امید اصغری

One of the most crucial steps in ore exploration is the recognition of geological patterns and features. These features contain mineralogy, lithology, alteration, rock texture, etc. This stage has always been associated with many challenges. Among the challenges of this stage, we can mention the time-consuming and costly nature of this stage and the need for high expertise and human resources to recognize these patterns and features. In recent years, deep learning and machine learning have been adopted in earth sciences. In this research, by using the architecture of U-net, ore and waste were separated, and the grade pattern was identified using the core box images. For this purpose, iron minerals were segmented using binary image segmentation, trial-and-error methods were used to optimize the network, and finally, the model's accuracy for identifying ore was 91%. The IoU metric was utilized for further evaluation; this metric is a suitable criterion for the final evaluation of the image segmentation model, which has reached 75% in recognition of iron ores. For the final evaluation of the obtained model, the grade outputs of the model and the XRF analysis results of one core were compared. The network error was evaluated at 9%, which shows the good accuracy of the obtained model according to the real data.

Singularity is the characteristic of various non-linear phenomena, such as hydrothermal processes in the Earth's crust, which produce deposits with high metal concentrations. The final result of these processes is the appearance of fractal or multi-fractal features, and several methods exist to identify these features. The singularity distribution mapping method is one of the multi-fractal analyses developed based on the singularity index and as a tool for separating anomalies from the background or for separating local anomalies in a region. In this study, the multi-variable singularity mapping method was used to determine geochemical anomalies to establish the relationship between various elements in the Qara Cher exploration area, located 42 km southwest of the city of Saqez in Kurdistan province. The database contains 1104 litho-geochemical samples with 10 analyzed elements, including Au, As, Ag, Cu, Sb, Sn, Bi, Mo, Zn, and Pb. Due to the compositional nature of the variables and subsequent false correlations in the closed system, principal components analysis (PCA) was applied to the data under isometric log ratio (ilr) transformation. The relationship between As and Cu on the first and second principal components shows the independent function of gold in the study area. The application of the singularity mapping method has highlighted some promising and potential areas for future explorations. These areas could be important for mineralization due to the presence of phyllic alteration, iron oxides, sulfide minerals, and high-grade gold cells. Based on the singularity mapping results, two different hydrothermal mineralization systems of intermediate (mesothermal) to high thermal and epithermal to mesothermal are proposed, respectively; for the southern and northern parts of the Ghare Char area. Nevertheless, due to the mesothermal (orogenic) gold mineralization systems in the known Kervian and Ghlgholeh gold deposits, located in the vicinity of the Qareh Char area, and also the high concentration of As and Sb in these deposits, the possible presence of orogenic gold mineralization is more compared to the other types. Therefore, it is recommended to use the exploration criteria of the orogenic gold deposits for further exploration in the Qareh Char area.

This research deals with the spatial simulation of rock types and the assessing the uncertainty in the domain boundaries in Golgohar Sirjan iron deposit. Based on truncated Gaussian simulation, a simulation approach is proposed to this end, in which the geological units are reproduced by examining the nature of geological boundaries and vertical and horizontal instability. For this purpose, at first, contact analysis is used to investigate the transition in the grade distribution when crossing a rock type boundary. In the next step, the drill holes data are divided into two domains according to the contact analysis results. The first domain includes top magnetite and oxide zone, and the second domain includes bottom magnetite. Next, the local probabilities model is reproduced based on the vertical proportion matrix (VPM). Finally, different stochastic realizations of rock type units are reproduced by using the improved truncated Gaussian simulation algorithm. In this proposed algorithm, soft (probabilities) and hard data played an equal role in the simulation process. The results show the capability of the proposed algorithm to reproduce the single-point statistics, two-point statistics, and the connectivity values obtained by the hard data and extractive block model.

