فهرست مطالب

ژئوفیزیک ایران - سال ششم شماره 4 (پیاپی 15، 1391)
  • سال ششم شماره 4 (پیاپی 15، 1391)
  • تاریخ انتشار: 1391/12/15
  • تعداد عناوین: 10
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  • محمد رضا ابراهیمی، محمد علی ریاحی صفحه 1
    برخلاف تبدیل فوریه که داده ها را روی دسته موج های سینوسی تصویر می کند، تبدیل آدامار داده ها را روی یک سری تابع های مربعی به نام تابع های والش تصویر می کند. در این مقاله از نشانگر جابه جایی نامتغیر یا طیف توان تبدیل آدامار، برای طبقه بندی رخساره های مخزن استفاده می شود. تبدیل موردنظر نسبت به تغییرات دیادیک حساس نیست و بنا به این خاصیت، تصادفی بودن رخساره های مخزن را به خوبی تشخیص می دهد. برای بررسی توانایی این نوع نشانگر، آن را روی داده های لرزه ای سه بعدی سازند سروک از یکی از میادین جنوب غربی ایران اعمال کرده ایم. رخساره های مخزن برای این میدان، براساس تخلخل دسته بندی شده اند. تعداد رخساره های تخلخل به کمک نگارهای تخلخل به دست آمده از چهار چاه موجود در منطقه، به چهار دسته تخلخل تقسیم شدند. درنهایت با استفاده از شبکه عصبی، کل مکعب لرزه ای با ضریب همبستگی 81 درصد به این چهار رخساره تخلخل تبدیل شده است.
    کلیدواژگان: تبدیل آدامار، تابع های والش، رخساره مخزن، تخلخل، سازند سروک، شبکه عصبی
  • علی رصا نجیبی، محمد رضا آصف، محمد نبی بیدهندی، رسول اجل لوئیان، غلام عباس صفیان صفحه 12
    در این پژوهش، به منظور بررسی تاثیر فشار همه جانبه بر سرعت امواج کشسان و مدول های یانگ دینامیکی (Ed) و استاتیک (Es)، آزمایش فراصوتی (التراسونیک) تحت فشار همه جانبه روی مغزه های سنگ آهک سروک مربوط به یکی از چاه های نفتی جنوب غرب ایران صورت گرفت. با نصب کرنش سنج، تغییرات طولی نمونه در حین آزمایش ثبت و Es در فشارهای متفاوت اندازه گیری شد. داده های به دست آمده از این آزمایش ها نشان دهنده افزایش سرعت امواج و متعاقب آن افزایش Ed، با افزایش فشار همه جانبه است که این روند افزایشی در فشارهای کمتر از 15 مگاپاسکال بیشتر است و حالت غیرخطی دارد. در فشارهای بالاتر، این روند افزایشی کاهش می یابد و تغییرات سرعت با فشار خطی می شود. در این تحقیق ملاحظه شد که با افزایش فشار همه جانبه نسبت Ed/Es به صورت نمایی کاهش می یابد که این پدیده مبین تاثیر بیشتر فشار همه جانبه در افزایش Es نسبت به Ed است. براساس مدل پیشنهاد شده در این تحقیق، با دقت خوبی می توان Esسازند را براساس Ed در فشارهای همه جانبه گوناگون برآورد کرد.
    کلیدواژگان: سنگ آهک، مدول یانگ دینامیکی و استاتیک، فشار همه جانبه، سرعت امواج کشسان
  • محمد رسول نیک بخش، میرستار مشین چی اصل صفحه 26
    در این تحقیق برای تعیین پارامترهای ساختارهای مدفون زمین شناسی به روش پتانسیل خودزا از توابع تحلیلی، گرادیان مختلط و تبدیل هیلبرت استفاده شده است. تبدیل هیلبرت را می توان از راه های متفاوتی همچون روش تبدیل فوریه و هما میخت عملی ساخت. در این تحقیق از عملگر هما میخت برای تبدیل هیلبرت پتانسیل اجسام هندسی کره، استوانه افقی استفاده شده است. پارامترهای ساختارهای مدفون بی هنجاری های پتانسیل خودزا (عمق، گشتاوردوقطبی، زاویه قطبیدگی و فاکتور شکل) از راه تعیین ریشه ها و نقاط تقاطع تابع تبدیل هیلبرت، گرادیان کامل پتانسیل بی هنجاری های مدفون به دست می آید. در این تحقیق این روش برای داده های مصنوعی بدون نوفه مورد بررسی قرار گرفته است.
