En este artículo, se describen dos métodos de modelado inverso basados en la descomposición de va... more En este artículo, se describen dos métodos de modelado inverso basados en la descomposición de valor singular amortiguado (DSVD) como inversor lineal y el algoritmo de optimización de Marquardt como inversor no lineal. El SVD amortiguado resuelve los problemas mal planteados y especifica directamente la contribución de la densidad de la superficie inferior. La inversión de Marquardt estima los parámetros del modelo. La eficiencia de ambos métodos se investiga utilizando los datos de gravedad sintéticos, con y sin ruido aleatorio, según se obtengan los resultados aceptables. Los enfoques introducidos se emplean para la interpretación de un conjunto de datos de gravedad real de Irán. La masa causante de la gravedad en el área de estudio son casi el depósito magmático con un alto porcentaje de dióxido de manganeso donde han penetrado dentro de las fracturas y aproximadamente se han formado las estructuras tabulares. Las estructuras invertidas de ambos métodosson casi correspondientes. ...
Journal of Environmental and Engineering Geophysics
This paper presents an improved nature-based algorithm, namely multivariable modified teaching le... more This paper presents an improved nature-based algorithm, namely multivariable modified teaching learning based optimization (MM-TLBO) algorithm, as in an iterative process can estimates the best values for the model parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MM-TLBO algorithm is to improve the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the radius ( R), depth ( h), shape factor ( q), density contrast ( ρ) and axis location ( x0) parameters. We apply MM-TLBO and TLBO methods for the residual gravity anomalies caused by the buried masses with a simple geometry such as spheres, horizontal and vertical cylinders. The efficiency of these methods are also tested by noise corruption synthetic data, as the acceptable results were obtained. The obtained results indicate th...
In this paper, Particle Swarm Optimization (PSO) algorithm is employed to invert the gravity anom... more In this paper, Particle Swarm Optimization (PSO) algorithm is employed to invert the gravity anomaly due to a finite vertical cylinder source. The PSO inversion determines the radius (R), density contrast (ρ), depth to top (z) and bottom (h) parameters of a gravity anomaly causative body and also the location of anomaly source (origin x0) and gravity value in the origin (gx0) whose amount is maximum. During an iterative process, PSO estimates the subsurface model parameters and the gravity response according to them at each iteration. A profound weak point of Particle Swarm optimization method is getting into local minimum as the PSO algorithm can not estimates the optimal solutions. In order to overcoming this problem, the code is run frequently and the abundance distributions of the estimated values for the different parameters is drawn. Average value of each range whose frequently distributions is maximum are considered mas best solution. To evaluate the proficiency of the PSO me...
A stable inversion method to estimate the depth to top, width and dip of a sheet-like geological ... more A stable inversion method to estimate the depth to top, width and dip of a sheet-like geological structure from polereduced magnetic field is introduced. The inverse modelling is based on Marquardt optimization algorithm. The performance of the proposed method is considered by the theoretical magnetic data due to some dyke–shape models, with and without random noise. The inverted parameters convergence demonstrates the ability of the inversion approach as a powerful and useful tool, especially where the data are corrupted with noise. We employ this method for interpreting a real magnetic data set produced by a tabular structure from Iran. The inferred structure has approximately a depth to top of 17.12 m, a width of 12.74 m and a dip of 100.8 degree anticlockwise from horizontal, i.e. 10.8 degree from vertical towards east.
In this paper, the scalene triangle geometric model is considered in order to simulate the anticl... more In this paper, the scalene triangle geometric model is considered in order to simulate the anticlinal structures as this model is closer to the reality. The required mathematical relationship is expanded to compute the gravity effect of the scalene triangle model. Furthermore, an improved particle swarm optimization algorithm, known as improved particle swarm optimization (IPSO), has been discussed which is considered as a global optimization technique, being capable of improving the global search of particles in the whole search space. The ability of finding the optimal solution is adjusted by inertia weight (w) and acceleration coefficients (c1 and c2). For testing the ability of the IPSO algorithm, a theoretical scalene triangle model was considered as z1=2 km, z2=5 km, i=70 deg., j=30 deg., and Δρ=1000 kg/m3. The IPSO inversion of the noise-free and noise-corrupted synthetic gravity data inferred the structures similar to the assumed one where the estimated objective function values are 0.0004 and 0.0817, respectively. The inverted parameters prove the stability and efficiency of the IPSO method. This method also has been applied for a real gravity data set due to an anticlinal structure from Iran which can be significant for its probable oil and gas potential. The values of the estimated parameters for the subsurface anticlinal structure from the IPSO inversion are z1=3.52 km, z2=5.37 km, i=28.93 deg., j=26.37 deg., and Δρ=346.4 kg/m3.
