فهرست مطالب

پژوهش های ژئوفیزیک کاربردی - سال دوم شماره 2 (پیاپی 4، پاییز و زمستان 1395)
  • سال دوم شماره 2 (پیاپی 4، پاییز و زمستان 1395)
  • تاریخ انتشار: 1395/11/06
  • تعداد عناوین: 6
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  • مسعود حسینی، ابوالقاسم کامکار روحانی، مهدی محمدی ویژه، سعید پرنو* صفحات 67-76
    شمار کابل ها و لوله های مدفون زیر سطح زمین در مناطق شهری، طی سال های گذشته به شدت افزایش یافته است. فقدان نقشه های دقیق زیر سطحی، باعث آسیب رسیدن به این خطوط در طی عملیات مختلف عمرانی می شود؛ بنابراین استفاده از یک روش غیر مخرب برای آشکار سازی این گونه اهداف زیرسطحی کاملا ضروری است. روش رادار نفوذی به زمین روشی غیر مخرب، سریع و کم هزینه با قدرت تفکیک بالا برای بررسی های نزدیک به سطح زمین است. در مقاطع GPR اهداف استوانه ای (لوله، کابل و غیره) و نقطه ای به صورت هذلولی نمایش داده می شوند. لذا تمایز بین این اهداف از اهمیت ویژه ای برخوردار است. در این پژوهش با برداشت سه بعدی یا شبکه ای، به وسیله ی دستگاه Noggin Plus با آنتن پوششی با فرکانس مرکزی 250 مگاهرتز، توانایی و عملکرد روش GPR در آشکارسازی تجهیزات زیرسطحی در یک منطقه شهری با شبکه نسبتا پیچیده ای از تاسیسات زیرسطحی مورد بررسی قرار گرفته است. این شبکه زیرسطحی متشکل از لوله های فلزی و غیرفلزی، کابل ها و کانال های زیرسطحی انتقال آب است. بعد از انجام پردازش های مناسب بر روی داده های شبکه ای، نقشه ها و مقاطع مختلف دوبعدی و سه بعدی GPR دارای مختصات افقی و عمقی با دقت بالا تهیه شده؛ که در این مقاطع ساختارهای زیرسطحی آشکارسازی شده است. علاوه بر این تخمین قطر لوله های غیر فلزی محتوی آب با دقت حدود یک سانتیمتر امکان پذیر شده است. با برداشت شبکه ای، پردازش های مناسب و به دنبال آن نقشه ها و مقاطع تهیه شده، اطلاعات مفید و دقیقی از اهداف زیرسطحی مدفون در منطقه برداشت به دست آمده است.
    کلیدواژگان: رادار نفوذی به زمین (GPR)، لوله های فلزی و غیر فلزی، پردازش و تفسیر داده ها، مدل سازی دوبعدی و سه بعدی، دانشگاه صنعتی شاهرود
  • شهریار خاص احمدی*، علی غلامی صفحات 77-87
    تبدیل رادون هذلولی یک تبدیل انتگرالی است؛ که با انتگرال گیری بر مسیر های هذلولی شکل سعی در به دست آوردن طیف سرعت داده های لرزه ای دارد؛ اما از آنجا که این تبدیل در دسته تبدیل های وابسته به زمان قرار می گیرد و برخلاف سایر تبدیل های رادون امکان محاسبه آن در حوزه فرکانس به ازای هر تک فرکانس وجود ندارد؛ باعث می شود تا تحلیل سرعت لرزه ای -که یکی از مهم ترین مراحل پردازش داده های بازتابی است- از جمله زمان گیر ترین مراحل نیز محسوب شود. از طرفی، زمان گیر بودن محاسبه عملگر های پیشرو و پسرو این تبدیل مانع از داشتن یک طیف سرعت با وضوح بالا به کمک الگوریتم های تزریق کننده تنکی می شود. در این مقاله، الگوریتم پروانه ای جهت حل سریع این تبدیل معرفی و سپس کاربرد آن در یک الگوریتم آستانه گذاری انقباضی جهت به دست آوردن یک طیف سرعت با وضوح بالا مورد بررسی قرار می گیرد. همان طور که در مثال های عددی نشان داده شده است، روش مطرح شده باعث کاهش زمان محاسبات تا چندین برابر نسبت به روش معمول در به دست آوردن یک طیف سرعت تنک خواهد شد.