    کلیدواژگان: گرادیان کامل، تبدیل هیلبرت، پتانسیل خودزا، هما میخت
  • سرمد قادر، فرهنگ احمدی گیوی، حکیم گلشاهی صفحه 35
    در این تحقیق، حل عددی معادلات آب کم عمق غیرخطی در صفحه f برحسب میدان های ارتفاع، واگرایی و تاوایی با استفاده از روش فشرده ترکیبی مرتبه ششم مورد بررسی قرار می گیرد و نتایج آن با روش های مرتبه دوم مرکزی، فشرده مرتبه چهارم، ابرفشرده مرتبه ششم و طیفی وار مقایسه می شود. برای این منظور، یک جت مداری به منزله شرایط اولیه درنظر گرفته می شود که با گذشت زمان به ساختارهایی پیچیده با مقیاس کوچک تر شکسته می شود. در این حل عددی، برای انتگرال گیری زمانی معادلات از فرمول بندی نیمه ضمنی سه ترازه استفاده شده است. در مورد معادله تاوایی، یک جمله فراپخش برای حفظ پایداری به حل عددی افزوده می شود. نتایج به دست آمده نشان از توانایی زیاد روش فشرده ترکیبی مرتبه ششم در شبیه سازی میدان های جریان پیچیده دارد. با وجود اینکه روش طیفی وار نسبت به سایر روش ها دقت بیشتری دارد، نزدیکی بسیار زیاد نتایج روش فشرده ترکیبی مرتبه ششم به نتایج روش طیفی وار امیدوار کننده است.
    کلیدواژگان: روش فشرده ترکیبی، دقت عددی، تفاضل متناهی، نیمه ضمنی، معادلات آب کم عمق غیرخطی، شبکه Z، جت مداری
  • احسان پگاه، عبدالرحیم جواهریان، داوود نوروزی صفحه 50
    در اکتشافات نفت سرعت سیر امواج در زمین به علت ناهمسانگرد بودن آن در جهت های افقی و قائم یکسان نیست. اما این فرض را که با حرکت در جهت افقی برای بیشتر مناطق، تغییرات سرعت لرزه ای کوچک است، می توان با دقت خوبی در صنعت اکتشاف ذخایر هیدروکربوری به کار برد که این نیز در نتیجه تغییرات کم در چگالی و خواص کشسانی لایه ها در این جهت است. تغییرات افقی سرعت عموما خیلی کندتر از تغییرات در راستای قائم است بنابراین اغلب منطقه برداشت را به ناحیه های کوچک تری تقسیم می کنند، به طوری که بتوان از تغییرات افقی در داخل هرکدام صرف نظر کرد و توزیع سرعت قائم یکسانی را به کار برد. اکثر روابط محاسبه اندازه خانک و دهانه کوچ که به سرعت وابسته هستند بر اصل فرض ثابت بودن آن استوار ند. در این مقاله محاسبه این دو کمیت در طراحی عملیات لرزه نگاری سه بعدی میدان نفتی اهواز با استفاده از مدل سرعت خطی صورت می گیرد. از طرفی چون اندازه خانک و دهانه کوچ از موثرترین عوامل تاثیرگذار بر کیفیت داده های برداشت شده و همچنین هزینه اجرای عملیات و پردازش داده ها هستند، لذا روش طراحی بیان شده در این مقاله که از محاسبات مربوط به مدل سرعت متغیر پیشنهاد شد باعث می شود که علاوه بر حفظ مناسب کیفیت داده های برداشت شده و دست یابی به مقادیر مطلوب کمیت های موثر در کیفیت اطلاعات، رابطه میان هزینه برداشت و اطلاعات به دست آمده نیز به شرایطی بهینه برسد.
