IRANIAN JOURNAL OF GEOPHYSICS
Year:2012 | Volume:6 | Issue:4|Papers Count:12

This study applies the translation invariant attribute (TIA) using the Hadamard transform of the seismic data to discriminate lithofacies. The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric operation on 2nreal numbers (or complex numbers, although the Hadamard matrices themselves are purely real). The Hadamard transform can be regarded as being built out of size-2 Discrete Fourier Transforms (DFTs), and is in fact equivalent to a multidimensional DFT of a size. It decomposes an arbitrary input vector into a superposition of 2*2*2...*2 Walsh functions.In mathematical analysis, the set of Walsh functions form an orthogonal basis of the square functions on the unit interval. The functions take the values -1 and+1 only, on sub-intervals defined by dyadic fractions. The orthogonal Walsh functions are used to perform the Hadamard transform, which is very similar to the way the orthogonal sinusoids are used to perform the Fourier transform. The Walsh functions are related to the Rademacher functions; They both form a complete orthogonal system.The Hadamard transform is particularly good at finding repeating, stacked vertical sequences. The dyadic shifts represent the invariant properties of the Hadamard transforms. The output of a translation invariant transform is insensitive to the dyadic shifts so that in geologic applications, the objective of using these transforms is to find a geologic pattern which have been analyzed anywhere in the time series, irrespective of their vertical position.If z is the output of a dyadic shift invariant transform, such as the Hadamard transform, of a sequence x, then the dyadic shift invariant power spectrum ( Sz2), is termed as the translation invariant attribute. The translation invariant attribute computation requires 2n input samples. If an input sequence does not have 2n samples, then either zero padding or quite a large time window can be used to make 2n samples.This attribute is applied in 3D seismic data of Sarvak Formation of one of the oil fields in the south-west of Iran. The Sarvak Formation for this oilfield is a carbonate unit gradually overlying the Kazhdumi Formation. The thickness of Sarvak Formation increases towards the west and varies between 582 m and about 700 m. The reservoir facies for this field are classified based on their porosities. Four porosity facies were selected by using porosity logs of four vertical wells drilled in this oil field. All the seismic data are converted to those categories by Artificial Neural Network (ANN). The neural network used here was a Two-layer Feed-forward network with Error Back Propagation (EBP) for learning algorithms. The transfer function of the hidden neurons was hyperbolic tangent and the transfer function of the output neurons was linear. Three different time slices of Hadamard transform, translation invariant attribute were presented. The correlation between the real porosity and the predicted porosity using ANN was estimated to be about 81%. Finally, all the seismic data were converted to porosity facies by using ANN and three time slices of the porosity facies were calculated and shown.

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Although the Hilbert Transform (HT) has been used in electrical engineering and signal analysis for a long time (Bracewell, 1965), its application in geophysical studies started in 1970' s. The HT is a method of direct solution. The aim of using the HT in geophysical studies is to obtain more than one equation containing the same structural parameters by utilizing the complex gradients of the available data. The roots and common intersection points of the anomaly and the complex gradients of the anomaly have been used to determine the structural parameters. Therefore, a±1 error sampling interval was expected for the determinations. In order to minimize the error, the most appropriate sampling interval should be chosenUp to the present time, the HT has been used extensively only in magnetic and seismic studies. But in the aforementioned studies, it has been used mostly as a Fourier Transform (FT). Taner (1979), in his study, obtained the HT through convolution by using a normalized Hilbert time-domain operator truncated to 61 points The Hilbert Transform (HT) is a mathematical transform function which shifts the phase of a signal as much as p/2 without changing its amplitude. With this definition HT is a linear system, which transforms odd and even functions, with equal amplitude to each other in space or frequency field. Since HT is a linear set, the system should have an input signal, a transfer function and an output function. The HT can be applied to the Fourier Transform (FT) and convolution methods.. In this study, the model parameters of which were unsolved so far, self-potential (SP) methods were determined with HT using convolution and FT methods and the results were compared. In this study, Structural parameters were determined directly from the geophysical anomalies using analytical functions of the complex gradients and the Hilbert Transforms can be applied to reach the above-mentioned situation. The Hilbert Transforms, which can be carried out in two different ways using the Fourier Transform and convolution methods, were used to provide the convolution method between the complex gradients of the anomaly. Structural parameters (electric dipole moment, polarization angle and depth) were then determined from the solutions of the constructed equations. This method was used for two models, a sphere and a horizontal cylinder, with synthetic data without any random noise. The results of this study are as follow: (1) The parameters were determined exactly for the theoretical models using the HT method. Especially, the location of the structure, which had not been determined before, was obtained precisely and directly from the anomaly for the self-potential method. (2) Before the interpretation of the field data with the HT method, the anomaly should be refined from noise. If this procedure has not been carried out, pseudo roots could be formed in the complex gradients of anomaly.