There are important deposits such as Sari Gunay epithermal gold, Dalli porphyry copper-gold, and Zarshuran Carlin deposits with a few common exploration features in the Zagros metallogenic province of Iran. This study used geological maps, remote sensing, geochemical, geophysical, mineralogical, petrographic, fluid inclusion and age dating information to characterize and identify exploration criteria of these deposits. Mineralization at Sari Gunay gold deposit is epithermal, which was formed in association with an alkaline magma and brecciated, altered dacite porphyry about 11 Ma. Mineralization at Zatshuran is Cralin with black shale and carbonate sedimentary hosts, formed indirectly in association with a deep alkaline magma about 14 Ma. Mineralization at Dalli deposit is copper-gold porphyry with diorite host, formed in association with a chalk alkaline magma about 21 Ma. Despite different host rocks, mineralization at Zarhuran and Sari Gunay gold deposits reveals some similarities. Among the common exploration criteria in the two deposits are Oligo-Miocene alkaline magma, mineralization depth of more than 300 meters, northeast trending structures, gold, arsenic and antimony geochemical association, presence of iron oxides such as jarosite and hematite, vuggy breccia textures, and silica and phyllic alteration hosting gold minerlization. The most important exploration criteria at the Dalli deposit, however, are Miocene chalk alkaline magmatism, depth of mineralization of more than 500 meters, strong potassic and phyllic alterations, presence of specularite mineral, northeast trending structures and strong high magnetic anomalies, associated with potassic alteration.

Calculation of variograms and spatial continuity is one of the first and most important processes in geostatistical modeling, which is a long and experience-oriented process. Due to the complexities of calculating experimental variograms, interpretation and fitting the appropriate model are always the main challenges in this field. This article presents an intelligent variogram modeling method using deep learning that can increase the speed of variogram modeling and also prevent common errors in manual variogram model fitting. In this method, two convolutional neural networks are used. The first CNN network converts the initial data into a 2D simulated map based on various variogram models. For this purpose, it is necessary to train the first network with initial data and their corresponding simulations. The output of this model is entered into the second convolutional neural network as input, and the variogram parameters (including range, azimuth, ratio, and nugget effect) are predicted. In this article, the proposed algorithm is implemented on synthetic 2D data and the parameters of the CNN models are optimized. The accuracy of the proposed model was 97 %, and then the proposed algorithm was used for variogram modeling of Nouchon area geochemical data, which included the elements Cu, Zn, and Pb. the accuracy of the obtained model compared to manual fitting was 90%.

Image processing of remote sensing for separation hydrothermal alteration, in the case of missing initial spectra of pixels, can be a challenge for the researcher. The previous researches has shown that accurate separation of hydrothermal alteration zones using Conventional methods of image processing based on Spectral Properties of pixels, is not possible. Therefore, this research is trying to present a multi-stage algorithm that identify and discriminate the hydrothermal alteration zones in western part of Kerman province with high accuracy. To achieve this goal, the principal component analysis method, Fractal Concentration-Area Model and Full Index Kriging (FIK) geostatistical model are used in combination. The results show the high accuracy of the FIK model in identifying and separating each of the phyllic, argillic and propylitic alterations in the study area. Also, to evaluate the classification error, the Confusion matrix was investigated. The results of the Confusion matrix showed that the FIK model performs well in terms of image classification. Also, given the high number of training pixels in the phyllic zone, the FIK model has been able to identify this type of alteration very well.

Facies are often imported in reservoir modeling because the petrophysical properties of interest are highly correlated with facies type. Knowledge of facies constrains the range of variability in porosity and other petrophysical properties. But on the other hand, proper study and modeling of facies requires considerable time and money in reservoir studies and also, due to the fact that the three-dimensional distribution of facies in many studies has not been able to significantly reduce uncertainty, Facial modeling has not received much attention, especially in carbonate reservoirs. In this study, after modeling the facies in a carbonate reservoir, comparison of porosity simulation has been performed using three-dimensional distribution of facies and without using it. In this study, SIS method was used to simulate facies and SGS method was used to porosity simulation. Also to investigate the reduction of model uncertainty with the seismic data integrating, Acoustics impedance has been used as secondary data in porosity simulation. Besides that, neural network analysis was performed on a set of seismic attributes to get facies probability cubes. These probability cubes was entered as a trend in the simulation of the facies. Examination of the error rate in blind wells showed that it is appropriate to use SIS and SGS geo-statistical methods in case of sufficient data in a carbonate reservoir and with the use of seismic data and the distribution of facies in porosity simulation, uncertainty was reduced to an acceptable level, with an average of 87% of the model being valid.