    کلیدواژگان: اندازه خانک، دهانه کوچ، مدل سرعت متغیر (خطی)، مدل سرعت ثابت، سازند آسماری، سازند فهلیان
  • مهدی صادقی، امین روشندل کاهو، حمید رضا سیاه کوهی، علی رضا حیدریان صفحه 62
    تجزیه طیفی داده های لرزه ای، حجم زیادی از داده در بسامد های مختلف تولید می نماید که می توان آن ها را بصورت مکعب های تک بسامد تجزیه نمود. از این مکعب ها که حاوی اطلاعات مفیدی از روند های ساختاری و نهشته های رسوبی می باشند، می توان جهت نمایش این روند ها استفاده نمود. در این مقاله سه روش نمایش این روند ها مورد بررسی قرار می گیرد. در روش اول با استفاده از برش زمانی از مکعب های تک بسامد، تغییرات ناشی از این الگوها نمایش داده می شود. در این روش مقاطع تک بسامد مختلف بررسی می گردند و یک مفسر با تجربه می تواند با مشاهده تغییرات این مقاطع با بسامد از تغییرات عرض و محتویات کانال اطلاعاتی بدست آورد. از آنجایی که فرکانس های پایین و بالا دارای اطلاعات متفاوتی از رویداد ها می باشند، تصاویر تک بسامد نمی توانند اطلاعات مورد نیاز از رویداد را بطور همزمان نمایش دهند. در دو روش دیگر مورد بررسی در این مقاله با استفاده از برانبارش رنگی، مقاطع RGB از این برش ها تهیه می شود که به دلیل داشتن محتویات بسامدی مختلف دارای اطلاعات بیشتری از نمایش تک بسامد می باشند. در این مقاله مقاطع RGB به دو صورت RGB معمولی و RGB با توابع پایه تهیه شده است. در روش RGB معمولی با استفاده از سه برش تک بسامد مجزا به ازای فرکانس های مختلف، مقاطع برانبارش رنگی تهیه می گردد. در این حالت اگرچه مشکل روش تصاویر تک بسامد تا حدودی برطرف می گردد، اما فقط از سه مقطع تک بسامدی استفاده شده و در عمل قسمت اعظمی از اطلاعات مقاطع تک بسامد دیگر همچنان نادیده گرفته شده اند. در روش RGB با توابع پایه با استفاده از پنجره هایی محدوده های بسامدی خاصی به عنوان مولفه های قرمز، آبی و سبز در نظر گرفته می شوند و مقاطع RGB به تصویر درمی آیند. مقایسه نتایج این سه روش نمایش برای نمایش کانال های مدفون نشان داد که روش برانبارش رنگی نسبت به روش تک بسامد با دقت بیشتری کانال ها را نشان می دهد و همچنین استفاده از توابع پایه بدلیل استفاده از اطلاعات بیشتر نتایج بهتری نسبت به روش RGB معمولی در نمایش کانال های مدفون ایجاد می کند.
    کلیدواژگان: کانال های مدفون، تجزیه طیفی، تبدیل فوریه زمان کوتاه، تبدیل S، برانبارش رنگی، مقاطع تک بسامد
  • محمد رضا سپهوند، فرزام یمینی فرد، غلام جواندولوئی صفحه 73
    پس از وقوع زمین لرزه 11 فروردین 1385 سیلاخور با بزرگای گشتاوری 1/6، شبکه لرزه نگاری موقتی متشکل از 10 ایستگاه ازسوی پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله برای ثبت پس لرزه های این زمین لرزه در منطقه نصب شد. تحلیل پس لرزه های ثبت شده در این شبکه، زون گسلی نسبتا پهن با روند کلی جنوب شرق- شمال غرب در راستای گسل اصلی عهد حاضر را نشان می دهد. تمرکز وقایع در عمق های بین 4 تا 11 کیلومتر بیانگر قابلیت شکنندگی پوسته در عمق های کم در این بخش از زاگرس است. نیم رخ های عمقی عمود بر گسل اصلی عهد حاضر، نشان دهنده شیب غالب روندهای پس لرزه ها به سمت شمال شرق است. توزیع مکانی ضریب b نشان دهنده کمتر بودن مقادیر این ضریب در بخش شمالی زون پس لرزه ها است که می تواند شاهدی بر تجمع تنش بیشتر در این منطقه نسبت به بخش های جنوبی باشد.
    کلیدواژگان: ضریب b، شبکه لرزه نگاری موقت، پس لرزه، سیلاخور، زاگرس
  • میثم زارعی، امین روشندل کاهو، حمید رضا سیاه کوهی، مهدی صادقی صفحه 85
    چون محتوای بسامدی داده های لرزه ای با زمان تغییر می کند باید از تبدیل های زمان – بسامد برای بررسی آنها استفاده کرد. تبدیل های زمان- بسامد متداول هرکدام دارای نقاط ضعف و قوت هستند. یکی از تبدیل های زمان – بسامد متداول توزیع ویگنر – وایل است که دارای قدرت تفکیک زمانی و بسامدی زیادی است، ولی به سبب حضور جمله های متقاطع، امروزه کمتر مورد استفاده قرار می گیرد. بنابراین استفاده از تبدیل هایی که بتوانند علاوه بر حفظ نقاط قوت این روش ها، نقاط ضعف آنها را برطرف کنند، بسیار سودمند است.