Usually, simplified models, such as shallow water model, are used to describe atmospheric and oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. This model is applied to a fluid layer of constant density in which the horizontal scale of the flow is much greater than the layer depth. However, the dynamics of a two-dimensional shallow water model is less general than three-dimensional general circulation models but is preferred because of its greater mathematical and computational simplicity.Taking intrinsic complexity of fluids, recently, numerical researches have been focused on highly accurate methods. Especially, for large grid spacing numerical simulation, the use of highly accurate methods have become urgent. This trend led to an interest in compact finite difference methods. The compact finite-difference schemes are simple and powerful ways to reach the objectives of high accuracy and low computational cost. Compared with the traditional explicit finite-difference schemes of the same-order, compact schemes have proved to be significantly more accurate along with the benefits of using smaller stencil sizes, which can be essential in treating non-periodic boundary conditions. Application of some families of the compact schemes to the spatial differencing in some idealized models of the atmosphere and oceans shows that compact finite difference schemes can be considered as a promising method for the numerical simulation of geophysical fluid dynamics problems.In this research work, the sixth-order combined compact (CCD6) finite difference method was applied to the spatial differencing of f-plane shallow-water equations in vorticity, divergence and height forms (on a Randall's Z grid). The second-order centered (E2S), fourth-order compact (C4S) and sixth-order super compact (SCD6) finite difference methods were also used for spatial differencing of the shallow water equations and the results were compared to the ones from a pseudo-spectral (PS) method. A perturbed unstable zonal jet was considered as the initial condition for numerical simulation in which it breaks up into smaller vortices and becomes very complex. The shallow water equations are integrated in time using a three-level semi-implicit formulation. To control the build-up of small-scale activities and thus potential for numerical nonlinear instability, the non-dissipative vorticity equation was made dissipative by adding a hyperdiffusion term. The global distribution of mass between isolevels of the potential vorticity, called mass error, was used to assess numerical accuracy. The CCD6 generated the least mass error among finite difference methods used in this research. By taking the PS method as a reference, the qualitative and quantitative comparison of the results of the CCD6, SCD6, C4S and E2S, indicated the high accuracy of the sixth-order combined compact finite difference method.

In oil exploration, because of the anisotropy of the earth, the velocity of the waves in horizontal and vertical directions are not uniform; however, with a good accuracy in exploration procedures, we can assume that in a layer, velocity changes are limited as a results of slow variations in density as well as the elastic properties of the layers in these horizontal directions. In general, variations of the above mentioned parameters in horizontal directions are much slower than in vertical ones. For this reason, the acquisition area is often divided into smaller areas; horizontal variations are neglected while the same vertical velocity distributions are applied in any sub-area.There are basically two methods in calculation of the bin size and migration aperture in a 3-D seismic survey design. The first method is based on using a constant velocity model which is not compatible with real conditions. In this model, we assume that the medium between the surface of the earth and the target layer is replaced with supposed layer and ascribe a constant amount velocity to this layer that is equal to the average velocity in medium between the surface and the target layer. The second method uses the model wherein the velocity changes with depth and therefore a linear velocity model is assumed which is more compatible with reality in comparison with the previous method. Whereas the linear velocity method can include all important wave propagation effects, it involves a certain circular logic. This method, involves building a detailed subsurface velocity model and uses ray tracing or other simulation techniques to customize the survey for the local subsurface.In Ahwaz Oil Field, the main target was Asmari Formation and the deep target was Fahlian Formation. The 3-D seismic survey design of Ahwaz Oil Field was performed on the main target located in the depth of 2900 m and the deep target located in the depth of 5000 m from the mean sea level. Ground level was about 15 to 40 m higher than the sea level in this area. By considering the check shot, VSP and sonic log data from 14 well logs, the image area was divided into 14 parts, so that the variations of the horizontal velocity could be neglected in each part and the constant contribution for the vertical velocity could be used. Finally, using the velocity values at the desired vertical depth to the reflection point (target depth), the dip angles of the target horizon (dip of reflector at the reflection Point) and the maximum frequency reflected from the main target, we were able to calculate the bin size and migration aperture in each part. At last, we could select a value for the bin size in this project.In this study, we examined the parameters of the velocity-dependent 3-D seismic survey design. These parameters included the bin size and migration aperture. Conventional formula for the bin size and migration aperture for Ahwaz Oil Field was carried out based on the linear model between the velocity and depth. As an intermediate between constant velocity and interval velocity model, we have given expressions valid for a linear velocity function. By using the linear velocity model, the design parameters incorporated first-order ray bending. Hence, this method was adjusted to the reality and led to better results compared to a constant velocity model.Linear V(z) is an attractive approximation for three reasons. First, this kind of velocity variation captures the first-order effect of the pressure and the temperature increases with depth. It does not require detailed knowledge of the subsurface velocities. Second, analytical expressions are available for the ray path geometry and travel times in such a medium. Third, the linear V(z) propagation allows turning waves which have potential for imaging dips beyond 90 degrees.Migration aperture is overestimated by constant velocity calculations, whereas the bin size is underestimated and this results in an increase in costs. On the other hand, calculations based on a linear velocity model require a less migration aperture and a larger bin size. The bin size and migration aperture are two sensitive economy parameters. Hence, using a larger bin size and a smaller migration aperture obtained from a linear velocity model, the cost of a 3-D seismic survey design will be decreased.

