نشریه پژوهش های ژئوفیزیک کاربردی
سال دوم شماره 1 (پیاپی 3، بهار و تابستان 1395)

Summary Estimation of residual statics in complex areas is one of the main challenging problems in seismic data processing. It has been shown that residual statics show itself as random noise in the frequency domain, and hence, can be treated as a denoising problem. Here, we develop an f-x domain denoising algorithm to attenuate the residual statics in seismic data. A subset of low frequencies are selected and denoised individually via a Tikhonov's type filter. The denoised section is cross-correlated trace-by-trace with the noisy one, and then, the maximum shifts are picked and applied to reduce the statics. This procedure is repeated until convergence is accomplished. Numerical tests show good performance of the proposed algorithm to compensate static effects on synthetic and field seismic data.
Introduction Static corrections are applied to compensate seismic data for the complex interaction between the incident wavefield and the near surface irregularities. Several methods have been developed in the literature for this purpose including traveltime inversion based methods and stack-power maximization methods. Recently, a new method has been proposed for residual static correction based on non-linear sparsity maximization. Here, we treat the problem by noise reduction tools in the f-x domain.
Methodology and Approaches Statics shift traces in time domain, so it changes the phase in frequency domain. A scaled version of statics vector adds to each frequency in the f-x domain, so the real and imaginary parts of each frequency in the f-x domain can be considered as noisy versions of the corresponding parts in the clean signal. The problem is formulated as b=x where b is a noisy mono-frequency signal, x is the clean signal, and n is some random noise. Therefore, we consider the following cost function: 22 x 22 arg min b x Dx  
Where  is the regularization parameter and D is the regularization operator. If we solve this problem using direct methods, it can be time consuming. In this paper, we use a Krylov subspace method for solving it. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularize the problem by projecting it onto a low dimensional ”signal subspace” adapted to the particular problem. In this paper, we use PRRGMRS, a Krylov subspace method. We select some low frequencies of the f-x domain and denoise them and take an inverse f-x transform. Then, we calculate statics using time shifts via cross-correlation. This procedure is repeated until convergence is accomplished.
Results and Conclusions We have proposed a new method for residual static correction based on denoising tools in the f-x domain. It has been shown that residual static shifts show itself as random fluctuations (like the effect of random noise) on data spectrum in the frequency domain. Therefore, these effects can be compensated by proper denoising tools in the f-x domain. An efficient algorithm has been proposed to achieve this goal. Applications of this algorithm on synthetic and real data confirmed high performance of the presented algorithm.

Summary Water and Gas injection are two major enhanced oil recovery methods in Iran. Gas (e.g. CO2) injection, is one of the most applicable methods of enhancing oil recovery in oil fields. In order to study the behaviour of seismic attributes, the compatibility of the prediction made by Gassman theory and GreenbergCastagna equations in the situation of CO2 saturated environment is investigated using lab data. It should be noted that the mentioned equations are based on some assumptions that are not always represent the real situation, thus, some incompatibility is anticipated. Therefore, their predictions are liable to be incompatible with real world wave behaviour. In this research, CO2 in dissolved phase is injected into pressurized sandstone samples in laboratory scale, and elastic waves are utilized in order to investigate the injection process. The variation of the propagation velocity of seismic waves and their amplitudes are studied versus variation of effective parameters e.g. confining pressure (close to reservoir pressure), pore pressure (close to reservoir pressure), transmission wave frequency, and CO2 density and phase. We have also used the collected laboratory data for wave propagation at supercritical saturation state to investigate the compatibility of the prediction made by Gassman theory and Greenberg-Castagna equations. Based on the results of various laboratory experiments, we can conclude that some of the developed equations are useful for estimation of velocity and amplitude of seismic waves. Verifications confirm that compatibility of the developed equations with laboratory results are more than 90 percent, and thus, the developed equations can be preferred to other related popular equations.
