مجله ژئوفیزیک ایران
سال چهارم شماره 1 (پیاپی 6، تابستان 1389)

Seismic wave propagation modeling is helpful in understanding waveform behavior involving velocity anomalies due to complicated geological structures. On the other hand, forward modeling is the kernel of inversion and tomography procedures, so developing forward modeling algorithms is an inevitable need. In order to model wave propagation, it is necessary to solve complete wave equation for 3D media. Because of limitations in computational resources, solving complete wave equation with all ideal considerations such as heterogeneity, anisotropy, and absorption, for 3D media is difficult. Thus by considering easier conditions we can solve wave equation with normal computers. Solving wave equation with computers needs to discretization techniques such as boundary integral, finite-element or finite-difference methods. Boundary integral methods are suitable for simple models while finite-element or finite-difference methods are predominantly used for heterogeneous models. Depending on the domain for which wave equation is going to be solved, we can categorize methods to time-space, frequency-space, Laplace, slowness-space and etc. Recently, the frequency domain finite-difference (FDFD) method has found extensive application in multi-source experiment modeling, especially in waveform tomography. Because of the special form of wave equation in the frequency domain, the modeling of multi-source experiments is a straightforward job. On the other hand, considering absorption mechanisms is easy. This study deals with wave propagation modeling in a 2D acoustic heterogeneous media, using the second-order approximation of acoustic wave equation in the frequency domain. The acoustic wave equation is formulated as the first-order hyperbolic system involving fields of pressure and particle velocities. This system is discretized using the second-order staggered grid stencil. To avoid spurious reflections from the model boundaries, a sponge-like perfectly matched layer (PML) is implemented. Solving wave equation in the frequency domain leads to a large matrix equation. The key step in the frequency domain finite-difference modeling that controls computational efficiency is the numerical inversion of the massive matrix. The matrix structure depends on the spatial derivatives approximation. In order to solve this system, different direct solvers can be used. The UMFPACK (unsymmetric multifrontal sparse LU factorization package) solver, which is embedded in MATLAB and has acceptable performance in solving the general system of equations, was selected for this study. For each frequency component, it is necessary to solve a large system of equations to obtain a single frequency component of the pressure wavefield. In this paper we review criteria to avoid numerical dispersion and errors during the finite-difference approximation, and time aliasing during frequency sampling. Choosing appropriate spatial and frequency discretization intervals is very important in FDFD modeling. Choosing large Δ (spatial discretization interval) values will cause the pressure field to be inadequately sampled in space and numerical dispersion. For the scheme presented here, we should have more than 10 grid points per minimum wavelength to keep dispersion errors small. On the other hand according to the sampling theorem, if, where tmax is maximum time and df is frequency components sampling interval, we encounter time aliasing. The present FDFD package is written in MATLAB programming language. MATLAB supports sparse algebra and makes possible the solution of large system of equations with minimum usage of memory, which is the main concern in FDFD algorithms. Examples of waveform modeling using FDFD are shown. In the first example, the headwave originating from a high velocity layer is modeled; in the second example, the wave behavior in a trap model is shown; and in the last example, a salt dome model is studied.