    طیف نگاشت تبدیل فوریه زمان کوتاه که مربع ضریب تبدیل فوریه زمان کوتاه است، نمونه هموار شده توزیع ویگنر– وایل است. طیف نگاشت تبدیل فوریه زمان کوتاه حاصل همامیخت دو بعدی توزیع ویگنر– وایل سیگنال و توزیع ویگنر– وایل تابع پنجره است. در این مقاله روش طیف نگاشت تبدیل فوریه زمان کوتاه واهمامیختی عرضه می شود که با اعمال عملگر دو بعدی واهمامیخت روی طیف نگار تبدیل فوریه زمان کوتاه به طور هم زمان باعث افزایش قدرت تفکیک در حوزه زمان-بسامد و کاهش جمله های تداخلی توزیع ویگنر – وایل می شود. در این مقاله، ابتدا قدرت تفکیک تبدیل فوریه زمان کوتاه واهمامیختی با تبدیلات زمان-بسامد مرسوم مقایسه شده و سپس کارایی نشانگرهای استخراج شده از این تبدیل برای شناسایی کانال های مدفون در داده های مصنوعی و واقعی سه بعدی بررسی و با تبدیل فوریه زمان کوتاه مقایسه می شود. با توجه به رفتار دامنه امواج لرزه ای در داخل کانال، در مورد سرعت امواج لرزه ای در رسوبات پرکننده کانال می توان اظهارنظر کرد. نتایج حاصل نشان دهنده برتری قابل قبول این تبدیل در مقایسه با تبدیل های زمان-بسامد متداول دیگر و کارایی نشانگرهای استفاده شده در شناسایی کانال های مدفون، است.
    کلیدواژگان: تبدیل های زمان، بسامد، طیف نگار، قدرت تفکیک، تبدیل فوریه زمان کوتاه واهمامیختی، واهمامیخت دو بعدی، نشانگرهای لرزه ای، کانال های مدفون
  • وحید ملکی، ظاهر حسین شمالی، محمد رضا حاتمی صفحه 96
    در تحقیق حاضر با استفاده از روش غیرخطی به مکان یابی مجدد زمین لرزه Mn = 6.5؛ML = 6.2؛ Mw = 6.3، محمدآباد ریگان و پس لرزه های حاصل از آن می پردازیم. زمین لرزه ریگان شامل 296 پس لرزه ثبت شده در مرکز لرزه نگاری کشوری (IRSC) است که در برخی موارد بزرگی پس لرزه ها نزدیک به زمین لرزه اصلی بوده است. داده های مورد استفاده در این تحقیق از ترکیب اطلاعات زمان رسید فاز های ثبت شده در ایستگاه های مرکز لرزه نگاری کشوری (IRSC) و پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله (IIEES) به دست آمده است. به این ترتیب با بررسی پس لرزه ها براساس زمان وقوع و بزرگای آنها و استفاده از قانون آموری در توصیف پس لرزه ها مشخص شد که زمین لرزه های ناحیه ریگان شامل دو زمین لرزه اصلی است که با عنوان زمین لرزه اصلی دوم شناخته شده است. به این ترتیب مکان یابی زمین لرزه ها برای دو پنجره زمانی متفاوت و به روش غیرخطی صورت گرفت. پنجره زمانی اول شامل زمین لرزه اصلی و 137 پس لرزه آن تا رخ دادن زمین لرزه اصلی دوم و پنجره زمانی دوم شامل زمین لرزه اصلی دوم و 159 پس لرزه به وقوع پیوسته پس از آن است. به منظور بهبود نتایج مکان یابی فقط پس لرزه هایی مورد بررسی قرار گرفته اند که حداقل در 5 ایستگاه ثبت شده باشند. بدین ترتیب پس از مکان یابی مجدد 222 پس لرزه مشاهده شد که زمین لرزه های به وقوع پیوسته در دو پنجره زمانی، به صورت کاملا مجزا از یکدیگر در رومرکز و عمق قرار گرفته اند. با بررسی وضعیت قرارگیری در رومرکز و مقاطع عمقی زمین لرزه ها به نظر می رسد که زمین لرزه اصلی ریگان به همراه پس لرزه های مورد بررسی در پنجره زمانی یک، روی ادامه گسل کهورک و در ناحیه جنوب شرقی گسل فعال بم به وقوع پیوسته اند. همچنین قرارگیری پس لرزه های با بزرگای Mn > 4 در ادامه گسل کهورک می تواند نشان دهنده به وقوع پیوستن دو زمین لرزه اصلی روی ادامه گسل کهورک باشد.