    کلیدواژگان: تحلیل سرعت، تبدیل رادون هذلولی، الگوریتم پروانه ای، وضوح بالا، تنکی
  • منصوره موچان، افسانه نصرآبادی *، حبیب رحیمی، محمدرضا سپهوند صفحات 89-102
    در این مطالعه ساختار سرعتی پوسته در زیر دو ایستگاه باند پهن شبکه لرزه نگاری ملی ایران (INSN)، آشتیان-اراک (ASAO) و نائین (NASN)، واقع در حاشیه شمال غربی ایران مرکزی نزدیک شهرهای آشتیان و نائین با روش برگردان هم زمان توابع گیرنده موج P و منحنی های پاشندگی سرعت فاز و گروه موج رایلی مورد بررسی قرار گرفت. جهت تعیین توابع گیرنده از روش تکرار واهمامیخت در حوزه زمان و دور لرزهایی با طول مسیر دایره بزرگ چشمه- گیرنده بزرگ تر از °30 و کوچک تر از °90 و بزرگای بیش از 5 استفاده گردید؛ که در فاصله سال های 2009 تا 2013 در این ایستگاه ها به ثبت رسیده اند. منحنی های پاشندگی سرعت گروه و فاز موج رایلی از مطالعه ی بر روی ساختار پوسته و گوشته ی بالایی فلات ایران در بازه ی دوره ی تناوبی 10 تا 100 ثانیه تامین شده است. توابع گیرنده، پاسخ ساختار محلی زمین به رسید تقریبا قائم امواج P در زیر یک لرزه سنج سه مولفه ای بوده؛ که به تباین های سرعت موج برشی حساس هستند. ناهماهنگی عمق- سرعت در اطلاعات توابع گیرنده باعث غیر یکتایی مسئله ی برگردان می شود؛ اما با دخالت دادن اطلاعات حاصل از سرعت مطلق برآوردهای پاشندگی و برگردان هم زمان این دو مجموعه ی داده ای، می توان بر این محدودیت غلبه کرد و به اطلاعات دقیق تری در مورد ساختار پوسته ای رسید. نتایج این مطالعه نشان می دهند که عمق ناپیوستگی موهو در زیر ایستگاه آشتیان-اراک (ASAO) 2±50 کیلومتر و در زیر ایستگاه نائین (NASN) 2±56 کیلومتر است و این عمق در حاشیه شمال غرب ایران مرکزی موهو به طور متوسط 2±53 کیلومتر است.
    کلیدواژگان: ایران مرکزی، ساختار پوسته ای، توابع گیرنده، برگردان هم زمان
  • وحید انتظار سعادت، سید هانی متولی عنبران* صفحات 103-112
    در مطالعات ژئوفیزیکی هنگام مواجهه با رسوبات ضخیم، توده ها و یا مدل سازی گوشته، چگالی به صورت یکنواخت نیست و دارای تغییرات در راستاهای مختلف است. این تغییرات ممکن است با افزایش عمق و یا در راستای افقی به صورت افزایش یا کاهشی باشند. در این تحقیق با استفاده از مطالعات پیشین، رابطه ای برای محاسبه آنومالی گرانی افقی و قائم حاصل از چندضلعی دوبعدی با سطح مقطع اختیاری و نامنظم و دارای تغییرات خطی چگالی در راستای افقی و قائم توسعه داده شده است. در ادامه کدی در محیط برنامه نویسی متلب و بر اساس فرمول توسعه داده شده، تهیه شده است و آنومالی گرانی را برای ساختارهایی که دارای چگالی خطی متغیر و یا چگالی ثابت هستند، محاسبه می کند. مدل مصنوعی به کار برده شده در این تحقیق، مدل مصنوعی دوبعدی است که دارای شکلی نامنظم است. در این مدل مصنوعی یک بار چگالی به صورت خطی در راستای قائم به طور افزایشی تغییر یافته است و سپس چگالی به صورت خطی و در راستای افقی به صورت افزایشی تغییر یافته و در هر دو حالت با مدلی که میانگین چگالی به کل توده نسبت داده، مقایسه شده است. نتایج محاسبات و مدل سازی بیان می دارد که مقدار این تفاوت محسوس است و نمی تواند نادیده گرفته شود. لذا در مواردی که نیاز به محاسبات اثر گرانی سنجی با دقت بالاتری است و یا در مطالعات بزرگ مقیاس که نیاز به مدل سازی گوشته است، می توان از اشکال دوبعدی چندوجهی با تغییرات خطی چگالی در راستاهای مختلف استفاده کرد.