The NW-SE-trending Zagros fold and thrust belt extends for approximately 1,800 km from a location some 300 km SE of the East Anatolian Fault in NE Turkey to the Strait of Hormuz, where the north-south-trending Zendan-Minab-Palami fault system (ZMP) separates the Zagros belt from the Makran accretionary prism. The NE limit of the Zagros belt is marked by the Main Zagros Reverse Fault which is rotated about a horizontal axis to form a steeply NE-dipping to sub-vertical reverse fault with a right-lateral component of movement of unknown magnitude (Wellman, 1966; Stöcklin, 1974; Berberian, 1995). The extension of the Main Zagros Reverse Fault to the NW of latitude ~33o is referred to as the Main Recent Fault (Tchalenko and Braud, 1974), and is a right-lateral strike-slip fault as indicated by earthquake focal mechanism solutions and field evidence (Talebian and Jackson, 2002; Bachmanov et al., 2004). There is no clear surface boundary to the frontal edge of the Zagros fold and thrust belt where folding is gentle both on land and beneath the Persian Gulf. However, the southern edge of the Zagros deformation front can be defined at different levels by the shape in map views of the oil- and gas fields (Talbot and Alavi, 1996), and also by the seismicity and topography (Jackson and McKenzie, 1984). The deformation within the Zagros fold and thrust belt is due to the relative convergence between Arabia and Eurasia since the Middle-Late Cretaceous era (Falcon, 1974; Stöcklin, 1974; Koop and Stoneley, 1982). However, the Zagros fold and thrust belt began forming during the main phase of the Zagros orogeny in the Late Miocene (Stöcklin, 1968; Stoneley, 1981; Hessami et al., 2001); current shortening at a rate of about 7 mm/yr (Tatar et al., 2002; Vernant et al., 2004b; Hessami et al., 2006) as well as active seismicity indicate that this deformation is still active. A moderate earthquake (MW = 5.9) struck the Fin region in the Hormozgan province on March 25, 2006 (07:28 GMT) with low damage. The main-shock was followed by 4 aftershocks with magnitudes larger than 5. Four stations were installed in the region for aftershock study. In this paper, the results from the‌ analysis of aftershock data recorded by these 4 stations and the neighboring dense network in the east are presented. Epicentral distribution of the aftershocks shows an E-W trend. Moreover, an alignment trending north consistent with the mainshock focal mechanism is clear at depth. This seismological evidence confirms that the Fin Earthquake occurred on a reverse fault dipping north. The epicentral distribution of aftershocks showed an east-west trend which indicates that the causative fault is in the east-west direction. Both focal mechanism solutions reported by the CMT catalog and body wave modeling results were also in agreement with this determination. A cross section view of the north-south direction showed a northward dip for the fault plane. There is no incidence between the strike of depth distribution of the aftershocks on the surface and the known folds of the region. Using these results, it was concluded that there is no direct relationship between depth faulting and surface folding, and that aftershocks were distributed lower than 5 km depth, which indicates that the Cretaceous Gurpi marls disallowed the faulting to reach the surface.

Increasingly high quality satellite magnetic measurements have been providing reliable magnetic data with crustal field models of improved resolution. This paper presents a new approach to delineate geothermal potential sites based on estimates of Curie depth from new crustal field models. After a period of 20 years without high quality, low-orbit satellite magnetic coverage, since the implementation of Magsat (1979-1980), a new generation of satellites has been launched and is measuring the magnetic field with unprecedented accuracy and resolution. Two satellites were launched into 800 km and 700 km altitude orbits, namely Ørsted (launched in 1999 and still providing scalar data) and SAC-C (launched in 2001, scalar magnetometer active until 2004), respectively, while the CHAMP satellite was launched in July 2000 into a lower orbit, initially at 450 km altitude. Temperature dependence of magnetic properties of rocks allows magnetic data to be used for estimating the thermal state of the crust in areas with few heat flow measurements. Rocks below their curie temperature may sustain induced or remanent magnetization, but above their curie temperature become practically non-magnetic. It is possible to calculate curie depth from magnetic data. The results of aeromagnetic studies presented by numerous authors show that curie depths obtained from magnetic measurements correlate well with the heat flux; high heat flux is found in areas of shallow curie depths and vice versa. Geothermal heat flux is one of the main parameters in determining geothermal potential sites. Direct heat flux measurements are scarce because they are difficult and expensive to obtain. This paper presents an indirect method to delineate geothermal potential sites. Considering the proven relation between curie depth and heat flux, the method presented in this paper is based on satellite magnetic data. In this method, curie depth is calculated from satellite magnetic field models. Therefore, one of the thermal boundary conditions is obtained for deep crust. Then, using a one dimensional thermal model, estimation of surface heat flux is discussed. A comprehensive investigation program is required for geothermal exploration projects. This program may include field investigations, geological, geophysical