فصلنامه فیزیک زمین و فضا
سال سی و ششم شماره 1 (بهار 1389)

Generally, the presence of noise in geophysical measurements is inevitable and depending on the type and the level it affects the results of geophysical studies. So, denoising is an important part of the processing of geophysical data. On the other hand, geophysicists make inferences about the physical properties of the earth interior based on the indirect measurements (data) collected at or near the surface of the earth. So, an inverse problem must be solved in order to take estimates of the physical properties in the earth. The vast majority of inverse problems which arise in geophysics are ill-posed; in other words, they have not unique and stable solutions. Regularization tools are used to find a unique and stable solution for such problems. The regularization uses a priori information about the solution to make it stable and to suppress high-frequency oscillations generated by the noise. One of the common ways to perform the regularization is expanding the unknown model (i.e. solution) with respect to an orthonormal basis, separating the model coefficients from that of the noise, and finally recovering the model. In singular value decomposition, the specific physical nature of the model under study is not considered when defining the basis. For homogeneous operators, such basis does not provide a parsimonious approximation of models which are smooth in some regions while having sharp local changes in others. This is due to the non-localized properties of the SVD basis vectors in space (time) domain. Wavelet-vaguelette decomposition (WVD) was introduced as a first approach for adapting wavelet methods to the framework of ill-posed inverse problems. It is a linear projection method based on wavelet-like function systems which have similar properties as the singular value decompositions. WVD are compared to the SVD construct near the orthogonal basis where the vectors are well localized in space (time) and frequency, thus producing less Gibbs-phenomenon at discontinuities. This property and existence of fast algorithm to compute the basis make wavelets a suitable candidate for solving inverse problems. Vaguelette-wavelet decomposition (VWD) is an alternative to WVD for solving ill-posed inverse problems. It is a linear projection method based on wavelet function systems. In VWD the noisy data are expanded in a wavelet series, generated wavelet coefficients are thresholded to obtain an estimate of the wavelet expansion of noise free data, and then the resulting coefficients are transformed back for smoothed data. Later on, the smoothed data are inverted for the desired model. In this paper we discuss: 1. The performance of sparsifying transforms (e.g. wavelet transform) for the denoising problem and their application to solve other linear inverse problems including WVD and VWD. 2. Comparing nonlinear Amplitude-scale-invariant Bayes Estimator (ABE) and hard- and soft-shrinkage filters to estimate signal coefficients in sparse domain for different levels of noise. 3. Introducing an efficient method to estimate the standard deviation of noise which is an important task in the experiments with single realization. The obtained standard deviation is then used to determine the regularization parameter in both wavelet- and SVD- based inversion methods. Finally, inversion of integration operator to find the variation rate of a function is used to show the performance of the introduced methods in comparison to the popular SVD method. The results indicate that a simple non-linear operation of weighting and thresholding of wavelet coefficients can consistently outperform classical linear inverse methods.

Occurrence of landslides depends on several factors such as the composition and structure of earth materials, rainfall level, temperature, groundwater regime and cover crops. Landslides are a main natural hazard in Iran, because of its special geological conditions and its mountainous active tectonic regime. Linear civil structures, such as roads, highways and railways, face serious problems in Iran, because of their long length which exposes them to several various geological features. For analyzing the stability of these structures, several geophysical methods, such as electrical tomography methods are frequently used. The main purposes of geophysical surveys are reconstruction of landslide geometry, detection of sliding surface (between sliding mass and bed rock), and exploration of the groundwater flow regime which is a stimulant factor before landslide occurrence.

Due to the remarkable advantages of wavelet transformation, this technique is now very common in gravity analysis. In this research the Green’s function occurring in the Poisson potential field theory is used to construct non-orthogonal, non-compact, continuous wavelets. This kind of wavelet is directly corresponded to upward continuation procedure. Simple geometrical forward models such as Sphere, Vertical and Horizontal Cylinder, Thin sheet and Vertical sheet are applied as forward models. First, analytical wavelet transform of the models is calculated, and then the amplitude and the location of the maximum of the product is applied as a new mathematical model (forward model). The new models have a mathematical relation with the source parameters such as depth and shape of anomaly. However, because of being normal the forward models do not have any relation with the physical parameter of density contrast. In order to examine the accuracy, precision, behavior and application of the offered method, the synthetic data for both noisy and noise-free data, has been applied. Subsequently, considering the applicability and expansion of the method for applied goals, some suitable real datasets have been used. For the purpose of gathering data and testing the algorithm, two sources of data were accessible: Institute of Geophysics University of Tehran and the National Iranian Oil Company. Formal permission was granted by both institutions. The outcome of this process was compared with the result of other established classical methods. The parameter of depth estimated by both methods is very close (about 400m difference for the depth of about 3.5km). After careful assessment, it became evident that results obtained from these comparisons are beneficial and useful. Real data are separated into regional and local signals using discrete wavelet analysis. The maximum points of wavelet transforms (worn diagrams) are also applied to interpret the depth of the anomaly compared to adjacent anomalies. The result obtained by inverting the data using the parameter of amplitude has less standard deviation compared to the location of the MSE, and is believed to be more accurate. It is observed that adding noise causes higher standard deviation; however after adding 20 percent noise in synthetic data, less than 6% error occurred in the parameter of depth (still yields good results) which shows remarkable stability against noise.

