INSTITUDE OF GEOPHYSICS

... 7 Heterogeneous Earth Models 1.2. ... 2 Three-Dimensional Wave Solutions References Additional Reading 35 36 42 47 54 54 59 69 69 CHAPTER 3 BODY WAVES AND RAY THEORY 3.1 The Eikonal Equation and Ray Geometry 3.2 Travel Times in a Layered Earth 3.3 ...

This radical revision of Professor Bullen's acclaimed and widely used text provides an introduction to modern seismological theory, with emphasis on both the physical models and the mathematical descriptions of earthquakes and their sources. The essential core of the ...

In this paper we have proposed a three-dimensional approach to determine depth of basement in which the density contrast varies parabolically with depth. This program based on Newton’s forward difference formula that with optimization of gravity anomalies calculate depths of basement reliefs indeed are anticlinal and synclinal structures has been buried under sediments. This structures are the causes of the positive and negative gravity anomalies. We assume the measured gravity fields have been distributed on a horizontal plane and also sedimentary basin is combined of juxtaposition 3-D cubic prisms. The measurement stations of the gravity field (grid nodes) coincide with center blocks. The initial depth is computed using gravity data and the estimated depths are adjusted with iteration. The advantage of the method is utilization of positive and negative gravity anomalies together as two inputs for written algorithm as well as application of a coded non-linear filter. The efficiency of the code is illustrated with a set of synthetic gravity anomalies. Further, the code is exemplified with the gravity anomalies of an offshore case study in the Persian Gulf, Iran. The purpose of exploratory project in this area will include the development of Hydrocarbon Fields.

The tilt angle, theta map, total horizontal derivative (TDX) and total horizontal derivative of the tilt angle (THDR) are among
local-phase filters as the edge detection and edge enhancement techniques can be a useful tool to interpret gravity maps most of
which are high-pass filters based on the horizontal or vertical derivatives of the potential field with different orders. The
windowed computation of the standard deviation (SD data) of an image is a simple measure of the local variability. Normalized
standard deviation (NSTD), an edge-detection filter, is based on ratios of the windowed standard deviation of derivatives of the
potential field. This filter helps geologic interpretation. Local-phase filters named above and NSTD are demonstrated using the
synthetic gravity data whose random noise has amplitude equal to 0.015 % of the maximum data amplitude was added to the data
set as well as on microgravity data of an aqueduct in Tehran urban environment, IRAN. The computer program was coded in
MATLAB.

A modified  iterative inversion method for 2D modeling of microgravity data and anomaly subsurface precinct determination using vertical microgravity gradient  data is presented in this paper. The method works step-by-step on a prismatic partition of the subsurface volume to contract the anomalous bodies and detect anomaly boundary with fit the observed gravity values to calculated gravity values. This method has immense efficiency for positive and negative density contrast and their vertical gradient. In order to find the required number of iterations for maximum compactness of the density distribution, the parameter variation function is proposed as a stopping criterion in the inversion procedure. inversion scheme is based on a weighted–damped least-squares algorithm. the density matrix correlation function is defined for the stopping criterion of the iteration in specify anomaly limited area based on inversion method. The Maxmum and minimum values of the density locate the anomaly subterraneous border. We have applied the approach to both synthetic data with and without noise and real data from a aqueduct in Iran.

در این مقاله روشی از مدل سازی دو بعدی ساختارهای تاقدیسی ارائه می گردد. تغییرات  چگالی رسوبات و لایه های زمین با عمق بصورت سهموی در نظر گرفته شده است که بر اساس تابع تباین چگالی سهموی (PDF) محاسبه می گردد. این ساختارها از نظر هندسی به مثلث متساوی الساقین شباهت داده می شوند. مدل سازی با محاسبه اثر گرانی یک مدل فرضی اولیه شروع می گردد و با تغییر پارامتر های مدل در هر تکرار خطای بین بی هنجاری گرانی محاسبه شده و گرانی اندازه گیری شده را به کمتر از مقدار خطای تعریف شده کاهش می دهد. کارایی الگوریتم نوشته شده برای بهینه سازی بی هنجاری های گرانی مربوط به مدل مصنوعی با و بدون بی هنجاری گرانی منطقه ای بررسی گردید و سپس داده های گرانی مربوط به ناحیه کرند واقع در شمال شرقی ایران که هدف تعیین حدود ساختار تاقدیس  بعنوان تله  هیدروکربنی می باشد، مورد تجزیه و تحلیل قرار گرفت. عمق ساختار تاقدیسی حدود 3000 متر تخمین زده شده است.

