the squared analytic signal amplitude calculated in the Fourier domain does not correspond to the true one. We derive an analytical expression for this pseudovertical derivative, providing a mathematical meaning for it. One significant difference between the pseudo and true vertical derivative is that the former possesses real roots, whereas the latter does not. Taking advantage of this attribute, we find using synthetic and field data that the pseudovertical derivative can be used for qualitative and quantitative interpretation of magnetic data, despite being nonphysical. As an example of the usefulness of this filter in qualitative interpretation, we convert the image of the pseudoderivative to a binary image where the anomalies are treated as discrete objects. This allows us to morphologically enhance, disconnect, classify, and filter them using the tools of shape analysis and mathematical morphology. We also illustrate its usefulness in quantitative interpretation by deriving a formula for estimating the depths of magnetic thin dikes and infinite steps. Our outcomes are also corroborated by the observation of outcrops found by field surveys.
- South America > Brazil (1.00)
- North America (0.93)
- Geology > Geological Subdiscipline (0.46)
- Geology > Structural Geology > Tectonics (0.46)
- North America > United States > New Mexico > San Juan Basin (0.99)
- North America > United States > Colorado > San Juan Basin (0.99)
- North America > United States > Arizona > San Juan Basin (0.99)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.72)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (0.46)
Bayesian reverse time migration with quantified uncertainty
Wang, Shuang (Jilin University) | Gong, Xiangbo (Jilin University) | Huang, Xingguo (Jilin University) | Rao, Jing (Beihang University) | Jensen, Kristian (Metis Privatistskole) | Han, Li (Jilin University) | Wang, Naijian (BGP Inc., Hebei Seismic Acquisition Technology Institute) | Zhang, Xuliang (BGP Inc., Hebei Seismic Acquisition Technology Institute)
ABSTRACT Reverse time migration (RTM) has been proven capable of producing high-quality images of subsurface structures. However, limited subsurface illumination combined with inaccurate forward modeling and migration velocities all lead to uncertainty in the seismic images. We quantify the migration uncertainty of RTM using an iterative inversion method based on a Bayesian inference framework. The posterior covariance matrix, computed at the maximum a posteriori (MAP) model, provides the foundation for estimating uncertainty. In the Bayesian inference framework, we combine an explicit sensitivity matrix based on a Green’s function representation with an iterative extended Kalman filter method. This enables us to determine the MAP solution of RTM and an estimate of its uncertainty. Numerical examples using synthetic data demonstrate how well the method can measure RTM uncertainty and produce reliable imaging results.
- Geophysics > Seismic Surveying > Seismic Processing > Seismic Migration (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
Research on focal mechanism of microseismic events and the regional stress during hydraulic fracturing at a shale play site in southwest China
Chen, Xin-Xing (Chengdu University of Technology) | Meng, Xiao-Bo (Chengdu University of Technology) | Chen, Hai-Chao (China University of Petroleum) | Chen, Xin-Yu (Chengdu University of Technology) | Li, Qiu-Yu (Optical Science and Technology (Chengdu) Ltd.) | Guo, Ming-Yu (Chengdu University of Technology)
ABSTRACT We develop a waveform-matching inversion method to determine the focal mechanism of microseismic events recorded by a single-well observation system. Our method uses the crosscorrelation technique to mitigate the influence of anisotropy on the S wave. Then, by conducting a grid search for strike, dip, and rake, we match the observed waveforms of P and S wave with the corresponding theoretical waveforms. A synthetic test demonstrates the robustness and accuracy of our method in resolving the focal mechanism of microseismic events under a single-well observation system. By applying our method to the events that have been categorized into two clusters based on spatial and temporal evolution recorded during the hydraulic fracturing operation in the Weiyuan shale reservoir, we observe that the two clusters have distinct focal mechanism and stress characteristics. The events in the remote cluster (cluster A) exhibit consistent focal mechanisms, with a concentrated distribution of P-axis orientations. The inverted maximum principal stress direction of cluster A aligns with the local maximum principal stress direction (). This implies that events in cluster A occur in a uniform stress condition. In contrast, the other cluster (cluster B) near the injection well exhibits significant variation in focal mechanisms, with a scattered distribution of P-axis orientations. The inverted maximum principal stress direction deviates from local maximum principal stress direction (), indicating that events in cluster B occur in a more complicated stress condition.
- North America > Canada > Alberta (0.47)
- North America > United States > Texas (0.47)
- Asia > China > Sichuan Province (0.29)
- Geology > Geological Subdiscipline > Geomechanics (0.94)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (0.70)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.68)
- Geology > Petroleum Play Type > Unconventional Play > Shale Play (0.50)
- North America > United States > Texas > Fort Worth Basin > Barnett Shale Formation (0.99)
- North America > Canada > Alberta > Western Canada Sedimentary Basin > Alberta Basin > Deep Basin > West Pembina Field (0.99)
- North America > Canada > Alberta > Western Canada Sedimentary Basin > Alberta Basin > Deep Basin > Pembina Field > Viking Formation (0.99)
- (2 more...)