    کلیدواژگان: مدل سازی دو بعدی، آنومالی گرانی، تغییرات خطی چگالی
  • بهنام بابایی، محمدعلی علی آبادی، مهدی فلاحی پور، حمیدرضا باغزندانی* صفحات 113-121
    روش های مغناطیسی و گرانی سنجی عمدتا در مراحل اولیه اکتشاف نفت به منظور شناسایی وضعیت زمین شناسی منطقه مورد نظر استفاده می شوند تا تصویری کلی از زیر سطح محدوده مذکور به دست آید. یکی از مباحث مهم در تعبیر و تفسیر این داده ها استفاده از روش های مدل سازی است؛ تا تخمین مناسبی از ساختار موجود از زیر سطح زمین را فراهم سازد. محققین همواره به دنبال ارائه روش های جدیدی در این زمینه بوده اند. یکی از این روش ها، وارون سازی ترکیبی داده ها (گرانی و مغناطیس سنجی) است. استفاده از روش وارون سازی ترکیبی داده های ژئوفیزیکی، موجب آشکارسازی بهتر پارامترهای مدل می گردد. در روش های ترکیبی که از دو یا چند نوع داده با ماهیت های مختلف با یکدیگر و به طور همزمان استفاده می شود با به کارگیری ضرایب خاص بین دو داده ارتباط ریاضی برقرار کرده که در این تحقیق با استفاده از انحراف معیار بین داده ها این امر محقق شده است. در ادامه داده های گرانی و مغناطیس منطقه گرمسار به منظور شناخت توده های نمکی منطقه با روش مدل سازی وارون و سپس مدل سازی وارون ترکیبی مورد بررسی قرار گرفت و در نهایت نتایج به دست آمده از هر دو روش مدل سازی باهم مقایسه گردید. بر اساس نتایج حاصل از این پژوهش استفاده از وارون سازی ترکیبی با استفاده از ضریب وزنی برای مناطقی که دارای داده های مغناطیسی و گرانی سنجی هستند ، توصیه می شود.
    کلیدواژگان: گرانی سنجی، مغناطیس سنجی، وارون سازی ترکیبی، ضریب وزنی
  • رضا لطیفی راد، علیرضا گودرزی *، محمدرضا سپهوند صفحات 123-144
    داده های لرزه ای بازتابی همواره شامل انواعی از نوفه از جمله نوفه های ناهمدوس (تصادفی) و همدوس می باشند. نسبت سیگنال به نوفه پایین؛ مراحل پردازش به خصوص برانبارش و مهاجرت را با مشکل مواجه می کند و در نهایت ممکن است منجر به یک تصویر غیر قابل تفسیر از ساختارهای زمین شود. از آنجا که فرض اساسی تبدیل فوریه پایا بودن سیگنال است، بنابراین برای سیگنال های ناپایا کاملا کارا نیست. با توجه به این که تبدیل موجک، تابع را در حیطه زمان و فرکانس با استفاده از تابع موجک همزمان نشان می دهد؛ بنابراین بر محدودیت های تبدیل فوریه غلبه کرده است. در این مقاله تلاش شده است تا روش نوفه زدایی SURE-LET در حوزه تبدیل موجک گسسته متعامد کاهشی و با استفاده از موجک های مختلف، به منظور تضعیف نوفه های تصادفی اعمال شود. در روش SURE-LET از هرگونه فرضیه ی پیشین بر روی سیگنال های عاری از نوفه اجتناب می گردد. در واقع روش SURE-LET به دو بخش اصلی تقسیم می شود: تضعیف کننده ی موجک که شامل بسط خطی توابع آستانه گذاری (LET) درون مقیاس است. سپس پارامترهای خطی برای به حداقل رساندن خطای نااریب اشتین (SURE)، بین داده های نوفه ای و عاری از نوفه، حل می شوند. با توجه به فرم درجه ی دوم برآورد MSE، پارامترها به راحتی با حل یک سیستم معادلات خطی، بهینه سازی می شوند. نتایج اعمال روش SURE-LET با موجک های مختلف نشان می دهد که موجک های سیملت و کویفلت خروجی بهتری نسبت به سایر موجک ها دارند. با توجه به میزان حفظ سیگنال در کنار تضعیف نوفه برتری روش SURE-LET بر روش های آستانه گذاری نرم و واهمامیخت حوزه f-x نشان داده شده است.