and geochemical studies. However, the potential application of satellite magnetic field models discussed in this paper can be widely used as a preliminary reconnaissance tool in the early stages of geothermal potential site selection projects. The study area in this paper covers a wide portion of eastern Iran, located within 28-36◦N and 56-64◦E. The calculations are based on satellite magnetic field model MF5 (developed from CHAMP mission). The results show that the curie depth in the study area is located within 24- 36 km indicating that the curie isotherm is shallower than the moho, and lies within the earth’s crust. The results show two areas with high heat flow. These areas are promising for detailed investigations. Increasingly high quality satellite magnetic data makes this new method very significant in future studies of geothermal site selection projects. Using a field model instead of raw satellite magnetic field observations is highly productive as the magnetic field measured by a satellite contains contributions from several different sources: the core, the crust, the ionosphere, and the magnetosphere. Only the field from the crust is related to the heat flux. Field modeling allows separation of various sources, thus allowing the crustal field to be isolated. Crustal magnetic field models will experience significant gains in resolution and accuracy over the coming years. The CHAMP mission is expected to continue, providing excellent quality data at solar minimum conditions and at steadily decreasing altitudes. Scheduled for 2011, the European Space Agency’s Swarm mission, a constellation comprising 3 satellites, will further improve the data basis for mapping crustal magnetic anomalies by providing direct measurements of the magnetic field gradient for the analysis. All the programming of this research was done in MATLAB R2008a.

The classification of lithofacies and their accurate representation in a 3D cellular geologic model is critical to understanding the field characteristics because permeability and fluid saturations for a given porosity and elevation above free water vary considerably among lithofacies. The best source of lithofacies information is the reservoir rock core samples from wells; however, cores are not commonly taken due to excessive expense. Since the availability of core samples is limited compared to the number of wells in the field, developing a method for estimating lithofacies in wells without cores is necessary. In this study, core lithofacies are extrapolated from cored wells (training wells) to uncored wells through the comparison of physical rock properties measured by wire-line logs. Associating well log data with lithofacies can be difficult due to the heterogeneous nature of rocks, especially carbonate rocks. Lithofacies can be defined using any set of rock properties; however, only lithofacies defined by variations in properties that affect well log response can be identified using well log data. Moreover, some useful rock properties, such as porosity and permeability, affect well log response. Artificial Neural Networks (ANNs) are computational models inspired by brain structure mechanisms and functions. The system employs a set of nonlinear and linear activation functions that do not require a priori selection of a mathematical model. Recent applications of ANN to geological studies have demonstrated its effectiveness in prediction, estimation and characterization. Neural networks have been developed and utilized for the solution of a variety of pattern recognition, classification, and signal identification and prediction problems. Neural networks utilized for the prediction of parameters and pattern classification are trained based on data-sets that contain a number of training patterns. Each training pattern is presented as a pair of two components: the input data and the respective classification outcome. After the neural network is trained, it may be applied to a new data-set which contains only the values of input parameters. The goal of this study is to establish a method for lithofacies classification utilizing well data and taking advantage of artificial neural network. Additionally, sonic log efficiency in improving of prediction of reservoir lithofacies is discussed. In this paper, the main goal is the classification of hydrocarbon reservoir lithofacies, applying an artificial neural network technique, specially back propagation (BP) and Levenberg- Marquwardt training algorithms, on gamma-ray, density, neutron, sonic, and photo electric effect (PEF) logs. Moreover, in this research, the efficiency of sonic log data in lithofacies estimation has been investigated. Paying attention to the fact that lithofacies determination from core experiments can be costly, in this approach, lithofacies identification expenses are reduced by eliminating the need to perform a coring operation. Data from four wellbores in a hydrocarbon reservoir was used. The network was trained primarily on one of the wells in which the core analysis was available and was subsequently tested in another well that did not play any role in the training phase. After achieving efficiency reliability, the network was applied in lithofacies estimation in two other wells (A1 and A2). The amount of MSE (mean squares error) in this method using only gamma-ray, density, neutron and photoelectric effect logs was 0.068 and 0.074 for wells A1 for A2, respectively. In the case of using a sonic log in addition to previous inputs, the MSE decreases to 0.052 for well A1 and 0.060 for well A2, which implies an estimation improvement.