Introduction Rock physics has an effective role in the estimation of petrophysical and reservoir parameters e.g. porosity, permeability, rock type, saturation, pore pressure, and fracture density using seismic attributes. As a result, various seismic attributes such as velocity, frequency and phase are used in order to estimate the above-mentioned petrophysical and reservoir parameters (Dodds et al. 2007, Adam 2006, Ruiping et al. 2006, Avseth 2005, Gray et al. 2002). In recent decades, various empirical relations are also developed for this purpose (pennebake 1968, Eaton 1972, Reynolds 1970, Domenico 1977, Castagna et al. 1985, Greenberg and Castagna 1992, Castagna et al. 1993, Krzikalla and Muller 2007, Toms et al. 2007, Lebedev et al. 2009, Han et al. 2010, Han et al. 2014, Liu et al. 2010, Eftekharifar and Han 2011). Gassman theory and Greenberg-Castagna equations are widely utilized as basic rock physics equations in world oil fields. However, these equations are based on some unreal hypotheses which cause their results to be not fully compatible with real situations, for example these hypotheses do not consider the distribution of fluids, and also, do not pay attention to the real situation of the rock and fluids; e.g. pore size, pore shape, fracture density, fracture aperture, heterogeneity, the fabric of matrix, pore pressure, confining pressure, fluid type, saturation, fluid distribution, viscosity, compressibility index, etc. Therefore, these equations need reform, especially when rock type, fluid type and reservoir situation varies. In this paper, based on laboratory experiments, some empirical rock physics equations are developed that are more compatible with reservoir conditions, and present a new approach for estimation of velocity and amplitude of seismic waves.
Methodology and Approaches In this research, a core holder has been designed in which measuring and controlling the confining, radial, axial and pore pressures have been feasible. Two transducers are put around the caps of core holder, in order to send and receive seismic waves. Transducers are in contact with plugs. The studied plugs having various grain sizes are taken from Berea sandstone formation in southwest of Australia. Three different CO2 densities or concentrations are injected and dissolved into plugs saturated with distilled water. In the next stage, elastic waves having different frequencies are passed plugs under various pressure/density situations, and consequently, velocities of the waves are recorded. Based on these laboratory experiments, some equations are developed using multi-regression method that are more compatible with reservoir conditions
Results and Conclusions In this paper, some novel equations, based on laboratory experiments, have been developed that not only are accurate but also are generalized. These equations or relations present a new approach in estimation of the velocity and amplitude of seismic waves. Based on the results, the authors of this paper prefer to give some practical recommendations as follow: • All laboratory tests have been carried out in room temperature, and thus, the authors suggest that a similar research to be repeated in the reservoir temperature, and new equations to be developed. • In the current research, just two seismic attributes (velocity and amplitude) are studied. The authors suggest that other seismic attributes are also investigated in future studies. • The majority of Iranian oil fields are carbonate reservoirs while this research has been carried out on sandstone. Thus, the authors suggest that similar studies have been carried out on carbonate plugs. • Repeating laboratory tests with reflected waves will help to approach more real results. • In all laboratory tests, the authors have investigated the effect of pressure growth on the tests. It will be useful that other researchers investigate the effect of pressure drop on the results.

Summary Magnetic induction caused by sea characteristics has recently been the focus of attention of several studies. Since water is an electrically conductive liquid, its movement in the Earth's magnetic field produces a transverse magnetic force at each unit of charge. Therefore, it seems essential to identify the factors affecting the fluctuations of these magnetic fields and the effect of these factors on the marine, navy, and military applications. In this research, the changes of magnetic fields caused by sea waves in the Strait of Hormuz have been investigated. For this purpose, we use the waves parameters obtained from numerical model of MIKE21, and then, calculate the magnetic field and observe the magnetic field fluctuations in the study region. The results show that the values of magnetic field vary between 0 and 0.2 nanotesla. Moreover, magnetic field values in Bandar Abbas coast and Iran shoreline within the study region are less than the magnetic field values in the Islands of Qeshm, Hormuz and Larak. In general, it can be said that the magnetic field fluctuations are completely caused by changes in the waves parameters so that the trend and pattern of changes of three variables of the waves including height, period, and magnetic field within the study region are almost the same. Therefore, due to the low height and low period of the waves in the Strait of Hormuz, the magnetic field caused by the waves is not considerable, and thus, its effect on magnetic field fluctuations is not also noticeable. As a result, in some maritime applications, like determination of the range of magnetic field fluctuations for the purpose of setting sensors of a torpedo and preventing the torpedo deviation from the goal, the effect of waves on the magnetic field fluctuations can be ignored.