Spectral decomposition of time series has a significant role in seismic data processing and interpretations. Since the earth acts as a low-pass filter, it changes the frequency content of the passing seismic waves. Conventional methods of representing signals in a time domain and frequency domain cannot show the time information and the frequency information simultaneously. Time-frequency transforms an upgraded spectral decomposition to a new step and can show time and frequency information simultaneously.Time-frequency transforms generate a high volume of spectral components, which contain useful information about the reservoir and can be decomposed into single frequency volumes. These single frequency volumes can overload the limited space of a computer hard disk and are not easy for an interpreter to investigate them individually; therefore, it is important to use methods to decrease the volume without losing information. The frequency slices are thus separated from these volumes and used for an interpretation.In this study, three different methods were used to represent a buried channel. In the first method, the numbers of the single frequency slices were investigated, variations of the frequency amplitudes in the slices were observed, and an expert interpreter could obtain some information about the channel content and lateral variation. Since different frequencies contain different types of information (low frequencies are sensible to channel content and high frequencies are sensible to channel boundaries), none of the slices were able to show all information simultaneously. In the next two methods using a color stacking method, the RGB plots were constructed which, due to the different frequency content, resulted in more information than the frequency slice representation method.An RGB image, sometimes referred to as a true color image, is an image that defines red, green, and blue color components for each individual pixel and has an intensity between 0 and 1. In this study, RGB plots were constructed in two different manners, RGB plots based on conventional RGB plot methods and RGB plots using basis functions. In the conventional method, three different frequency slices were mapped against the red, green and blue components. Although this method obviates some drawbacks of the single frequency plots, it uses only three slices and practically ignores a big part of information. Using basis functions and defining windows, the interpreter was able to introduce some frequency intervals and plot them against the primary components and use the total bandwidth or its major part. Three simple raised cosine functions having different frequency centers and different periods were chosen. The image quality strongly depended on these two parameters. Longer window widths will introduce longer frequency widths into every primary component and resulted in smoother color combinations for images and very short periods had the same results as the conventional RGB plot method. Different centers showed different details. Low frequency centers showed channel content properties, and high frequency centers showed channel boundaries and fine branches.In this study, the spectral decomposition was first performed on land seismic data from an oil field in Iran using a short time Fourier (STFT) transform and an S transform. Then three demonstration methods were applied for channel detection. Finally it was shown that how RGB color stacking method represented buried channels in more precise images and how a basis function based RGB represents better results than the conventional RGB method.