The Anticlines are the main hydrocarbon traps on land or at sea. This structure is considered as ... more The Anticlines are the main hydrocarbon traps on land or at sea. This structure is considered as the target of the many projects of gravity exploration all over the world. Artificial neural networks (ANNs) are used in order to solve prediction, estimation, and optimization problems. In this paper, the feed-forward neural network (FNN) is applied for modeling the anticlinal structure using gravity anomaly profile and the back propagation algorithm is used for artificial neural network training. Moreover, the scalene triangle model is employed to describe the geometry of anticlinal structure in analyzing gravity anomalies. In terms of neural network training, eight features among the synthetic gravity field variations curves along 22500 profiles are defined. These gravity profiles are computed based on different values of the scalene triangle parameters consisting of the top depth, bottom depth, limb angles and density contrast. The defined neural network contain three layers, eight n...
The tilt angle, theta map, total horizontal derivative (TDX) and total horizontal derivative of t... more The tilt angle, theta map, total horizontal derivative (TDX) and total horizontal derivative of the tilt angle (THDR) are among local4phase filters as the edge detection and edge enhancement techniques can be a useful tool to interpret gravity maps most of which are high4pass filters based on the horizontal or vertical derivatives of the potential field with different orders. The windowed computation of the standard deviation (SD data) of an image is a simple measure of the local variability. Normalized standard deviation (NSTD), an edge4detection filter, is based on ratios of the windowed standard deviation of derivatives of the potential field. This filter helps geologic interpretation. Local4phase filters named above and NSTD are demonstrated using the synthetic gravity data whose random noise has amplitude equal to 0.015 % of the maximum data amplitude was added to the data set as well as on microgravity data of an aqueduct in Tehran urban environment, IRAN. The computer program...
journal of sciences islamic republic of iran, 2019
Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpr... more Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpretation. In this paper, 2D discrete wavelet transform (DWT) is employed as a method to delineate the boundary of the gravity anomaly sources. Hence, the GRACE’ satellite gravity data is decomposed using DWT. DWT decomposites a single approximation coefficients into four distinct components: the approximation, horizontal, vertical and diagonal. For evaluating the efficiency of wavelets, both the noisy and free-noise synthetic gravity data, have been decomposed at level 1 with six discrete two-dimensional wavelets. In this manuscript, the satellite gravity data of a part of the Makran region (in the south-east of Iran) is decomposed by DWT in order to detect the Saravan Fault trend. The outcome indicates the acceptable performance of the Haar and Biorthogonal mother wavelets in detecting the edges of the real and synthetic gravity anomaly sources. Also, the results demonstrate that the sat...
This paper presents a nature-based algorithm, titled multivariable teaching-learning-based optimi... more This paper presents a nature-based algorithm, titled multivariable teaching-learning-based optimization (MTLBO) algorithm. MTLBO algorithm during an iterative process can estimates the best values of the buried structure (model) parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MTLBO algorithm is to modify the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the depth (z), amplitude coefficient (k), shape factor (q), angle of effective magnetization (θ) and axis location (x0) parameters. We employ MTLBO method for the magnetic anomalies caused by the buried structures with a simple geometric shape such as sphere and horizontal cylinder. The efficiency of the MTLBO is also studied by noise corruption synthetic data, as the acceptable results were obtained. We have applied the...
In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the ... more In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. Ac...
Tilt angle filter is an interpretation method that is used to determine the source borders locati... more Tilt angle filter is an interpretation method that is used to determine the source borders locations from potential fields data. Moreover, the tilt angle is applied for estimation of the anomaly source depth, such as contact-depth method and tilt-depth method. In this paper an application of the tilt angle technique obtained from the first vertical and horizontal gradients of the gravity anomaly from semi-infinite vertical cylindrical source is described. The technique is based on the tilt angle and derivatives ratio. In this approach the depth estimates are proportional to the computed tilt angles and their distances from the cross section center of the anomaly cause on the surface. This new method is termed the tilt-distance-depth (TDD). The method is demonstrated using synthetic gravity data, with and without random noise, and real gravity data from Iran. The results are also compared with the solutions from Euler deconvolution technique and inverse modelling using Modelvision so...