Introduction The magnetic fields in a sea are affected by the Earth’s core, the solar winds, and sea water movements. In the absence of these movements, their effects on the magnetic fields equal zero. These magnetic fields have the frequency of ocean waves, which are in turn affected by wind. Therefore, analyzing the magnetic fields caused by these waves and their fluctuations have recently been the focus of attention. The application of magnetic field in exploration and identification of underwater equipment and communications, the adjustment of torpedoes, magnetic sensors, and also the effect of magnetic field fluctuations on subsurface navy and military equipment, all reminds the importance of studying magnetic field fluctuations. This magnetic field can be generated by sea features such as waves. As a result, it is obvious that magnetic field fluctuation range is affected by several sources. Hence, to be able to attribute the magnetic field to the sea waves, the effect of other sources needs to be eliminated. This elimination is possible only through numerical calculations and mathematical formulas. The Strait of Hormuz is considered to be one of the most important waterways in the world that has high fluctuation rates in the wave characteristics due to its connection to the Sea of Oman and the Indian Ocean and therefore, plays an important role in the magnetic field fluctuations caused by the waves.
Methodology and Approaches In this research, the bathymetry map of the study region has been obtained from GEBCO Database. Then, grid generation and interpolation of the bathymetry data have been conducted using the mesh generation subroutine of MIKE21-MIKE ZERO software package. The mesh, which includes irregular elements of triangular shapes, has been produced to discretize the computational domain considering geometry and bathymetry problems. The final mesh, which has been used in this model, includes 49819 elements and 27915 nodes. Two water borders in the west and east of the Strait of Hormuz and two land areas in the north and south of the Strait have been considered in this study. The data of the sea borders that consist of the heights, periods and the directions of the waves are used for implementation of the simulation.
After implementation of the model, in order to calculate the waves induced magnetic fields, we use the output data of wave model (MIKE21-SW). Afterwards, the data are inserted into the calculating equations of magnetic field and as a result, the magnetic field in the study region is calculated.
Results and Conclusions This study shows that the amounts of magnetic-filed due to sea waves in the study region vary between 0 and 0.2 nanotesla, which are not considerable amounts. The fluctuation of the waves has a direct effect on the size of magnetic field. As expected, magnetic field changes directly relate to the changes in the waves parameters so that their changes are almost the same.

Summary This paper introduces a sparse inversion methodology for large-scale magnetic survey data. The minimum support constraint is used in the stabilizer term and leads to models with sharp boundaries. The subsurface under the survey area is divided into a large number of cubes with fixed geometry and unknown susceptibility. In this case, the number of model parameters is much larger than the number of data. Then, transforming from the model space to the data space yields a much smaller system of equations that can be solved quickly. The conjugate gradient algorithm is used to obtain the numerical solution of this system of equations. The proposed algorithm has been applied on a synthetic model consisting of multiple bodies, and also, on real data from Tigh Nuo Ab area in south of Birjand, Iran. Both synthetic and real cases have demonstrated the efficiency of the presented algorithm.