ABSTRACT The impermeable caprock within a geothermal system serves the purpose of effectively sealing the reservoir, resulting in an elevation of both pressure and temperature. This sealing mechanism plays a crucial role in the long-term preservation of the system while also contributing to its overall sustainability. Caprock failure subsequent to seismic activity near a geothermal site can lead to the permeation of the caprock structure, resulting in diminished sealing capabilities and a decline in the reservoir temperature. In addition, this process alters the geochemical composition of the water by creating a hydrothermal mixture zone that disrupts the resistivity structure of the caprock, which is typically characterized by low resistivity values due to its substantial clay content and mineral alteration. This study focuses on investigating the integrity of the caprock at the Çanakkale-Tuzla geothermal field in Turkey, where water temperature and conductivity were reported to have decreased after a moderate-magnitude earthquake and subsequent aftershocks. For this purpose, we have performed magnetotelluric (MT) measurements, a method known for its sensitivity to geochemical reactions. These measurements are conducted along two parallel profiles that encompassed a total of 32 stations. The particle swarm optimization (PSO) technique is used to overcome the subtle difficulties associated with conventional inversion methods in modeling the MT data of complex formations. This is the first study that overcomes the difficulties emanating from the caprock failure by modeling MT data using PSO. Our modeling approach produces resistivity images that we interpreted as the signature of the failed caprock following the earthquake at the study site. Our results appear to confirm the documented geochemical changes, or hydrothermal mixture zone around the caprock structure.
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (1.00)
- Geology > Petroleum Play Type (1.00)
- Geology > Geological Subdiscipline (1.00)
- Energy > Oil & Gas > Upstream (1.00)
- Energy > Renewable > Geothermal > Geothermal Resource (0.49)
ABSTRACT The explicit finite-difference (EFD) method is widely used in numerical simulation of seismic wave propagation to approximate spatial derivatives. However, the traditional and optimized high-order EFD methods suffer from the saturation effect, which seriously restricts the improvement of numerical accuracy. In contrast, the implicit FD (IFD) method approximates the spatial derivatives in the form of rational functions and thus can obtain much higher numerical accuracy with relatively low orders; however, its computational cost is expensive due to the need to invert a multidiagonal matrix. We derive an explicit strategy for the IFD method to reduce the computational cost by constructing the IFD method with the discrete Fourier matrix; then, we transform the inversion of the multidiagonal matrix into an explicit matrix multiplication; next, we construct an objective function based on the norm to reduce approximation error of the IFD method. This explicit strategy of the IFD method can avoid inverting the multidiagonal matrix, thus improving the computational efficiency. This constant coefficient optimization method reduces the approximation error in the medium-wavenumber range at the cost of tolerable deviation (smaller than 0.0001) in the low-wavenumber range. For the 2D Marmousi model, the root-mean-square error of the numerical results obtained by this method is one-fifth that of the traditional IFD method with the same order (i.e., 5/3) and one-third that of the traditional EFD method with much higher orders (i.e., 72). The significant reduction of numerical error makes the developed method promising for numerical simulation in large-scale models, especially for long-time simulations.
Estimation of the subsurface electromagnetic velocity distribution from diffraction hyperbolas by means of a novel automated picking procedure: Theory and application to glaciological ground-penetrating radar data sets
Dossi, Matteo (Roma Tre University) | Forte, Emanuele (University of Trieste) | Cosciotti, Barbara (Roma Tre University) | Lauro, Sebastian Emanuel (Roma Tre University) | Mattei, Elisabetta (Roma Tre University) | Pettinelli, Elena (Roma Tre University) | Pipan, Michele (University of Trieste)
ABSTRACT We have developed an auto-picking algorithm that is designed to automatically detect subsurface diffractors within ground-penetrating radar (GPR) data sets, to accurately track the hyperbolic diffractions originating from the identified scatterers, and to recover the subsurface electromagnetic (EM) velocity distribution, among other possible analyses. Our procedure presents several advantages with respect to other commonly applied diffraction tracking techniques because it can be applied with minimal signal preprocessing, thus making it more versatile and adaptable to local conditions; it requires only limited input from the interpreter in the form of a few thresholds for the tracking parameters, thus making the results more objective; and it does not involve pretraining as opposed to machine-learning algorithms, thus removing the need to gather a large and comprehensive image database of all possible subsurface situations, which would not necessarily be limited to only examples of diffractions. The presented algorithm starts by identifying those signals that are likely to belong to diffraction apexes, which are then used as initial seeds by the auto-tracking process. The horizontal search window used during the auto-tracking process is locally adapted through a rough preliminary estimate of the size of each diffraction. In addition, multiple seeds within the same apex can produce several acceptable hyperbolas tracking the same diffraction phase. The algorithm thus selects the best-fitting ones by assessing several signal attributes while also removing redundant hyperbolas and the expected false positives. The algorithm is applied to two glaciological GPR profiles, and it is able to accurately track the vast majority of the recorded diffractions, with very few false positives and negatives. This produces a statistically sound EM velocity distribution, which was used to assess the state of the surveyed alpine glacier.
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (1.00)
- Geophysics > Electromagnetic Surveying (1.00)