Geologically, Anticlines are the most important geological structures amongst regional studies an... more Geologically, Anticlines are the most important geological structures amongst regional studies and hydrocarbon exploration methods. In general, inversion of gravity anomalies is non-unique in the sense that the observed gravity anomalies in a survey can be explained by a variety of density distributions. To resolve such an ambiguity, the anomalous mass should be estimated by a suitable geometry with a defined density contrast. Since anticlinal structures have mostly two non-isocline skirt, therefore utilization of the isosceles triangular model will be accompanied by a large error in the forward modeling. We have proposed using two adjoining right triangle for resolving mentioned problem. The density has been assumed constant. In this paper, a new method for anticline structure modeling based on feed forward neural network is presented. The network is trained by synthetic data as input and output. For feed forward neural network training we have used the back-propagation algorithm. The results indi¬cate that feed forward neural networks, if adequately trained, can predict the 2D form of anticline structure. The proposed method was applied to gravity data from Korand in Iran. The modeling results show high similarity with the attained results from seismic operation.
DESCRIPTION A modified iterative inversion method for 2D modeling of microgravity data and anomal... more DESCRIPTION A modified iterative inversion method for 2D modeling of microgravity data and anomaly subsurface precinct determination using vertical microgravity gradient data is presented in this paper.
In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. On... more In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. One of them is GPS/Levelling customary method as a criterion where the geoid undulation and height anomaly are computed by subtracting the ellipsoid height attained via GPS from the orthometric height and normal height, respectively. Another approach is Sjöberg's equation. We have used of the ICGEM website for definition of the variables of the Sjöberg's equation, as the applied reference model is the EGM2008 global geopotential model and WGS84 reference ellipsoid. The investigations are performed over the stations of the GPS/Leveling network related to three selected areas in desert, mountain and flatland namely the Lout, Zagros and Khuzestan in Iran and afterward the correlation coefficient between the geoid-to-quasigeoid separation calculated using the satellite data in Sjöberg's equation and GPS/Levelling method is estimated. The results indicate a straight correlation betw...
En este artículo, se describen dos métodos de modelado inverso basados en la descomposición de va... more En este artículo, se describen dos métodos de modelado inverso basados en la descomposición de valor singular amortiguado (DSVD) como inversor lineal y el algoritmo de optimización de Marquardt como inversor no lineal. El SVD amortiguado resuelve los problemas mal planteados y especifica directamente la contribución de la densidad de la superficie inferior. La inversión de Marquardt estima los parámetros del modelo. La eficiencia de ambos métodos se investiga utilizando los datos de gravedad sintéticos, con y sin ruido aleatorio, según se obtengan los resultados aceptables. Los enfoques introducidos se emplean para la interpretación de un conjunto de datos de gravedad real de Irán. La masa causante de la gravedad en el área de estudio son casi el depósito magmático con un alto porcentaje de dióxido de manganeso donde han penetrado dentro de las fracturas y aproximadamente se han formado las estructuras tabulares. Las estructuras invertidas de ambos métodosson casi correspondientes. ...
Journal of Environmental and Engineering Geophysics
This paper presents an improved nature-based algorithm, namely multivariable modified teaching le... more This paper presents an improved nature-based algorithm, namely multivariable modified teaching learning based optimization (MM-TLBO) algorithm, as in an iterative process can estimates the best values for the model parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MM-TLBO algorithm is to improve the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the radius ( R), depth ( h), shape factor ( q), density contrast ( ρ) and axis location ( x0) parameters. We apply MM-TLBO and TLBO methods for the residual gravity anomalies caused by the buried masses with a simple geometry such as spheres, horizontal and vertical cylinders. The efficiency of these methods are also tested by noise corruption synthetic data, as the acceptable results were obtained. The obtained results indicate th...
In this paper, Particle Swarm Optimization (PSO) algorithm is employed to invert the gravity anom... more In this paper, Particle Swarm Optimization (PSO) algorithm is employed to invert the gravity anomaly due to a finite vertical cylinder source. The PSO inversion determines the radius (R), density contrast (ρ), depth to top (z) and bottom (h) parameters of a gravity anomaly causative body and also the location of anomaly source (origin x0) and gravity value in the origin (gx0) whose amount is maximum. During an iterative process, PSO estimates the subsurface model parameters and the gravity response according to them at each iteration. A profound weak point of Particle Swarm optimization method is getting into local minimum as the PSO algorithm can not estimates the optimal solutions. In order to overcoming this problem, the code is run frequently and the abundance distributions of the estimated values for the different parameters is drawn. Average value of each range whose frequently distributions is maximum are considered mas best solution. To evaluate the proficiency of the PSO me...