    کلیدواژگان: مکان یابی مجدد، روش غیرخطی، پس لرزه، محمدآباد ریگان
  • ملیحه کاظمی صفحه 112
    نسبت سرعت های امواج تراکمی به برشی در تعیین خواص پتروفیزیکی سنگ ها اهمیت زیادی دارد. نسبت Vp/Vs درحکم شاخصی برای تشخیص هیدروکربورها در نظر گرفته می شود. محاسبه سرعت موج برشی از نگاره صوتی برشی دو قطبی (DSI) در مقایسه با روابط تجربی دارای عدم قطعیت کمتری است. در این مقاله با استفاده از نگاره صوتی برشی دو قطبی روابط همبستگی بین Vp و Vs در سازندهای کنگان و دالان در مجاورت یک چاه در میدان پارس جنوبی مورد بررسی قرار می گیرد و با رابطه تجربی بین Vp و Vs کاستاگنا مقایسه می شود. با استفاده از روابط همبستگی محاسبه شده از نگاره صوتی برشی دو قطبی، Vs برای دو چاه دیگر در میدان مورد بررسی که فاقد نگاره های صوتی برشی دو قطبی بودند، به دست می آید. در این دو چاه با استفاده از داده های VSPفاکتور کیفیت (Q) تعیین می شود. ازآنجاکه فاکتور کیفیت فاکتوری با ارزش در تحقیقات مخازن محسوب می شود، در این تحقیق نسبت Vp/Vs به دست آمده از نگاره صوتی برشی دو قطبی و همچنین رابطه تجربی کاستاگنا با نسبت QP/QS مقایسه و روشن می شود که نسبت Vp/Vs از نگاره صوتی برشی دوقطبی در مقایسه با نسبت Vp/Vs از رابطه کاستاگنا تطابق بهتری را در ناحیه مخزنی نشان می دهد.
    کلیدواژگان: نسبت Vp، Vs، نگارهDSI، روابط همبستگی، رابطه کاستاگنا، فاکتور کیفیت و نسبت QP، QS
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  • Mohammad Reza Ebrahimi, Mohammad Ali Riahi Page 1
    This study applies the translation invariant attribute (TIA) using the Hadamard transform of the seismic data to discriminate lithofacies. The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric operation on 2n real numbers (or complex numbers, although the Hadamard matrices themselves are purely real). The Hadamard transform can be regarded as being built out of size-2 Discrete Fourier Transforms (DFTs), and is in fact equivalent to a multidimensional DFT of a 2*2*2...*2 size. It decomposes an arbitrary input vector into a superposition of Walsh functions. In mathematical analysis, the set of Walsh functions form an orthogonal basis of the square functions on the unit interval. The functions take the values -1 and +1 only, on sub-intervals defined by dyadic fractions. The orthogonal Walsh functions are used to perform the Hadamard transform, which is very similar to the way the orthogonal sinusoids are used to perform the Fourier transform. The Walsh functions are related to the Rademacher functions; They both form a complete orthogonal system. The Hadamard transform is particularly good at finding repeating, stacked vertical sequences. The dyadic shifts represent the invariant properties of the Hadamard transforms. The output of a translation invariant transform is insensitive to the dyadic shifts so that in geologic applications, the objective of using these transforms is to find a geologic pattern which have been analyzed anywhere in the time series, irrespective of their vertical position. If z is the output of a dyadic shift invariant transform, such as the Hadamard transform, of a sequence x, then the dyadic shift invariant power spectrum (Σz2), is termed as the translation invariant attribute. The translation invariant attribute computation requires 2n input samples. If an input sequence does not have 2n samples, then either zero padding or quite a large time window can be used to make 2n samples. This attribute is applied in 3D seismic data of Sarvak Formation of one of the oil fields in the south-west of Iran. The Sarvak Formation for this oilfield is a carbonate unit gradually overlying the Kazhdumi Formation. The thickness of Sarvak Formation increases towards the west and varies between 582 m and about 700 m. The reservoir facies for this field are classified based on their porosities. Four porosity facies were selected by using porosity logs of four vertical wells drilled in this oil field. All the seismic data are converted to those categories by Artificial Neural Network (ANN). The neural network used here was a Two-layer Feed-forward network with Error Back Propagation (EBP) for learning algorithms. The transfer function of the hidden neurons was hyperbolic tangent and the transfer function of the output neurons was linear. Three different time slices of Hadamard transform, translation invariant attribute were presented. The correlation between the real porosity and the predicted porosity using ANN was estimated to be about 81%. Finally, all the seismic data were converted to porosity facies by using ANN and three time slices of the porosity facies were calculated and shown.