Propagation of radio waves through the troposphere is based on minimum travel time between transmitter and receiver. The troposphere layer affects the propagation of GNSS signals and causes errors in point positioning due to (1) delay of the signal, and (2) change of the curvature of the signal path. For this reason GNSS users apply models for tropospheric error corrections. One of the commonly used models, which is applied in both scientific and commercial software packages is the Saastamoinen model. Since the tropospheric error, unlike the ionosphereic error, cannot be removed via dual frequency receiver observations, application of the tropospheric models based on meteorological information can always improve point positioning accuracy. This becomes more essential in the case of Precise Point Positioning (PPP), which has real-time applications. Atmospheric delays have two components. Wet delay is caused by atmospheric water vapor and dry delay by all other atmospheric constituents. The dry delay can be predicted to better than 1 mm with surface pressure measurement. Wet GNSS delay is highly variable and cannot be accurately predicted from surface observations. In this paper the wet Saastamoinen model is evaluated based on Zenith Total Delay (ZTD) computed from one year (2005) of permanent GNSS observations of the National Cartography Center (NCC) of Iran. The wet Saastamoinen model is dependent on constants, which are estimated from local observations. Our evaluation procedure can be summarized as follows: 1- GNSS ZTD is estimated from GNSS observation equations. 2- ZTD is computed from surface pressure, temperature and humidity observations. 3- Root Mean Square (RMS) between the two above solutions is determined. 4- The value of RMS is used as an efficiency test of constant coefficients of the Saastamoinen model. The results of our test computations show that the constant coefficients of the Saastamoinen model have enough accuracy for the tropospheric corrections needed for PPP applications and as such there is no need to estimate those constants based on local atmospheric observations.

Potential fields are due to complex distribution of sources related to susceptibility and mass density variations for magnetic and gravity field respectively. In researching the lateral heterogeneous of different geological bodies, in particular their edge location potential field has some advantages. We mainly refer to linear features such as fault, folding axis, dyke, trend and border of the geological units as well as to circular featurs such as crates and buried voids when mentioning geological bodies. Usually, the edge detection and edge enhancement techniques are used to distinguish between geological bodies with different depths and sizes. Edge detection methods are based on the position of the maximum or zero-crossing points associated with vertical derivative, horizontal derivative and analytic signal filters. These methods which are famed to derivative-based filters use different orders, but some instability may occur in high-order derivatives since any kind of noise or non-harmonic signal will be correspondingly enhanced with desired signals simultaneously. Another difficulty is that in the filtered image, the smaller amplitude features (which may be of considerable importance) may be hard to discern. Other edge detection methods are local phase filters (edge enhancement methods) based on the phase variation of the derivative quantities. The advantage of these filters is their flexibility to produce new filters with most applicability just with partial variation. The edge enhancement methods mainly include Tilt angle (TA), Total Horizontal derivative of the tilt angle (THDR), theta map, Hyperbolic Tilt Angle (HTA) and normalized horizontal derivative.

This research presents a numerical tool to estimate the Green's function operator matrix of intraplate faults. Having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. This information could be employed to predict the location of future powerful earthquakes. To implement fault sliding in FE calculations, Soft Material Technique as a simple method is applied. In this technique, the fault is modeled by a flexible (very low elasticity modulus) thin element. This material not only prevents fault planes overlapping, but exhibits a good consistency with the physical behavior of fault. In other words, this material ignores the strength of neighboring rocks ready to trigger sliding. In this research, without involving the nonlinear contact problem, two sides of the fault are dislocated as one unit, and the ground surface deformation is measured.

The simple method for height determination is spirit leveling. The leveled height differences are path-dependent. Ergo height from spirit leveling is not unique. The problem can be solved by converting the path-dependent leveled height differences into unique path-independent height differences (Vanicek and Krakiwsky, 1986). The difference between the potentials of two close equipotential surface can be written as: (1) Practically, instead of potential, it is better to use geopotential numbers: (2) Having derived geopotential numbers, we can compute various height systems such as dynamic height, orthometric height and normal height. According to (1), with gravity measured along the leveling line, the potential difference as a path-independent quantity can be determined. In this method we can only compute geopotential numbers for points where we can establish a leveling path. On the other hand with geoid height at hand and the availability of geodetic height from GPS, we can compute orthometric height. With computation of mean gravity, orthometric height can be converted to geopotential number. But there are still some open problems with computation of geoid and mean gravity. The aim of this paper is the presentation of a new method for computation of geopotentail numbers based on solving the fixed geodetic boundary value problem. With the availability of GPS coordinates for the point on the Earth’s surface, the outer boundary of the Earth can be regarded as a known and fixed boundary. With boundary observations on the Earth’s surface at hand, we deal with a fixed geodetic boundary value problem. The problem is defined as follows

Magnetic data inversion has a prominent role in geo-structural investigations. As lots of geological structures, such as faults, dykes, contacts etc are elongated in a specific direction, 2D algorithms became widespread during the previous years. Modifying the existing algorithms on 3D data inversion, a method has been proposed for 2D inversion of profile magnetic data, based on the physical parameter distribution method. The subsurface is divided into a large number of infinitely long horizontal prisms, with square cross section and unknown susceptibilities.