A stable inversion method to estimate the depth to top, width and dip of a sheet-like geological ... more A stable inversion method to estimate the depth to top, width and dip of a sheet-like geological structure from polereduced magnetic field is introduced. The inverse modelling is based on Marquardt optimization algorithm. The performance of the proposed method is considered by the theoretical magnetic data due to some dyke–shape models, with and without random noise. The inverted parameters convergence demonstrates the ability of the inversion approach as a powerful and useful tool, especially where the data are corrupted with noise. We employ this method for interpreting a real magnetic data set produced by a tabular structure from Iran. The inferred structure has approximately a depth to top of 17.12 m, a width of 12.74 m and a dip of 100.8 degree anticlockwise from horizontal, i.e. 10.8 degree from vertical towards east.
In this paper, the scalene triangle geometric model is considered in order to simulate the anticl... more In this paper, the scalene triangle geometric model is considered in order to simulate the anticlinal structures as this model is closer to the reality. The required mathematical relationship is expanded to compute the gravity effect of the scalene triangle model. Furthermore, an improved particle swarm optimization algorithm, known as improved particle swarm optimization (IPSO), has been discussed which is considered as a global optimization technique, being capable of improving the global search of particles in the whole search space. The ability of finding the optimal solution is adjusted by inertia weight (w) and acceleration coefficients (c1 and c2). For testing the ability of the IPSO algorithm, a theoretical scalene triangle model was considered as z1=2 km, z2=5 km, i=70 deg., j=30 deg., and Δρ=1000 kg/m3. The IPSO inversion of the noise-free and noise-corrupted synthetic gravity data inferred the structures similar to the assumed one where the estimated objective function values are 0.0004 and 0.0817, respectively. The inverted parameters prove the stability and efficiency of the IPSO method. This method also has been applied for a real gravity data set due to an anticlinal structure from Iran which can be significant for its probable oil and gas potential. The values of the estimated parameters for the subsurface anticlinal structure from the IPSO inversion are z1=3.52 km, z2=5.37 km, i=28.93 deg., j=26.37 deg., and Δρ=346.4 kg/m3.
The Anticlines are the main hydrocarbon traps on land or at sea. This structure is considered as ... more The Anticlines are the main hydrocarbon traps on land or at sea. This structure is considered as the target of the many projects of gravity exploration all over the world. Artificial neural networks (ANNs) are used in order to solve prediction, estimation, and optimization problems. In this paper, the feed-forward neural network (FNN) is applied for modeling the anticlinal structure using gravity anomaly profile and the back propagation algorithm is used for artificial neural network training. Moreover, the scalene triangle model is employed to describe the geometry of anticlinal structure in analyzing gravity anomalies. In terms of neural network training, eight features among the synthetic gravity field variations curves along 22500 profiles are defined. These gravity profiles are computed based on different values of the scalene triangle parameters consisting of the top depth, bottom depth, limb angles and density contrast. The defined neural network contain three layers, eight n...
The tilt angle, theta map, total horizontal derivative (TDX) and total horizontal derivative of t... more The tilt angle, theta map, total horizontal derivative (TDX) and total horizontal derivative of the tilt angle (THDR) are among local4phase filters as the edge detection and edge enhancement techniques can be a useful tool to interpret gravity maps most of which are high4pass filters based on the horizontal or vertical derivatives of the potential field with different orders. The windowed computation of the standard deviation (SD data) of an image is a simple measure of the local variability. Normalized standard deviation (NSTD), an edge4detection filter, is based on ratios of the windowed standard deviation of derivatives of the potential field. This filter helps geologic interpretation. Local4phase filters named above and NSTD are demonstrated using the synthetic gravity data whose random noise has amplitude equal to 0.015 % of the maximum data amplitude was added to the data set as well as on microgravity data of an aqueduct in Tehran urban environment, IRAN. The computer program...
journal of sciences islamic republic of iran, 2019
Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpr... more Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpretation. In this paper, 2D discrete wavelet transform (DWT) is employed as a method to delineate the boundary of the gravity anomaly sources. Hence, the GRACE’ satellite gravity data is decomposed using DWT. DWT decomposites a single approximation coefficients into four distinct components: the approximation, horizontal, vertical and diagonal. For evaluating the efficiency of wavelets, both the noisy and free-noise synthetic gravity data, have been decomposed at level 1 with six discrete two-dimensional wavelets. In this manuscript, the satellite gravity data of a part of the Makran region (in the south-east of Iran) is decomposed by DWT in order to detect the Saravan Fault trend. The outcome indicates the acceptable performance of the Haar and Biorthogonal mother wavelets in detecting the edges of the real and synthetic gravity anomaly sources. Also, the results demonstrate that the sat...