Introduction Nowadays, inversion algorithms are widely used for the interpretation of magnetic survey data. The associated formulation for the inversion of the data is ill-posed so that regularization is needed. This introduces reasonable stabilizing conditions on the solution and leads to a unique solution. Furthermore, desired characteristics for a reconstructed solution can be obtained by incorporating specific constraints in the stabilization term. Specifically, for potential field data inversion, it is standard to use a compactness constraint introduced by Last and Kubik (1983) or its extension known as the minimum support constraint, which has been developed by Portniaguine and Zhdanov (1999). In this paper, we adopt the use of the minimum support constraint that leads to a model with sharp boundaries and blocky features. For large-scale magnetic data, the inversion process is always challenging and powerful computational algorithm are required to make the solution process feasible. Here, the data-space inversion methodology is used to reduce the computational time.
Methodology and Approaches The subsurface domain is divided into a large number of fixed cubes with unknown susceptibility values. Here, the number of the cubes is M and the number of the data is N, in which N Results and Conclusions A model, comprising of four different bodies, is used to test the efficiency of the presented algorithm. The data are generated at 3500 stations and are contaminated with random noise. The subsurface domain is discretized into 52500 cubes. The data-space inversion process is completed in less than one minute. The recovered model has sharp boundaries and is close to the original model. Finally, the algorithm is used on magnetic data over Tigh Nuo Ab area located in south of Birjand, Iran. The results show that the subsurface anomaly is extended to a depth of 80 m.

Summary Temporal changes in the earth magnetic field occur in the frequency band of millihertz to a few hertz. Amplitudes of variations above 0.1 Hz are usually much smaller than 1 nT, changes of 50-100 nT over periods of a few hours are not uncommon. Total-field aeromagnetic surveys typically require days or weeks to complete. An airborne magnetometer measures variations in the magnetic field caused by flying over magnetic geological structures and by temporal variations in the earth magnetic field. The most common method of estimating and removing the effects of time variations is called leveling. The standard procedure of leveling the data requires additional tie-lines flown perpendicularly to the original lines. In this study, a leveling approach is used without the need for tie-lines. The method, used in this paper, utilizes nine-point Hanning filter to creat a smooth representation of the regional magnetic field. The leveling errors are the difference between the flight-line raw magnetic data and the derived regional magnetic field. The magnitude of the error is minimized through least square method with a firstdegree function, and the correction involves only a diurnal correction (DC) shift. The technique is applied to the aeromagnetic data set acquired in Moalleman area, Semnan, Iran. The results show that the stripy effects are removed and the unleveled data is improved.
Introduction Aeromagnetic data have to be leveled for removing temporal variation effects from the observed anomalies. The leveling of aeromagnetic data is an important step in interpretation procedure. We can assume that the total magnetic intensity is invariant within the altitude variations of the aircraft. As such, measured data at intersection points, should record same values. Differences at cross points (where tie-lines intersect the flight lines) are attributed to leveling errors. The flight-lines are then leveled using leveling errors. Due to strong gradients in the anomaly magnetic field and the low flight altitude at modern surveys, errors at intersection points are commonly larger than the potential accuracy of modern high-resolution aeromagnetic surveys (e.g., Methodology and Approaches Leveling aeromagnetic data can be carried out using two methods. In the first method, leveling the data is made using tie-line. Leveling the data in the second method is carried out without the need to tie-lines. Corrections, which have to be performed before leveling, include diurnal and heading corrections. If required, an international geomagnetic reference field (IGRF) correction has to be applied. By using a nine-point Hanning (3*3 convolution) filter, any highfrequency noise is removed, and the regional magnetic field data, which are free of leveling errors, are derived. The differences between unleveled magnetic data and derived regional magnetic field data should be minimal. Therefore, we can write:Mr=(mr1, mr2, … , mrN)T
Md=(md1, md2, … , mdN)T
X= (x1, x2, … , xN)
∆d = md - mr
|∆d-f(x)|2 = min
where Mr is the derived regional magnetic field data, Md is unleveled magnetic line data and f(x) is the error function. The function f(x) can be defined as first-degree polynomial and is determined in a least-square sense along each line in the survey.