The Zagros mountain belt is approximately 1500 km long, 250–400 km wide, and runs from eastern Turkey, where it connects to the North and East Anatolian faults, to Oman Gulf, where it dies out at Makran subduction zone. The Zagros Mountains were formed by closure of the Neotethys Ocean and collision of Central Iran and Arabia plates. GPS studies estimate a convergence rate of 22 mm/yr between Arabian and Eurasian plates and the Zagros accommodates about 6.5±2 mm/yr of the overall shortening in Iran. However this rate is not constant along the Zagros and increases from 4.5 mm/yr in the northwest to 9 mm/yr in the southeast. Changes in the rate and direction of convergence across the Zagros cause changes in its strike and diversity of the deformation mechanism.The Main Recent Fault (MRF) and the Main Zagros Reverse Fault (MZRF) are located in the northwest and northeast of the Zagros collision zone, respectively, in a suture zone between central Iran and the Arabian plate. Based on GPS and seismology studies, the MZRF is presently inactive. On the contrary, as evidenced by high seismicity and the occurrence of earthquakes with magnitudes as large as 7, like 1909 Doroud Earthquake, the MRF is one the major active strike-slip faults in the Middle East. Geological studies on the MRF fault have identified the fault segmentation and the existence of pull-apart basins. The Main Recent Fault strikes NW–SE and can be traced as a narrow, linear series of fault segments from near the Turkey–Iran border at 37oN for over 800 km to the SE. Based on strain partitioning theory, the strike-slip MRF fault is a response to a horizontal component of oblique convergence between Arabian and Eurasian plates and Zagros’s reverse fold belt accommodates the vertical component of this convergence.Seismological studies based on the teleseismic data have limited the location accuracy because they rely on global velocity models. Therefore, microearthquake local studies complement the teleseismic information because they locate seismic events with an accuracy of a few kilometers which is an order of magnitude better than teleseismic locations.The 2006 Silakhur earthquake with a magnitude of 6.1 and its aftershocks recorded by a local seismic network provide a unique opportunity for a high resolution study of the Doroud section of the MRF. The results of the aftershock analysis are presented in this paper.After occurring March 31, 2006 Silakhur Earthquake, Mw 6.1, a temporary seismic network including 10 stations was installed by International Institute of the Earthquake Engineering and Seismology for nearly two months. An aftershock analysis revealed a wide zone of the aftershocks trending southeast northwest. Another trend in east-west direction was deduced from the epicentral distribution of the aftershocks in the west of the Boroujerd. Depth distribution of the aftershocks showed that the majority of the aftershocks located in 4-11 km depth range, verified the brittle crust uppermost layer in this part of the Zagros. Depth profile showed the northeast trending of the aftershocks. The spatial distribution of the b value showed low values in the northern part of the aftershock zone that its reason could be the higher stress concentration in this region relative to the southern part.

Time representation was the first way to describe a signal, and later on the frequency representation was introduced as another important way to describe a signal for its physical significance. Due to the non-stationary property of seismic data, time-frequency transform has to be used to analyze it. During the last decade, spectral decomposition techniques have proven to be an excellent tool to describe thin beds associated with channel sands, alluvial fans, and the like. However, with the traditional spectral decomposition method based on the short time Fourier Transform, it is difficult to acquire the accurate time-frequency spectrum for non-stationary seismic signals. Recently, the emergence of seismic attribute co-rendering, principal component analysis, cluster analysis, and neural networks has partially solved the problem, but the extraction of spectral attributes from spectral-decomposition tightly linked to the geology has more advantages over other approaches. Popular time–frequency methods have some disadvantages.A good time resolution requires a short window and a good frequency resolution require a narrow-band filter, i.e. a long window, but unfortunately, these two cannot be simultaneously realized. The Wigner-Ville Distribution (WVD) of a signal is the Fourier Transform of the signal’s time-dependent auto-correlation function, a quadratic expression which is bilinear in the signal. As a result, the cross-terms appear in the locations of the resulting time-frequency spectra that either interfere with the interpretation of auto-terms or for which we can provide no physical interpretation. Due to the existence of cross-terms, WVD is not often used. Reduction of the cross-terms is achieved by manipulating the ambiguity function as a mask that reduces the cross-terms while preserving the time and frequency resolution of WVD.The short-time Fourier Transform (STFT) spectrogram, which is the squared modulus of the STFT, is a smoothed version of WVD. An STFT spectrogram is a 2-D convolution of the signal WVD and the utilized window function. In this paper, we introduce a Deconvolutive Short-Time Fourier Transform (DSTFT) spectrogram method, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram. Compared to the STFT spectrogram, the spectrogram obtained by this method shows a significant improvement in the time-frequency resolution. In this study, we extract two attributes namely the peak frequency and the peak amplitude, based on the Deconvolutive Short-Time Fourier Transform. The maximum frequency attribute is directly related to the thickness of the thin-bed, like channel, and the maximum amplitude attribute also responds to the thin-bed.We use instantaneous seismic attributes: maximum instantaneous frequencies and their associated amplitudes, as a tool to detect seismic geomorphologic bodies and to identify thin layers. Then we use attributes extracted by Deconvolutive Short Time Fourier Transform to detect the burial channel in both synthetic and real 3D seismic data. Usually, the center of the channel is recognized by the lower maximum frequency and when the thickness of the channel gets thinner away from the center of the channel, the maximum frequency increases correspondingly. Therefore, this attribute could clearly describe the distribution of channel both vertically and horizontally. Results of this study on the synthetic and real seismic data examples illustrate the good performance of the DSTFT spectrogram compared with other traditional time-frequency representations.