    کلیدواژگان: نوفه تصادفی، تبدیل موجک، آستانه گذاری، برآورد خطای نااریب اشتین، بسط خطی آستانه
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  • Masoud Hosseini, Abolghasem Kamkar Rouhani, Mahdi Mohammadi Vizheh, Saeed Parnow* Pages 67-76
    Summary Geophysical methods can effectively be used for delineation and maintenance of man-made subsurface installations. These installations are suitable targets for detection by ground penetrating radar (GPR) method. In this non-invasive method, high frequency electromagnetic (EM) waves in the frequency range 10 to 1000 MHz are used for detection, demonstration and investigation of shallow subsurface structures. The most important advantage of this method over other geophysical methods its high resolution, high speed of survey and nondestructiveness. In urban areas where the ground surface is covered by asphalt and also noise level is high, it not possible to use other geophysical methods while obtain high resolution data without destruction of the asphalt. However, the GPR method with shielded antenna acts well in urban areas. This method can present a three-dimensional (3-D) picture from the subsurface in which an accurate estimation of the subsurface structures can be made. In this method, EM waves, generated by the GPR transmitter, are sent into the ground and the reflections from the subsurface structures are received by the GPR receiver. The GPR waves are intensively attenuated in high conductive subsurface media and hence, the depth of penetration of GPR waves in this method is limited. In this research work, the depth of penetration of the GPR waves in the study area decreases to less than 2 meters. In this research, an urban survey area where various metallic and non-metallic pipes have been buried is selected, and then, GPR survey is performed on a grid in the area. As a result of processing and interpretation of the acquired GPR data, the subsurface targets at different depths are detected with relatively good accuracy and resolution.
    Introduction Nowadays, transmission of fuels, water and other energy resources by buried pipes, tanks and cables in urban areas is a substantial necessity for human beings. This leads to creation of huge and costly underground networks. Following creation of such networks, a very important matter is the maintenance of these man-made installations to prevent them from possible destructions. These destructions to the installations are not normally observable at the ground surface as the installations are located in the subsurface areas. These destructions that can occur due to different reasons can cause considerable financial losses and also irreparable environmental contaminations. In this regard, geophysical methods can be used for delineation and maintenance of these installations. Often there is a sufficient physical contrast between these installations and their surrounding media. Thus, these installations are suitable targets for detection by GPR method. In this method, high frequency EM waves in the frequency range 10 to 1000 MHz are used for detection, demonstration and investigation of shallow subsurface structures.
    Methodology and Approaches In this research work, GPR method has been used in an urban survey area where various metallic and non-metallic pipes have been buried. The GPR survey has been performed on a grid in the area, and then, the GPR data have been acquired using 250 MHz Noggin Plus GPR system with shielded antenna. Following processing and interpretation of the GPR acquired data, two-dimensional (2-D) and 3-D maps and depth cross-sections are obtained. As a result of this GPR survey, the subsurface targets at different depths in the 3-D maps have been detected with relatively good accuracy and resolution. These 3-D maps can considerably help the interpreter to interpret the GPR data reliably and accurately. Moreover, significant and relatively comprehensive information from these 3-D maps is obtained. 3-D presentation of the GPR data is very useful in the 3-D visualization of the subsurface, and thus, can indicate the targets more precisely.
    Results and Conclusions In this research work, the depth of penetration of the GPR waves in the study area was less than 2 meters. 2-D and 3-D GPR maps and depth cross-sections were obtained as a result of processing and interpretation of the GPR acquired data. Moreover, the subsurface targets at different depths in the 3-D maps were well detected with relatively good accuracy and resolution. 3-D presentation of the GPR data is very useful in the 3-D visualization of the subsurface, and thus, can indicate the targets more precisely. The results of this research indicate that non-invasive, fast and cheap GPR method has considerable advantages over other geophysical methods in civil engineering applications.