This paper presents a nature-based algorithm, titled multivariable teaching-learning-based optimi... more This paper presents a nature-based algorithm, titled multivariable teaching-learning-based optimization (MTLBO) algorithm. MTLBO algorithm during an iterative process can estimates the best values of the buried structure (model) parameters in a multi-objective problem. The algorithm works in two computational phases: the teacher phase and the learner phase. The major purpose of the MTLBO algorithm is to modify the value of the learners and thus, improving the value of the model parameters which leads to the optimal solution. The variables of each learner (model) are the depth (z), amplitude coefficient (k), shape factor (q), angle of effective magnetization (θ) and axis location (x0) parameters. We employ MTLBO method for the magnetic anomalies caused by the buried structures with a simple geometric shape such as sphere and horizontal cylinder. The efficiency of the MTLBO is also studied by noise corruption synthetic data, as the acceptable results were obtained. We have applied the...
In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the ... more In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. Ac...
Tilt angle filter is an interpretation method that is used to determine the source borders locati... more Tilt angle filter is an interpretation method that is used to determine the source borders locations from potential fields data. Moreover, the tilt angle is applied for estimation of the anomaly source depth, such as contact-depth method and tilt-depth method. In this paper an application of the tilt angle technique obtained from the first vertical and horizontal gradients of the gravity anomaly from semi-infinite vertical cylindrical source is described. The technique is based on the tilt angle and derivatives ratio. In this approach the depth estimates are proportional to the computed tilt angles and their distances from the cross section center of the anomaly cause on the surface. This new method is termed the tilt-distance-depth (TDD). The method is demonstrated using synthetic gravity data, with and without random noise, and real gravity data from Iran. The results are also compared with the solutions from Euler deconvolution technique and inverse modelling using Modelvision so...
Geologically, Anticlines are the most important geological structures amongst regional studies an... more Geologically, Anticlines are the most important geological structures amongst regional studies and hydrocarbon exploration methods. In general, inversion of gravity anomalies is non-unique in the sense that the observed gravity anomalies in a survey can be explained by a variety of density distributions. To resolve such an ambiguity, the anomalous mass should be estimated by a suitable geometry with a defined density contrast. Since anticlinal structures have mostly two non-isocline skirt, therefore utilization of the isosceles triangular model will be accompanied by a large error in the forward modeling. We have proposed using two adjoining right triangle for resolving mentioned problem. The density has been assumed constant. In this paper, a new method for anticline structure modeling based on feed forward neural network is presented. The network is trained by synthetic data as input and output. For feed forward neural network training we have used the back-propagation algorithm. The results indi¬cate that feed forward neural networks, if adequately trained, can predict the 2D form of anticline structure. The proposed method was applied to gravity data from Korand in Iran. The modeling results show high similarity with the attained results from seismic operation.
DESCRIPTION A modified iterative inversion method for 2D modeling of microgravity data and anomal... more DESCRIPTION A modified iterative inversion method for 2D modeling of microgravity data and anomaly subsurface precinct determination using vertical microgravity gradient data is presented in this paper.
In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. On... more In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. One of them is GPS/Levelling customary method as a criterion where the geoid undulation and height anomaly are computed by subtracting the ellipsoid height attained via GPS from the orthometric height and normal height, respectively. Another approach is Sjöberg's equation. We have used of the ICGEM website for definition of the variables of the Sjöberg's equation, as the applied reference model is the EGM2008 global geopotential model and WGS84 reference ellipsoid. The investigations are performed over the stations of the GPS/Leveling network related to three selected areas in desert, mountain and flatland namely the Lout, Zagros and Khuzestan in Iran and afterward the correlation coefficient between the geoid-to-quasigeoid separation calculated using the satellite data in Sjöberg's equation and GPS/Levelling method is estimated. The results indicate a straight correlation betw...
Determination of potential fields' anomaly borders is a useful help to their interpretation. Ther... more Determination of potential fields' anomaly borders is a useful help to their interpretation. There is various technique of edge detecting that is applied in image processing. In this paper, the canny edge detection (CED) method has been proposed as boundary enhancement of the magnetic and gravity potential field data. For 2-dimensional bounds, residual potential field map is first smoothed by using a 2-D Gaussian filter. Afterwards, computing the horizontal gradients of the smoothed map and then using the gradient magnitude and direction to estimate borders strength and direction at every pixel. In this research, a new procedure to define the thresholds has been suggested. The results obtained from the synthetic data set, with and without random noise , have been discussed. The method is demonstrated on real gravity and magnetic data set surveyed from Iran.
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