Major earthquakes are often associated with large earthquakes which have a magnitude smaller than the main shock known as aftershocks. The occurrence of aftershocks with different magnitudes and times is a random process and therefore in the area affected by the main shock, it can cause greater damage than the main shock, and hence they are very important.Study of aftershocks can be useful to get information from tectonic activites and causative faults. Many studies have considered the aftershocks of large earthquakes, such as Omori (1894), Otsu (1961) and kisslinger (1996). Among the aftershock studies, the exact relocation of the main earthquake and its aftershocks help us find the causative fault and the releasing energy associated with that fault. Many studies have used relocation methods to examine the aftershocks. Some of these methods are Hong et al (2008), Hugh et al (2009) and Zhao et al (2011).Due to the complexity of the earth sub-layers and the three-dimensional structure of the crustal velocity and also the seismic wave path from the source to stations, there is a nonlinear relationship between the arrival time of seismic waves at the stations and the hypocenter of the earthquake. In order to simplify the earthquake location problem solving, most methods and programs use linearized relationships. Most of these methods and algorithms are based on the Geiger’s principles (Geiger, 1912). Using the linearized relationships reduces the accuracy of earthquake location due to losing the higher terms of Taylor series. It may also lead to failure in determining the location of earthquakes using a suboptimal network, e.g. where the earthquake is located outside the seismic network. Thurber (1985) showed that when the depth of an earthquake was smaller than the closest distance to the station, determining the focal depth was not possible in linearized methods. Furthermore, using higher terms of Taylor series is required to calculate higher degree derivatives, which are very complex and sometimes impossible, using a three-dimensional velocity model.In order to avoid calculating the partial derivatives, Tarantola and Valette (1982) presented a method that determines the location of earthquakes with fully non-linear relationships with no need to calculate the partial derivatives. The basic theory of nonlinear probabilistic method to determine the location of the earthquakes was introduced by Tarantola and Valette (1982) and Tarantola (1987). In this study, we used a nonlinear probabilistic method based on Tarantula and Valette theory and NonLinLoc program (Lomax et al, 2000) to relocate the earthquakes.The Rigan earthquake with Mn=6.5 occurred on Dec 20, 2010 in the Southeastern region of Iran. After this earthquake, a lot of aftershocks occurred in this area which in some cases the magnitude of aftershocks was in order of the main shock. The largest aftershock with a magnitude Mn=6.0 occurred after 37 days which itself included a lot of aftershocks. To improve the quality of data, in this study we combined the arrival time data from the Iranian Seismological Center (IRSC) stations and the data from the International Institute of Seismology and Earthquake Engineering (IIEES). Due to the lack of proper station coverage in the southeastern region of Mohammad Abad Rigan, we added IIEES stations data in this area which greatly helped us increase the station coverage.Regarding the lack of a proper regional velocity model in the Eastern and the Southeastern regions of Iran, we used Tatar et al (2003) local velocity model and determined the depth of Moho based on Dehghani and Makris (1983) study in an order of 55 km.In this study, we used Omori’s law to specify the energy release in the media and occurrence of aftershocks chronologically. We found that a large number of aftershocks have occurred in two different time windows near the two large earthquakes; in this regard, we divided the data based on these two time windows. The first time window contained the main shock with Mn=6.5 and aftershocks until the occurrence of second earthquake with Mn=6.0. The second time window contained the second earthquake Mn= 6.0 and its aftershocks.In order to get good results, we considered those earthquakes recorded at least by five stations. Finally, we could relocate 222 aftershocks out of 296 aftershocks associated with Rigan area. The relocation results of the earthquakes showed that the two main earthquakes and their aftershocks were distributed in the epicenter and the focal depth separated completely. They also showed two different fault trends. Relocated aftershocks in the first time window showed a fault trend parallel to Kahurak Fault, and aftershocks with Mn>4 in the second time window showed a fault trend parallel to Kahurak fault.

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