    Keywords: Ground, Penetrating Radar (GPR), Metallic, Non-Metallic Pipes, Data Processing, Interpretation, Two, Dimensional (2, D), Three, Dimensional (3, D), Modeling, Shahrood University of Technology
  • Sharyar Khas Ahmadi*, Ali Gholami Pages 77-87
    Summary The conventional velocity analysis sums the amplitudes of events along hyperbolic trajectories and converges the energy in the corresponding intercept time and slowness or velocity. This makes the velocity analysis as one of the most time consuming seismic data processing steps. On the other hand, this algorithm suffers from low resolution due to several reasons. In this paper, we use the Butterfly algorithm to calculate the forward and adjoint operators of the hyperbolic Radon transform in a much faster way, compared to the conventional integration in the time domain. Moreover, by applying it to fast iterative shrinkage-thresholding algorithm (FISTA), a high-resolution velocity panel is obtained.
    Introduction In many of seismic data processing steps, such as time and depth migration, normal moveout correction and multiple attenuation, the velocity versus time information is necessary. Obtaining this information from common midpoint gathers is not only a time-consuming process, but also needs high-resolution panels. The conventional time integration method takes abundant CPU time, which makes the use of iterative sparsity promoting algorithms to obtain a sparse velocity panel, a hard task. The Butterfly algorithm with a complexity of 2( log ) O N N can reduce the computation time by several orders of magnitude. Then, by computing both forward and adjoint operators of the hyperbolic Radon transform using this algorithm, a fast iterative shrinkage algorithm can be used to obtain a sparse Radon panel.
    Methodology and Approaches Hyperbolic Radon transform can be treated as an inverse problem and results in a sparse velocity panel using a 21 ll  norm cost function. Fast iterative shrinkage-thresholding algorithm is a simple, fast and common approach to solve this kind of cost functions. The main step of this algorithm involves the computation of the forward and adjoint operators, which in the case of hyperbolic Radon transform can be a bottleneck in a time manner. Unlike other timeinvariant Radon transforms, the hyperbolic Radon transform cannot be performed in frequency domain effectively. Butterfly algorithm can provide accurate approximations of these operators in a much less time required. The basic idea is that if the data and model domains are restricted to smaller subsets, a low-rank approximation of the Radon integral kernel can be constructed using Chebyshev interpolation for each variable separately. The underlying structure of the Butterfly algorithm is a pair of quad trees of data and model domains, which divide them into smaller subsets. This division at each level of these trees makes the existence of a low-rank separated approximation of the kernel. Then, the Radon panel is computed in three major steps, which include reducing equivalent data sources, transferring to the model domain and extending to all model points.
    Results and Conclusions As it is shown, the conventional velocity panel suffers from near and far offset artifacts, which reduce the accuracy of velocity picking and hence, velocity model building. On the other hand, analyzing common midpoint gathers for velocity-time information could be time expensive in the presence of large data size. We have applied the Butterfly algorithm on the hyperbolic Radon transform, which effectively evaluates the velocity panel with an accurate approximation in only 2( log ) O N N operations. The result of the two methods is the same. However, the computational time of the Butterfly algorithm is less than that of the conventional one by several orders. The performance of this algorithm has also been tested on an iterative sparsifying algorithm to obtain a high-resolution velocity panel. Furthermore, the performance of the proposed method has been tested using other high resolution velocity analysis methods. As it is illustrated in synthetic and real data examples, velocity analysis can be carried out with high accuracy using the proposed method.