The key input parameters for mine planning and all subsequent mining activities is based on the block models. The block size should take into account for the geological heterogeneity and the grade variability across the deposit. Providing grade models of smaller blocks is more complex and costly than larger blocks, but larger sizes cannot represent areas with high spatial variability accurately. Hence, a unique block size is not an optimal solution for modeling a mine site. This paper presented a novel algorithm to create an adaptive block model with locally varying block sizes aiming to control dilution and ore loss in Sungun porphyry copper deposit of Iran with a complex geometry characterized by multiple dikes. Three grade block models with different block sizes and simulated by direct block simulation are the inputs of algorithm. The output is a merged block model, assigning the smaller blocks to the complex zones, such as ore-waste boundaries, and larger blocks to the continuous and homogeneous zones of the ore body. The presented algorithm is capable to provide an accurate spatial distribution model with a fewer number of blocks in comparison to the traditional block modeling concepts.

With the increase in complexity of mineral deposits, understanding the grade variability is of high significance in getting enough information about the deposit, preventing financial losses and identifying optimized plans during and after exploitation. Likewise, mineralogical variability, grade, alteration, … can highly effect metal recovery. Modeling these parameters is seriously substantial in order to have an optimized exploitation of the mine and to minimize the risks and costs. This study used the dataset of 91 drill holes from Sari Gunay epithermal gold deposit located in north-west of Iran to model gold grade and the recovery resulted from leaching tests. Initially, the oxide and sulphide zones were distinguished using Indicator Kriging and Simulation. Then the gold grade and recovery in each zone were modeled with the application of sequential Gaussian simulation and the developed block model. The grade-recovery curve was then drawn to estimate the total tonnage amount of the deposit which was related to the sulphide zone in more than 70%. Then with the help of recovery simulation data, the grade×recovery was considered a preferable parameter in depicting the curve and estimating the reserve.

The study area is the Yeganlly and Qinranjeh area, southwest of Zarshuran gold mine, 35 km away from Takab city, West Azarbaijan province. The study area is located on the southwest edge of the mine. Only 17 borehole data were available for this study and were evaluated. Geophysical data includes 17 parallel profiles with a length of about 735 meters with a 30 meter distance electrode and a polar-bipolar mapping array according to the topography of the area. The objective of introducing and presenting a method for simulation and single-multivariate estimation using the most widely used methods, such as usual cracking, ordinary cokriging, sequential simulation, sequential coexistence simulation, in order to reproduce more precisely the initial region variables and Secondary will be. Geophysical data was constructed of a so-called sulfide factor. After normalizing, for each variable, the variography chart was drawn and estimated using the Kriging method according to the variogram in the borehole coordinates. Then, by normalizing the data in the specimen, analysis of the main components on the variables was performed using SPSS software. The output of this part was two factors that the fact that the amount of gold mineralization was high was introduced as a mineralization factor. Now, with two existing factors, namely, the sulfide factor (geophysical factor) and the gold mineralization factor in the studied area, the combined interactions between the built-in block models were combined with the estimation and simulation; ultimately, validation was also performed by evaluating and estimating two boreholes Isolated randomly using other specimens at the end. It was found that according to the evaluated results, when estimating the gold grade when using sulfide factors and mineralization in coking, the gold monorangle estimation by conventional Kriging estimation is closer to the real values of gold.

