**Authors**

**Abstract**

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.

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.

**Keywords**