    Keywords: Velocity Analysis, Hyperbolic Radon Transform, Butterfly Algorithm, High Resolution, Sparsity
  • Mansoure Mochan, Afsaneh Nasrabadi *, Habib Rahimi, Mohammad Reza Sepahvand Pages 89-102
    Summary In this study, crustal velocity structure beneath two broadband seismic stations of Iran National Seismic Network (INSN), Ashtian-Arak (ASAO) and Naein (NASN) located in northwest of the Central Iran seimotectonic zone near the Ashtian and Nain cities have been investigated by joint inversion of P receiver function and of Rayleigh wave phase and group velocity dispersion curves. To determine the receiver functions, we have used iterative deconvolution in time domain proposed by Ligorria and Ammon (1999). which is more stable with noisy data in comparison to frequency domain. The fundamental mode Rayleigh wave group and phase velocities dispersion curves have been provided by the study of Rahimi et al. (2014) on the structure of crust and upper mantle of the Iranian Plateau for the period interval of 10-100 sec. The result of this study suggests that Moho discontinuity depth beneath Ashtian-Arak station (ASAO is 50 ± 2 km and beneath Naein station (NASN), it is 56 ± 2 km. Relative high crustal thickness beneath NASN station in comparison to other regions of central Iran can be attributed to abut the region to the Sanandaj–Sirjan zone (SSZ) and Urumieh– Dokhtar magmatic assemblage (UDMA). It can also attributed to the existence of thick Magma masses in Urumieh– Dokhtar magmatic assemblage and increase of the density and relative thickness of the area based on the isostasy theory. The average Moho depth in northwest edge of Central Iran is 53 ±2 km.
    Introduction Iran is situated in one of the world seismic regions and the possibility of occurring destructive earthquakes in most regions of the country has given a great significance to recognition of Iranian seismic nature from a seismotectonic standpoint. The seismicity within Iran suggests that much of the deformation is concentrated in the Zagros, Alborz and Kopeh Dagh mountains, and also, in east Iran, surrounding Central Iran and the Lut desert, which are virtually aseismic and behave as relatively rigid . The aim of this research is the study of the crustal structure and Moho discontinuity of the northwest of the Central Iran from analysis of receiver function and surface waves dispersion.
    Methodology and Approaches Receiver functions are the response of the local earth structure to the near-vertical arrival of p waves under a threecomponent seismogram and are susceptible to shear wave velocity contrasts. The depth-velocity trade-off in receiver function causes non-uniqueness in the inverse problem. However, by incorporating information of absolute shear wave from dispersion estimates and joint inversion of these two datasets, this shortcoming can be compromised. In this study, crustal velocity structure beneath two broadband seismic stations of INSN, i.e. ASAO and NASN located in northwest of the Central Iran seimotectonic zone near the Ashtian and Nain cities have been investigated by joint inversion of P receiver function and of Rayleigh wave phase and group velocity dispersion curves. To determine the receiver functions, we use iterative deconvolution in time domain proposed by Ligorria and Ammon (1999) which is more stable with noisy data in comparison with frequency domain and teleseismic events with source-receiver great circle paths larger than 30° and smaller than 90° with magnitudes more than 5.0 that are recorded at time period of 2009 to 2013. The 210 desired RFs have been recorded at two permanent stations. To remove high frequencies, Gaussian parameter 1.0 has been used. In order to eliminate the source, path and instrument effects, deconvolution of the vertical component from the horizontal components of the seismograms is used. For increasing signal to noise ratio, RFs have been clustered in 20˚ azimuthal and less than 15˚ epicentral distance ranges. Finally, the RFs are stacked. The fundamental mode Rayleigh wave group and phase velocities dispersion curves have been provided by the study of Rahimi et al. (2014) on the structure of crust and upper mantle of the Iranian Plateau for the period interval of 10-100 sec. In this way, more accurate information about the crustal structure can be obtained. Joint inversion of two independent data sets has been performed by considering combination of appropriate weighting parameter from Herrmann and Ammon program (2003). Minimizing standard error between real and predicted data is the criteria for getting to desired final and close to earth real model.
    Results and Conclusions The result of this study suggests that Moho discontinuity depth beneath ASAO is 50 ± 2 km and beneath NASN is 56 ± 2 km. Relative high crustal thickness beneath NASN station in comparison to other regions of central Iran can be attributed to abut the region to the Sanandaj–Sirjan zone (SSZ) and Urumieh–Dokhtar magmatic assemblage (UDMA). It can also attributed to existence of thick Magma masses in Urumieh–Dokhtar magmatic assemblage and increase the density and relative thickness of the area based on the isostasy theory. The average Moho depth in northwest edge of Central Iran is 53 ± 2 km.