As the best linear estimator, Kriging is now a well-established method in all types of  2D and 3D modeling, including geochemical mapping, rock types modeling, geophysical mapping, and resource estimation. In general, a multi-stage approach can be used for evaluating kriging parameters. The first step in the assessment of mineral resources using linear geostatistics is to remove outlier data and to find the best de-cluster size. After this stage, variogram models in the area under study must be provided by a spherical model. In this context, investigating kriging performance has always been of interest to numerous researchers. Evaluating kriging implementation for different applications has been a growing field of study in the last few decades. Although many authors have discussed various kriging parameters, it seems necessary to conduct more detailed reviews on range searching, high and low nugget effect, as well as 2D and 3D estimations. In this paper, an optimal search range was determined using quantitative kriging neighborhood analysis (QKNA), and the utility of this search range was explored by assessing kriging efficiency. To this end, the borehole dataset of the Gol-E-Gohar No.1 mine was used. In total, 2579 samples (of length 3 m) make up the database for this study.  In this research, the dataset was divided into two zones based on their associated geological domains. Based on the aforementioned parameters, 180 estimation strategies were generated for each rock type. The results indicate that the optimal search ranges of zone 1 are 688, 226, and 152, and the optimal search ranges of zone 2 are 482, 233, and 303.

An accurate modeling of sophisticated geological units has a substantial impact on designing a mine extraction plan. Geostatistical simulation approaches, via defining a variogram model or incorporating a training image (TI), can tackle the construction of various geological units when a sparse pattern of drilling is available. The variogram-based techniques (derived from two-point geostatistics) usually suffer from reproducing complex and non-linear geological units as dyke. However, multipoint geostatistics (MPS) resolves this issue by incorporating a training image from a prior geological information. This work deals with the multi-step Single Normal Equation Simulation (SNESIM) algorithm of dyke structures in the Sungun Porphyry-Cu system, NW Iran. In order to perform a multi-step SNESIM algorithm, the multi-criteria decision-making and MPS approaches are used in a combined form. To this end, two TIs are considered, one for simulating dyke structures in the shallow depth, and two for simulating dyke structures in a deeper depth. In the first step, a TI is produced using geological map, which has been mined out during the previous exploration operations. After producing TI, the 35 realizations are simulated for the shallow depth of deposit in the area under study. To select the best realization (as a TI for the next step) of the simulation results, several statistical criteria are used and the results obtained are compared. To this end, a hybrid multi-criteria decision-making is designed on the basis of a group of statistical criteria. In the next step, the dyke structures in the deeper depth are also simulated by the new TI.

This work aims at figuring out the spatial relationships between the geophysical and geological models in a case study pertaining to copper-sulfide mineralization through an integrated 3D analysis of favorable target. The Ghalandar Skarn-Porphyry Cu Deposit, which is located in NW Iran, is selected for this research work. Three geophysical surveys of direct current electrical resistivity and induced polarization tomography along with magnetometry are performed to construct the physical properties of electrical resistivity, chargeability, and magnetic susceptibility, respectively. Inverse modeling and geostatistical interpolation are utilized to generate the physical 3D models. A 3D model of Cu grade is generated using ordinary kriging; however, the indicator kriging method is run to design a 3D model of rock types through incorporating the drilling results. Block models of geophysical and geological characteristics are cast in a similar 3D mesh to investigate their relationships in copper mineralization. A concentration-volume multi-fractal method is utilized to divide each model into its sub-sets, where the most productive portions in association with Cu-bearing mineralization are distinguished. Note that sub-sets of geophysical models are spatially matched with geological models of Cu grade and rock types. The zones with low electrical resistivity, high chargeability, and low magnetic susceptibility correspond to the main source of Cu mineralization in a dominated skarn rock type setting.