بمنظور محاسبه بی¬هنجاری گرانی بوگه، چگالی میانگین توپوگرافی بایستی محاسبه گردد تا بتوان اثر گرانشی پستی و بلندیها را از روی داده گرانی حذف نمود. در این مقاله یک روش بر اساس محاسبه بعد فرکتال جهت تعیین چگالی بهینه سطحی معرفی شده است. بعد از دسته بندی داده¬های گرانی در فاصله های مشخص بر اساس دایره های متحدالمرکز، واریوگرام واریانس در برابر فاصله برای بی¬هنجاریهای بوگه محاسبه شده با چگالی های گوناگون ترسیم می گردد. اصلی ترین بخش از منحنی احتمالا توپوگرافی حمایت شده پوسته ای را نشان می دهد. از بعد فرکتال آن برای رسیدن به برآورد چگالی بوگه استفاده می شود. در نهایت بعدهای فرکتالی محاسبه شده را در مقابل چگالی رسم نموده و چگالی مربوط به کوچکترین بعد، چگالی بهینه منطقه مورد مطالعه می باشد. از این روش برای محاسبه چگالی بهینه منطقه شرق دریاچه¬ی ارومیه استفاده شده است. مقدار چگالی بدست آمده برای این منطقه 1/2 گرم بر سانتیمتر مربع می باشد که با چگالی میانگین تشکیلات زمین شناسی منطقه مطابقت دارد.

اندازه گیری فیلتر (صافی) های فاز محلی که از ترکیب گرادیان های افقی و قائم گرانی با مرتبه های مختلف حاصل شده اند با تعیین مرز و حدود چشمه مولد بی هنجاری کمک بسیار مفیدی در تفسیر نقشه های گرانی می نماید . فیلترهای فاز محلی در تفسیر داده های گرانی که با اهداف زمین شناسی مهندسی و یا اکتشاف معدن برداشت شده اند، بدلیل نزدیکی بی هنجاری به سطح زمین دارای کارآیی بالاتری می باشند.  در این مقاله یازده فیلتر فاز محلی معرفی می شود و پاسخ اعمال این صافی¬ها  بر روی داده های گرانی حاصل از مدل مصنوعی مکعب ، با و بدون نوفه نشان داده شده است. عملکرد هر کدام از این فیلترهای فاز محلی متفاوت می باشد. نتایج حاصل از اعمال فیلترهای مختلف به داده گرانی مصنوعی نشان می دهد که این صافی¬ها دارای کارایی موثری در تعیین مرز و حدود بی¬هنجاری با دقت بالا می باشند.
در این مقاله کارآیی فیلتر های فاز محلی بر روی داده های واقعی گرانی مربوط به یک گنبد نمکی در آذربایجان ایران مورد بررسی قرار گرفته است. با توجه به نتایج حاصل شده از اعمال این فیلترها به داده های گرانی گنبد نمکی ، فیلتر زاویه تیلت هذلولی بهترین جدایش مرز بی هنجاری را نشان می دهد . همچنین فیلترهای  نقشه تتا و مشتق افقی کل نرمال شده مرز بی هنجاریها را با دقت بیشتری نسبت به سایر فیلتر ها نمایان ساخته اند. با در کنار هم قرار دادن نقشه های خروجی از این صافی¬ها و نیز نقشه های دیگری که در تفسیر کیفی و کمی منطقه مورد مطالعه لازم می باشند مانند نقشه فراسو ، نقشه تعیین عمق اویلر و . . . و نیز استفاده از اطلاعات زمین شناسی در نهایت می توان بهترین گزارش از محدوده هدف مورد اکتشاف ارائه نمود.