    Keywords: Central Iran, Crustal Structure, Receiver Function, Joint Inversion
  • Vahid Entezar Saadat, Seyed Hani Motavalli Anbaran* Pages 103-112
    Summary We present a formula for computing the horizontal and vertical gravitational anomalies due to an arbitrary n-sided polygon in a two-dimensional (2D) space with a linear density variation in horizontal and vertical directions. In the analysis of gravity data over thick sedimentary basins or lithospheric scale studies, density contrast can sometimes be approximated by a continuous function decreasing or increasing linearly with depth. We developed a MATLAB code to calculate the gravitational anomaly of an n-sided polygon having linear density variation and compare the anomaly with that of a same n-sided polygon having mean constant density. There is a significant difference in the amount of anomalies that cannot be ignored.
    Introduction When we face geological structures, which are approximately linear, the problem can be solved by analysis of 2D forms. Any 2D body of irregular cross section can be approximated by a polygon and for gravity modeling, an algorithm can be developed based on this polygon. It is well recognized that density of sedimentary rocks increases with depth, and also, there is a linear density decreasing with depth in mantle structure. We present a modified algorithm for computing the gravitational acceleration due to a polygon with linear density variation in horizontal or vertical directions. Considering some geological assumptions, a theoretical geometrical model will be constructed. 2D models are constructed in (X,Z) coordinates and are composed of a series of polygons whose apices define the model geometrically. This is the first stage in the modeling process. The second stage is to modify the shape of the body until a best fit is obtained between the theoretical and observed anomalies. A change in the shape of the body is easily accomplished by computer in the polygon method by changing the coordinates of the vertices.
    Methodology and Approaches It is known that the vertical and horizontal component of gravitational attraction due to a 2D body is equal to the line integral being taken along its perimeter. Using this method, it is possible to model the geological structures by polygons. If we assume a constant amount for the density contrast, the density gets out from the integration but if there is a variable density, it should be taken into account in the integration. Many methods have been suggested for calculation of gravity anomalies due to irregular 2D bodies having a uniform density contrast. In this paper, we solve the line integral with linear density variation in horizontal or vertical directions and use these results in a MATLAB code in order to compute the vertical and horizontal gravitational anomalies.
    Results and Conclusions To compare the differences in gravitational anomalies due to a model having linear density variation in horizontal or vertical directions and a model having mean uniform density, we construct a 2D synthetic model containing arbitrary cross section. The results show that the differences are noticeable in both horizontal and vertical gravity attraction. A similar method can be developed for computation of magnetic anomalies of a body having linear magnetic susceptibility variations in horizontal or vertical directions.
    2D
    Keywords: 2D Modeling, Gravity Anomaly, Linear Density Variation
  • Behnam Babaei, Mohammadali Aliabadi, Mahdi Falahipour, Hamid Reza Baghzendani * Pages 113-121
    Summary Magnetic and gravity geophysical survey methods are mainly used in preliminary stages of exploration activities to achieve a general structural image of the area, and consequently, to obtain information as a basis for future exploratory stages. One of the most important issues in the interpretation of gravity and magnetic data is to use modeling methods in order to accurately identify subsurface structures. One of the procedures in modeling process is the inversion of gravity and magnetic data. In general, the inversion of geophysical data reveals two sets of parameters, namely physical and geometric parameters, for each of the subsurface structures. Inverse modeling of the acquired gravity and magnetic data have been used to identify the mass of salt in Garmsar area. In this regard, first, the results of inverse modeling of both sets of gravity and magnetic data have been compared, and then, combined inverse modeling of the data has been made. Based on the results of this study, a combination of magnetic and gravity data inversion using appropriate weighted coefficients is recommended.
    Introduction As there is a close relationship between gravity and magnetic methods, these two methods are set into the group of potential field geophysical methods. Inverse modeling of geophysical data leads to determination of physical and geometric parameters of subsurface structures. Combined inversion of the data from gravity and magnetic methods has been used in this study to identify subsurface salt structures in Garmsar area
    Methodology and Approaches After applying necessary correction on both gravity and magnetic data, the Bouguer anomaly in gravity method and total intensity anomaly in magnetic method were obtained. Then, inverse modeling of the gravity and magnetic data was performed using ZondGM2D software, and finally, combined inversion of the data was made by coding in MATLAB software.