In many numerical simulations of fluid dynamics problems, especially those possessing a wide range of length and time scales (e.g., geophysical flows), low-order numerical schemes are insufficient. Compact finite difference schemes, introduced as far back as the 1930s, have been found to be simple ways of reaching the objectives of high accuracy and low computational cost. Compared with the traditional explicit finite difference schemes of the same order, the compact schemes are more accurate with the added benefit of using smaller stencil sizes, which can be essential when treating non-periodic boundary conditions. In recent years, the number of studies devoted to the application of compact schemes to spatial differencing of geophysical fluid dynamics problems has been increasing. This work focuses on the application of a three-point fourth-order compact finite difference scheme for numerical solutions of bottom gravity current over a slope. The governing equations used to perform the numerical simulation are the vorticity-stream function-salinity formulation of the two dimensional viscous incompressible Boussinesq equations. The details of spatial and temporal discretization of the governing equations are presented. For spatial differencing of the equations, the second-order central and a three-point fourth-order compact finite difference schemes are employed. In addition, the second-order two-stage predictor-corrector leapfrog scheme is used to advance the governing equations in time. Derivation of the consistent boundary condition formulation to generate stable numerical solution without degrading the global accuracy of the computations is also presented. To derive the required numerical boundary conditions for salinity and vorticity fields at lateral, top and bottom boundaries of the computational domain, the fourth-order one-sided (forward and backward) compact relations are used. Two values for the salinity and a fixed value for bottom slope angle are used to perform the numerical simulations. Qualitative comparison of the results indicates better performance of the fourth-order compact scheme with respect to the second-order method. Furthermore, the computed value of the rate of the head growth of the gravity current generated by the fourth-order compact scheme is in agreement with existing numerical results, which indicates the accuracy of simulations in a quantitative manner. For the test cases used to perform the simulations in the present work, it was observed that the values of salinity and vorticity generated by the second-order method on bottom boundary were too noisy. While, values of salinity and vorticity generated by the fourth-order compact scheme, especially on the bottom boundary of computational domain, do not show this property and are more accurate than those generated by the second-order method. In addition, the numerical results show that the fourth-order compact scheme can successfully simulate the formation of vortices in the tail section of the gravity current, while the second-order scheme fails.

One of the most important goals of magnetic data interpretation is to determine location, depth and shape of the magnetic anomaly. Extensive use of magnetic surveys in the field of mineral exploration, geology and environmental application make earth scientists to present suitable interpretation schemes. Neural networks are part of a much wider field called artificial intelligence which have computer algorithm that solve several types of problems. The problems include classification, parameter estimation, parameter prediction, pattern recognition, completion, association, filtering, and optimization. The NNs are used in different aspects of interpretation and modeling of geophysics data. They are used for inverting geophysical data involving problems for which no easy solutions exist. In this paper, Feed Forward Neural Network (FNN) is used for the magnetic anomaly modeling with assumption an infinite depth extent dike. The method can estimate all the geometric parameters of the dike; horizontal location on profile, width, depth and dip. We used a three layer FNN; consisting of 11 neurons in the input layer, 20 neurons in the hidden layer and 4 neurons in the output layer. For the first and hidden layers, and the last layer sigmoid and linear activation functions are used, respectively. Here, the horizontal location, width, depth and dip of the dike were defined as the output and the magnetic profile data as the input of the neural network. The training of the network was done through synthetic data which were produced by forward modeling. For preventing the neural network from holding to any particular sequence, the input data were assigned in a random and then, the profile related to these data was obtained by dike equation. For the FNN to recognize the pattern of the profile data, some parameters are defined as the input of the FNN. These parameters should be separated. In other words, they must have a relation with the geometrical parameters of the dike. In definition of the parameters from the Anomaly curve, maximum and minimum points, width of curve in points of 75% and 50% of maximum, area of positive and negative parts of anomaly curve are used. Furthermore, the width and depth of the dike may be found through using a horizontal derivative of anomaly and a derivative of Hilbert transform. Horizontal derivation of Anomaly curve and Hilbert transform of horizontal derivation, especially from their intersection points, are also used as input parameters of neural network. The validity of this method was tested by using of noise-free and noise-corrupted synthetic models that satisfactory results were obtained. Then the Morvarid mine, which located at a distance of 30Km south east of Zanjan, near Aliabad village, is chosen as a real data application. The outputs show a good accordance with the Euler method and the tranches results. The FNN inversion provides satisfactory results despite the noise. Various techniques are applied for interpretation of magnetic data. Most of them estimate only the depth. So, careful determination of dip, depth and width of the dike are the benefits of the use of the FNN.