Results and Conclusions leveling is necessary before processing and interpretation of aeromagnetic data. The standard procedure of leveling the data is performed using tie lines. The acquisition of aeromagnetic data over the tie lines are expensive. In this paper, the aeromagnetic data have been leveled using a new approach without the need for tie lines. It has also been shown that this approach can save about 10% of the operational cost. This scheme has the major advantages such as leveling is done computationally, not manually, and also, leveling large data set is made in less than an hour. This technique has been tested on a real aeromagnetic data set acquired from an area in north of Moalleman, Semnan, Iran. In the analysis of the two applied leveling techniques, we see that the least square method improves the quality of the unleveled raw data better than in the tie line technique.

Summary The improvement of seismic data resolution in hydrocarbon exploration, especially in complex structures is of great importance. There are two types of resolution in surface reflection seismic data: horizontal resolution and vertical resolution. Vertical or temporal resolution is expressed by means of the tuning thickness and horizontal or spatial resolution is expressed by means of the Fresnel zone. Tuning thickness is defined as a quarter of the dominant wavelength at the position of the target layer. It is the minimum thickness by which the top and bottom of the layer is separable. The tuning thickness is related to interval velocity of the target layer and the dominant frequency of traveling wave at the depth of the target layer. Thus, the increase in the dominant frequency of seismic data can help to increase the vertical resolution.
Introduction Based on the convolution model, the seismic trace is a convolution of the earth reflectivity series with a seismic source wavelet. The seismic source wavelet is a frequency band-limited signal and the earth reflectivity series is assumed to be white noise, which is un-limited frequency bandwidth signal. Many methods have been introduced to enhance the vertical resolution of reflection seismic data. Each of them has advantages and disadvantages that are due to the assumptions and theories governing their issue. Inverse Q-filter, different deconvolution methods and time-variant spectral whitening are the basic methods of the resolution improvement. In the deconvolution procedure, the band limited seismic source signature is compressed by various methods to increase the frequency band of seismic source wavelet.
Methodology and Approaches In this paper, the vertical resolution of surface reflection seismic is increased using scaling property of Fourier transform. According to this property, when the value of scaling factor is selected greater than one, the scaled seismic trace in comparison with original seismic trace is compressed and its amplitude spectra are shifted to higher frequency band. In this way, the vertical resolution of seismic trace is increased. When the value of scaling factor is selected less than one, the scaled seismic trace compared to original seismic trace is extended and its amplitude spectra are shifted to lower frequency band, and thus, the vertical resolution of seismic trace is decreased. In this paper, a filter is designed based on Fourier transform of scaled and original source wavelet. Then, the filter is applied on seismic trace in frequency domain, and as a result, inverse Fourier transform of filtered signal is computed. The obtained signal is an improved resolution seismic trace.
Results and Conclusions The proposed algorithm has been tested on both synthetic and real seismic sections and the results have been compared to the frequency deconvolution method. The synthetic seismic section has been created from a wedge model by a 35 Hz Ricker wavelet. The enhanced resolution seismic section is obtained by applying the designed filter on the seismic traces. In the obtained section, the dominant frequency is shifted to 70 Hz and frequency bandwidth is expanded. Moreover, the tuning thickness after the filtering is reduced from 12.5 m to 6.25 m indicating that the vertical resolution is improved. In the real case, the dominant frequency is increased from 25 to 40 Hz. After filtering the seismic section as described above, we can see that the resolution is increased, and thin layers, which were not clear in the original section, become visible in the filtered seismic section. Therefore, the results of applying the proposed method on synthetic and field data show that we can efficiently obtain high resolution seismic section using the proposed method. Note that there is a trade-off between resolution and signal-to-noise (S/N) ratio in the time scaling transform of seismic trace. The S/N ratio is reduced a little after the filtering the trace.