    Results and Conclusions The inverse modeling results of the acquired gravity and magnetic data in the study area indicate chimney salt masses. The movement of salt toward the ground surface has created differences in the models. Integrated inversion of the gravity and magnetic data has resulted in determination of the depth and lateral spreads of salt bodies in the subsurface of the area with good accuracy.
    Keywords: Gravity, Magnetic, Joint Inversion, Weighting Factor
  • Reza Latifirad, Alireza Goudarzi *, Mohammad Reza Sepahvand Pages 123-144
    Summary In seismic data processing, the processing steps are completely affected by the data quality. Reflection seismic data are often affected by various noises including random and coherent noises. Low signal to noise ratio can produce problems for stacking and migration steps, which ultimately leads to poor interpretation. There are many methods that can be used for noise removal or attenuation of seismic data. The basic assumption of the Fourier transform is that it considers stationary signal, thus, for non-stationary signals, it is not always applicable. Based on this fact that the wavelet transform decomposes a function by translation and stretching, it can provide time-scale representation of a signal. In this paper, we have used SURE-LET method for noise removal in the wavelet transform domain. In the SURE-LET method, any assumptions of noise free signals are avoided.
    Introduction The purpose of seismic data acquisition is to acquire data with the lowest possible noise level. The presence of noise in seismic data is inevitable (Yilmaz, 2001). To improve the signal-to-noise ratio, we can use two approaches: first, changing the seismic energy source or receiver array design and second, processing the seismic data for noise reduction. Considering the source of energy is absorbed by the earth, the increase of seismic energy sources or weighted receiver arrays is limited (Sheriff and Geldart, 1995). Therefore, reduction the noise in order to increase the signal to noise ratio of seismic data is very important. Morlet (1981) showed that by changing the width of the window, wavelet transform could provide better timefrequency distribution. By wavelet transform, various denoising methods based on thresholding of wavelet coefficients have been proposed. Donoho and Johnstone (1994) presented thresholding theory. Chang et al. (2000) presented Bayes shrink method to remove noise. The sensitivity of the soft thresholding function (to the upper limit of the threshold) for the minimization, does not give suitable results. Luisier et al. (2007), to optimize Stein’s Unbiased Risk Estimate (SURE), used another principle, such that the noise attenuation to be expressed as a linear expansion of thresholding (LET) functions. In fact, by combining the SURE and LET and solving a system of linear equations, the noise is attenuated. SURE is an unbiased statistical estimate of the mean squared error (MSE) between an original unknown signal and a processed version of its noisy observation. This estimate depends only on the observed data and does not require any prior assumption on the noise-free signal (Luisier et al., 2010). Blu and Luisier (2007) presented SURELET method based on pointwise thresholding function for image denoising. Luisier et al (2010) used SURE-LET method for orthonormal wavelet domain video denoising.
    Methodology and Approaches Wavelet-based noise removal techniques including assumptions for the data are as follow (Luisier et al., 2007): 1. The statistical description of the distribution coefficients 2. A non-linear estimation of statistical parameters, 3. Finding the best noise attenuation algorithms for a variety of statistics For example, Chang et al. (2000), in The Bayes shrink approach, modeled wavelet coefficients of each sub-band with a general Gaussian distribution (GGD). Then the threshold is obtained for each sub-band for the Bayesian framework. For the SURE-LET method, the previous assumption of the noise-free signals is avoided. This method acts by calculating the unbiased estimates of the mean square error between the signal and denoised signal. There are other methods using SURE approach. For example, the sensitivity of the soft thresholding function to the upper limit of the threshold, in the minimization, does not give suitable results. Luisier et al. (2007) to optimize SURE, used another principle so that the noise attenuation as a linear combination of denoising elements (LET) was expressed. In fact, by combining the SURE and LET and solving a system of linear equations, the noise is attenuated.
    Results and Conclusions The SURE-LET method comprises of two main sections: noise attenuator that consists of the interscale LET, and then, the linear parameters for minimizing of SURE between noisy and noise-free signals. Regarding secondary order estimation (MSE), the parameters are improved easily by solving a LET. The results of this study shows that Symlets and Coiflets provide better results using SURE-LET method for denoising non-stationary seismic signals.
    Keywords: Seismic Random Noise, Wavelet Transform, Thresholding, Stein's Unbiased Risk Estimate (SURE), Linear Expansion of Thresholding (LET)