The borehole gravity meter (BHGM) is recognized as an important logging tool for obtaining formation bulk density. The
derived apparent densities from BHGM are equal to the formation bulk densities when the instrument passes through beds
which are horizontal, infinite ly extended laterally, uniformly thick, and constant in the density. The vertical gradient of
gravity in a borehole is directly proportional to the bulk density of the horizontal formation between the measurement points.
In perfectly flat uniform geology, the BHGM densities will match the normal gamma-gamma density log data. By comparing
the BHGM and gamma-gamma densities, we can determine changes in geology up to several hundred feet from the well. The
BHGM density and Gamma-Gamma density differ because the borehole gravity investigates a greater volume of rock, Sees
little effect from environment closed to the well and is not related to the electron density. By Poisson's equation, the vertical
gradient of gravity in a uniform medium is proportional to the medium's density. In this paper has been illustrated the
determination the density and porosity of the layers of a well in Virginia, USA using of its downhole gravity and gammagamma
log data.

Determination of potential fields' anomaly borders is a useful help to their interpretation. There is various technique of edge detecting that is applied in image processing. In this paper, the canny edge detection (CED) method has been proposed as boundary enhancement of the magnetic and gravity potential field data. For 2-dimensional bounds, residual potential field map is first smoothed by using a 2-D Gaussian filter. Afterwards, computing the horizontal gradients of the smoothed map and then using the gradient magnitude and direction to estimate borders strength and direction at every pixel. In this research, a new procedure to define the thresholds has been suggested. The results obtained from the synthetic data set, with and without random noise , have been discussed. The method is demonstrated on real gravity and magnetic data set surveyed from Iran.

— So far, various edge detection methods have been proposed for potential field interpretation. Recognition of the anomaly source boundary can accelerate and facilitate the gravity field analysis. Wavelet transform (WT) is one of these suggested approaches. Several discrete and continuous mother wavelets have been defined. In this study, has been used of 2D discrete wavelet transform (DWT) as a method for determination of gravity anomaly source boundary. The DWT leads to a decomposition of the approximation coefficients in four distinct components: the approximation, horizontal, vertical and diagonal. For comparing the efficiency of wavelets, the synthetic gravity anomalies, with and without added random noise, have been decomposed at 1 level with six discrete, two-dimensional wavelets: Haar, Biorthogonal, Coiflets, Symlets, Discrete Meyer and Daubechies. In this study, for anomaly edge enhancement has been proposed a new formula namely HVC that is computed from the square root of the sum of the squares of the horizontal and vertical components. The results indicate the acceptable performance of the Haar and Biorthogonal wavelets in delineating the edges of the gravity anomaly sources.

Horizontal and vertical gradients, and filters based on them such as the analytic signal, tilt angle, theta map and so on, as edge detection play an important role in the interpretation and analysis of gravity field data. Normalized derivatives methods are used to equalize signals from sources buried at different depths. A new derivative operator is introduced in this paper, which is based on the tilt angle of the horizontal and vertical derivatives of the total horizontal gradient of gravity data set, normalized by the analytic signal amplitude (THA). This paper compares the results of this method with other common local-phase filters. Filters are demonstrated on synthetic and real gravity data (Source code in Matlab format is available from the author on request.).

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Tilt angle filter is an interpretation method that is used to determine the source borders locations from potential fields data. Moreover, the tilt angle is applied for estimation of the anomaly source depth, such as contact-depth method and tilt-depth method. In this paper an application of the tilt angle technique obtained from the first vertical and horizontal gradients of the gravity anomaly from semi-infinite vertical cylindrical source is described. The technique is based on the tilt angle and derivatives ratio. In this approach the depth estimates are proportional to the computed tilt angles and their distances from the cross section center of the anomaly cause on the surface. This new method is termed the tilt-distance-depth (TDD). The method is demonstrated using synthetic gravity data, with and without random noise, and real gravity data from Iran. The results are also compared with the solutions from Euler deconvolution technique and inverse modelling using Modelvision software.

In this paper, two techniques for calculating the geoid-to-quasigeoid separation are employed. One of them is GPS/Levelling customary method as a criterion where the geoid undulation and height anomaly are computed by subtracting the ellipsoid height attained via GPS from the orthometric height and normal height, respectively. Another approach is Sjöberg's equation. We have used of the ICGEM website for definition of the variables of the Sjöberg's equation, as the applied reference model is the EGM2008 global geopotential model and WGS84 reference ellipsoid. The investigations are performed over the stations of the GPS/Leveling network related to three selected areas in desert, mountain and flatland namely the Lout, Zagros and Khuzestan in Iran and afterward the correlation coefficient between the geoid-to-quasigeoid separation calculated using the satellite data in Sjöberg's equation and GPS/Levelling method is estimated. The results indicate a straight correlation betw...