Since in exploratory works the number of collected data are much smaller than area of the study area therefore finding a strong tool for deposit spatial modelling with according to limited collected points is very important. According to study deposit characteristics different geostatistical simulation algorithms are presented with the ability to generate different models of deposits for the solution of this problem. The existence or absence of high skewness of exploratory collected data in study area is one of the reasons for using sequential indicator simulation method or sequential Gaussian simulation method. In this article according to the type of study activities of programing network graphical evaluation and review technique (GERT) for explorative projects management and creation a suitable model in use of sequential gaussian simulation and sequential indicator simulation were used. For implement the possible network activities used of geochemical data of Dali Cu-Au porphyry deposit. Comparison of SIS simulation results on gold data for high Skewness with results of SGS simulation on copper data for low skewness indicates correlation top of these two elements is the existence of Cu-Au porphyry resource along the NE-SW in in Dali area. The results adaptation of the survey method with geological evidence proved work steps.

Dilution can best be defined as the proportion of waste tonnage to the total weight of ore and waste in each block. Predicting the internal dilution based on geological boundaries of waste and ore in each block can help engineers to develop more reliable long-term planning designs in mining activities. This paper presents a method to calculate the geological internal dilution in each block and to correct the ultimate grade of each geological block according to the internal dilution values that have already been calculated for each one of them. In this regard, the input data is first indexed based on the lithological logs of drill holes. The occurrence probabilities of ore and waste in each block are calculated via 100 realizations using the sequential indicator simulation. Dilution is computed as the ratio of waste rock tonnage to the total tonnage of ore and waste. Furthermore, joint simulation of the continuous variables is performed for each mining block using the minimum/maximum auto-correlation factors. In the next step, for each block, the final grade variables including iron and iron oxide are computed by considering the calculated internal dilution. These analyses are applied to the Gohar Zamin iron ore deposit, and the actual internal dilution calculated based on the lithological logs of blast holes is compared with the same values obtained based on the proposed method in each block. The results obtained were found to be satisfactory.

Determination of ore body domain is the main step in the beginning of a mining project. The mine designing, mining and processing plant planning would be implemented based on this domain. Traditional methods characterize this domain graphically and would not concentrate error and uncertainty, but Geostatistics as a powerful tool is able to determine this domain using spatial statistics. Ore domain is a district variable that can be modeled by different simulation methods, such as Truncated Gaussian simulation (TGS). TGS simulates the domain according to the simulation of one Gaussian function and rock type rule. Furthermore, simple relations can be applied for determination of ore domain, for example, Distance Function (DF). DF defines the ore boundary by the Euclidian distance between each point and the nearest dissimilar point and the distance calibration.
Statistical and geostatistical validations are applied to find the best realization of TGS. The DF and TGS results are compared by assessing confusion matrices, overall error and precision of the modeled domains. Moreover, different plans, and section are qualitatively compared. Validation and comparisons indicate that TGS is a more efficient way to model the ore domain. Therefore, Gol Gohar mine was studied and after the implementation of both methods showed that TGS compared to DF results in more precise domain simulation. TGS algorithm is able to reproduce the small scale anisotropies versus, better results at large scale anisotropies using DF algorithm.
Key words: Geostatistics, Ore Domain, Truncated Gaussian simulation, Distance Function,

Large percentages of world hydrocarbon reservoirs are fractured reservoir and fracture distribution in these reservoirs are not distributed randomly. Fracture distribution in fractured reservoir depends on the combination of structures, lithology, reservoir thickness, fault, and other fracture controllers. For accurate fracture modeling, these factors should be integrated with well data. For this purpose, fracture density of three wells in Marun oil field is used. Fracture related seismic attributes such as instantaneous frequency, curvature, and dip is extracted from seismic data. Geological and petrophysical features, which control fracture density, are modeled by the integration of seismic and well data. By the integration of these factors and fracture density in wells, fracture density is modeled by artificial neural network. In this study, the continuous fracture model is properly modeled and the results demonstrate 82% correlation with well data. This continuous fracture model has a relatively good relation with transmissibility map and the transmissibility map satisfies high fracture density in the south limb of anticline. Most fracture densities are located in the southern limb of anticline and this seems to be suitable region for field development.