Reservoir properties, such as porosity and permeability, can be derived at well locations from core samples or well log measurements. Since these properties vary laterally from one well to another, it is normally very difficult to predict reservoir properties away from wells. Seismic data, particularly 3D surveys, contain valuable information about the lateral variation of reservoir properties. When wells fall within the seismic coverage, it is logical to predict reservoir properties between wells by interpreting seismic data and using reservoir properties at well locations as spatial control points. Artificial neural networks (ANN) may be used to aid the estimation of reservoir properties between wells. In this case, a training sample set of input and output data pairs can be collected. The input of neural networks is seismic data relevant to the reservoir at well locations. The expected output from neural networks is reservoir properties at well locations. This paper uses a local linear neuro-fuzzy model to predict reservoir properties from seismic attributes in one of the oil fields in the central region of Iran. The fundamental approach with the locally linear neuro-fuzzy model is dividing the input space into small linear subspaces with fuzzy validity functions. Any linear model produced, along with its validity function, can be described as a fuzzy neuron. Thus, the total model is a neuro-fuzzy network with one hidden layer and a linear neuron in the output layer, which simply calculates the weighted sum of the outputs of locally linear neurons. An incremental tree-based learning algorithm, a locally linear model tree (LOLIMOT), is appropriate for tuning rule premise parameters, i.e. determining the validation hypercube for each locally linear model. In iteration, the worst performing locally linear neuron is determined and then divided. All of the possible divisions in the p dimensional input space are checked, and the best is performed. The splitting ratio is simply adjusted as 1/2, which means that the locally linear neuron is divided into two equal halves. The fuzzy validity functions for the new structure are updated. Their centers are identical with the centers of the new hypercubes and the standard deviations are usually set as 0.3. Just one parameter, the embedding dimension, should be defined before running the algorithm. In this work, the number of attributes is the embedding dimension. To evaluate the performance of a locally linear neuro-fuzzy model in extracting the relationship between seismic attributes and reservoir property, this method was applied in an oil field located in central Iran. This field has two exploration wells. Additionally, a 3D seismic survey, recorded with a one-millisecond sampling interval, covers the area of the reservoir. First, the logs were mapped to the time domain and then blocked it at each one millisecond to resolve the frequency difference of the logs and seismic data. Then, multi-attribute analyses were performed and the best seismic attributes, which had good correlations with porosity, were found to be acoustic impedance and amplitude weighted cosine phase. By applying the locally linear neuro-fuzzy model to train and validate the network, good results were obtained. The correlation coefficient between the modeled and original logs was 80% and the error was 2.6% in validation. Finally, to compare the neuro-fuzzy model with traditional methods, the work was repeated with a probabilistic neural network (PNN) and a multi-layer forward neural network (MLFN). The results obtained by applying the MLFN (correlation 83% and error 4.5) and PNN (correlation 68% and error 5.7) were not better than neuro-fuzzy model.