Red beds have been widely studied by palaeomagnetic methods for what they can tell us about the history of sedimentary basins and their subsequent deformation (Collinson, 1974, Turner, 1979a,b and 1981, McCabe and Elmore, 1989, Elmor, et al., 1993 and 2000). This study has investigated the palaeomagnetism of the Cambrian red sediments (Dezou and Dahou Formation) of the eastern margin of Central Iran. Davoudzadeh and Schmidt, (1984), have done some work on the region which includes these rocks and discuss the few rotations of the Central Iran micro plates. The aim of this study is to consider the AMS results to investigate the palaeo force field on the rock located at the northern side of the Persian Gulf

Rational functions are of great interest to engineers and geoscientists. The rational polynomial coefficient (RPC) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging. Numerical instability of normal equations is the only single obstacle to the implementation of these functions. Practically, estimating rational function coefficients using available control points is mostly an ill-posed problem. Condition number of the normal matrix in the linear parametric model is relatively large. Therefore, a regularization method has to be employed in order to stabilize the equations. Implementation of the regularization technique improves the solution in the linear parametric model. The optimum value of the regularization parameter is estimated using the generalized cross validiation technique. Moreover, simplification of the observation equations leads to a linear observation model which is the most frequently utilized approach for estimation of the unknown coefficients. However, rigorous modeling is recast in a combined adjustment model. Due to nonlinearity of the combined model, the initial values of unknown parameters are needed. The initialization process can be done using the estimated parameters from the linear parametric model

In this research, a new mathematical modeling on strength changes due to reservoir elastic stresses across the preexisting fault plane is introduced. The method has been applied to the Dalpari fault, which is one of the potential seismic sources in the vicinity of the Karkheh reservoir. In this method the distribution of total stress across the fault cannot be determined because the initial stress is unknown; the pore pressure due to the reservoir is also not considered. The mathematical modeling method has been explained briefly in the following. The lake first is divided into small rectangles of sides a and b by two sets of orthogonal straight lines, one set conveniently east-west and the other north-south. The mean water depth h in each rectangle with area S is estimated, and the water pressure on the floor of the rectangle is replaced by a vertical force F =? gS h at the center of rectangle. It is clear that rather smaller rectangles lead to more precise modeling, hence, each rectangle with increasing h is divided into some parts. The water pressure of the lake is simulated by a set of point forces F which applied in the -X3 direction and acting on the rectangles. We define now a mathematical model of the single force F in the elastostatic fields using the delta function conception

The interaction between the solar wind and the earth’s magnetosphere results in the transport of magnetic flux into the magnetotail and to avoid a continued buildup in the tail, there is a return convection of magnetic flux from the magnetotail into the night-side dipole-like region and from there to the day-side. Since there is energetic plasma with this magnetic flux, hence electric currents exist that disturb the magnetic intensity in the earth’s surface (substorms) and particularly by interaction with the earth’s ionosphere producing auroral activities. We have compared magnetotail variations with auroral activities during 3 substorms using GEOTAIL, Polar UVI and 4-Cluster spacecraft data. In the substorm event on 15 December 1996, auroral breakups and intensifications were highly correlated with fast plasma flows, with the variations in the north-south magnetic field and with the total pressure in the magnetotail. GEOTAIL was located around X~ -21, and several fast tailward flows were observed in the early expansion phase with the southward magnetic field and the total pressure enhancement, associated with plasmoids. These flows were observed simultaneously with or within 1min of auroral breakups or pseudobreakups. In the late expansion or recovery phase, some fast earthward flows were observed with small auroral intensifications. More investigations imply that the total pressure in the magnetotail significantly decreases during auroral breakups or poleward expansion of the auroral bulge. The duration of the expansion and the maximum size of the auroral bulge are closely correlated with the duration and amount of total pressure decrease in the magnetotail, respectively. These results also imply that the substorms are the response of magnetosphere to solar wind and its frozen-in magnetic field. Also in the substorm event on September 2002 investigation of Cluster data shows that direction reverse of fast plasma flow is highly correlated with total pressure variations in the magnetotail by magnetic disturbs.

Cumulus convection, as a meso-scale phenomenon, results in the release of latent heat and vertical drift of energy that by part could affect the large scale field of energy, humidity, and momentum of the atmosphere. Since the current numerical models are unable to resolve the singular cumulus convective clouds that are important from a meteorological point of view, it is used to apply some sort of approximation of them in their models. The method of approximating is called parameterization and closure problem. The fundamental idea of these methods is, to approximate the small and meso-scale part of variables by their large scale part. Furthermore we know the large scale part of fields tends to damp the small and meso-scale parts including cumulus convection activities