This study deals with the imputation methods of censored values in the multivariable geochemical data. Presence of the missing values causes limitation in the use of most of statistical methods, e.g. principle component analysis. Excluding the samples which include missing values bias the results and leads to the loss of information. Due to this, consideration of an appropriate approach to deal with missing values is necessary in the analysis of incomplete datasets. In this paper considering the nature of geochemical data, various approaches for imputing the missing values, which have been suggested in the recent years and are easy to be used in the R statistic software, are introduced. Finally, using the complete dataset of the Zafarghand region, these methods are compared with each other. Results show that the application of the multivariable methods in the imputation and particularly the ilr-EM method is preferable to the other methods.

Saltwater intrusion into freshwater in coastal areas has been a serious concern for many countries. Providing fresh water in some regions is very crucial. In fact، the areas that are prone to encountering salt water zones should be checked meticulously. The preferred method for such investigation is a precise 3-D model of distribution of fresh and salt water In order to reach such a model، reliable measurements and comprehensive resistivity interpretations are needed. The purpose of this study is to use geostatistical simulations in order to provide a 3-D aquifer model from the results of the resistivity studies. This means to delineate the boundary of saltwater and freshwater in the aquifer. Geostatistical simulation provides a robust tool for presentation of the results achieved from interpretation of resistivity data. Geostatistical simulations by assessing the risk and uncertainties regarding the measurements at hand، provides a method for a precise economical study and therefore a more detailed financing and planning scheme. Most of the prediction/estimation methods involve، in some way، an averaging method in which smoothing and reducing the amplitude of fluctuations among their characteristics are happened. However، geostatistical simulation methods are able to reproduce the minor and local differences more precisely than other methods. In other words، the simulation does not reduce the variance of the data so the minimum and maximum values are reproduced. The required data for this study were acquired in Borazjan plane in the Boushehr province، south of Iran. 82 Vertical Electrical Sondage (VES) with Schlumberger array were conducted along with 6 profiles in the Study area. The distance between 2 subsequent measurements are 200 m، and lateral distance between 2 neighbor profiles is 1000 m. Distances between current electrodes (AB) are increased from 1. 5 m to 1000 m. Each logarithmic decade contains 6 different measurements. Direction of survey oriented North-West to South-East in each profile. After the data gathering، with the use of electrical software، apparent resistivity sections are provided. In the next step، data are inverted using a software and the standard curves. The best multi-layered ground for the Earth is obtained. After the interpretation of the initial data، the real resistivity values of the aquifer are introduced to sequential Gaussian simulation algorithm as input data. Regarding the concept of 1D resistivity inversion، those maps and sections are considered important that manifest coherent amplitude of resistivity variations. In this study، those simulations are considered and used that are capable to reproduce coherent amplitude of resistivity values. For this reason، we use Sequential Gaussian Simulation method which includes such a characteristic in nature، for simulation of the aquifer. For this reason، data are normalized into Gaussian distribution. In order to investigate the anisotropy in the region، a directional variography is done; then the best variogram model is chosen using the cross validation test. The anisotropy shows range/sill variations of the variogram in different orientations; thus the variogram is a useful tool for identification the heterogeneities in the investigation area. Using 50 m×50 m×10 m blocks and the sequential Gaussian simulation algorithm، 100 times simulations were performed and 100 realizations were obtained. The simulation results (realizations) are only acceptable when they can reproduce the identical histogram/variogram، which in this case is the histogram and the variogram of the raw data of the aquifer. After the simulation results were validated the E-type map is derived. This map shows the average value simulated for each block by averaging the values of the 100 realizations. This map is a 3-D model of the real resistivity distribution within the aquifer. The increase of the resistivity values can be observed in this map. Among the most important results، obtained from the realizations، are the probability maps. These maps show the probability of exceeding a defined value، and are driven by counting the number of times that the resistivity value of a block has passed a certain resistivity value in the all realizations. In fact، the probability map can be assumed as a good factor for determination of drilling position for freshwater exploitation. Using the probability maps، the freshwater positions can be identified with the probability of 1 or very close to 1. In order to make a comparison between the data of the drilled well which is placed in the farthest distance between the two profiles، and the estimated model، a network was designed by which it was possible to estimate the aquifer resistivity values at the position of the well. The acquired resistivity values، using the Geostatistical simulation within the designed network and the resistivity values in the aquifer in the position of the well، proves the accurate estimation of the model in accordance with the reality of the aquifer.

Magnetic survey is one of the most important geophysical methods extensively used inmineral explorations. Therefore, the interpretation and modeling of this data is very important before doing any drilling exploration. Modeling this data makes it possible to choose the best position for drilling. In this study, the magnetic data of Morvarid Zanjandeposit has been modeled and a 3D model of the magnetic susceptibility has been achieved. The results were compared with the real model created with drilling explorationdata. There are many inversion algorithms for modeling the magnetic data. However, a principal difficulty with the inversion of the potential data is the inherent nonuniqueness. By Gauss’ theorem, if the field distribution is known only on a bounding surface, there are infinitely many equivalent source distributions inside the boundary that can produce the known field. A second source for nonuniqueness is the fact that the magnetic observations are finite in number and are inaccurate. If there exists one model that reproduces the data, there will be other models that will reproduce the data to the samedegree of accuracy. Faced with this extreme nonuniqueness, authors have mainly taken two approaches in the inversion of magnetic data. The first one is the parametric inversion in which the parameters of a few geometrically simple bodies are sought in a nonlinear inversion and the values are found by solving an overdetermined problem. This methodology is suited for anomalies known to be generated by simple causative bodies, but it requires a great deal of a priori knowledge about the source expressed in the form of an initial parameterization, an initial guess for the parameter values, and limits on the susceptibility allowed.In the second approach to inverting magnetic data, the earth is divided into a large number of cells of fixed size but of unknown susceptibility. Nonuniqueness of the solution is recognized and the algorithm produces a single model by minimizing an objective function of the model subject to fitting the data. Based on the second approach, Li and Oldenburg (1996) formed a multicomponent objective function that had the flexibility to generate different types of models. The objective function incorporates an optional reference model so that the constructed model is close to that. It penalizes roughness in three spatial directions, and it has a depth weighting designed to distribute the susceptibility with depth. Because there is no depth resolution inherent in the magnetic field data, the recovered model is occurred near the surface and takes away from its original position. The depth weighting function helps to locate the recovered model in its real position. Li and Oldenburg (1996, 2000) proposed relations for the depth weighting function. Additional 3-D weighting functions in the objective function can be used to incorporate further information about the model. The user can incorporate other information about the inversion model. The information might be available from othergeophysical surveys, geological data, or the interpreter’s qualitative or quantitative understanding of the geologic structure and its relation to the magnetic susceptibility.In principle, this algorithm can be applied to large-scale data. Numerically, however,the computational complexity increases rapidly with the increasing size of the problemand the solution of a large-scale inversion of magnetic data is faced with two majorobstacles. The first one is the large amount of computer memory required for storing thesensitivity matrix. And the second obstacle is the large amount of CPU time required forthe application of the dense sensitivity matrix to vectors. These two factors directly limitthe size of practically solvable problems. To encounter these obstacles, Li and Oldenburg(2003) used the fast wavelet transform along with thresholding the small waveletcoefficients to form a sparse representation of the sensitivity matrix. The reduced size ofthe resultant matrix allows the solution of large problems that are otherwise intractable.The compressed matrix is used to carry out fast forward modeling by performing matrixvector multiplications in the wavelet domain.The algorithm used in this study is based on the mentioned multicomponent objectivefunction and the fast wavelet transform is used to make a sparse representation of thesensitivity matrix to reduce the time and computer memory required for inversion.