    Keywords: Hadamard transform, Walsh function, reservoir facies, porosity, Sarvak Formation, neural network
  • Alireza Najibi, Mohammad Reza Asef, Majid Nabi Bidhendi, Rasul Ajalloeian, Gholam Abbas Safian Page 12
    Young’s modulus measured as the slope of a stress-strain curve under static loading conditions (Es) in the lab is an essential rock mechanical parameter for geomechanical analyses of oil wells. Examples of these analyses are wellbore stability analysis, estimation of the in-situ stresses, and the reservoir compaction survey. However, Es is obtained by destructive laboratory tests on selected core samples along the well length. Therefore, information on the value of Es along the well length is often discontinuous and limited to a cross well with a core. On the other hand, based on the theory of elasticity, well-known equations are available to calculate Young’s modulus under dynamic (compressional and shear wave) loading conditions which is the dynamic Young’s modulus (Ed). Nevertheless, Ed for intact core specimens is very often two or three times or more larger than Es. This is partly because in case of a dynamic loading strain, the amplitude is 10-6 or 10-7, while in the static moduli strain, amplitude is typically 10−2– 10−3. Static moduli, measured as the slopes of the stress–strain curves, differ from small strain amplitude dynamic (elastic) moduli because of plasticity or nonlinear effects. Also, porosity and micro-cracks in rock core specimens affect this phenomenon. Accordingly, many attempts have been made to predict Es based on other nondestructive parameters namely compressional and shear wave velocities (Vp and Vs) in the lab. Fortunately, geophysical logs in many hydrocarbon reservoirs provide Vp and Vs data continuously along the well length. Therefore, it is possible to calculate Ed continuously in the well. For this reason empirical equations have been developed to estimate Es based on Ed along the well length. Furthermore, a correlation between Ed and Es at in-situ conditions is more difficult than in the lab. This is because Vp and Vs measurements increase by increasing in-situ confining stresses. This is in turn because confining stresses reduce the anisotropy elements such as porosity and micro-cracks. As a result, Vp and Vs Ed often will increase with the burial depth. Similarly, laboratory experiments indicate that stress-strain measurements on rock core specimens under the static loading and triaxial confining stresses (similar to the well depth) will increase Es with an increase in the confining stresses. In this research, laboratory experiments were carried out on limestone rock core specimens of Sarvak Formation obtained from an oil well in the South West of Iran. The specimens were placed in a cell under confinement. Compressional and shear wave velocities at different confining stresses were measured. Experiments were accomplished in the dry conditions up to a maximum confining pressure of 50 MPa. Simultaneously, the values of the axial load and axial strain were recorded. It was noticed that with an increase in confining stresses, Vp and Vs will increase. Likewise, at lower confining stresses, Vp and Vs increase exponentially while after a critical confining stress of 15 MPa, exponential equation will turn to linear. Constants of the linear and exponential equations for Sarvak formation were extracted with excellent accuracy. Based on these measurements, Ed and Es were calculated at different levels of confining stresses. It was observed that with an increase in confinement, the ratio of Ed/Es will decrease and approach to unity at higher confinements. This means that with an increase in confining stresses, Es will increase faster (compared to Ed). According to the findings of this research, a correlation between Ed and Es should be made with extreme care to account for the impact of the confining stress at any depth of interest. This is very often ignored throughout the well length. Finally, based on laboratory experiments, an empirical equation was developed to predict Es from Ed at different confining stresses.
    Keywords: Limestone, static, dynamic Young's moduli, confining pressure, elastic wave velocity
  • Mohammad Rasool Nikbakhsh, Mirsattar Meshinchi Asl Page 26
    Although the Hilbert Transform (HT) has been used in electrical engineering and signal analysis for a long time (Bracewell, 1965), its application in geophysical studies started in 1970's. The HT is a method of direct solution. The aim of using the HT in geophysical studies is to obtain more than one equation containing the same structural parameters by utilizing the complex gradients of the available data. The roots and common intersection points of the anomaly and the complex gradients of the anomaly have been used to determine the structural parameters. Therefore, a ± 1 error sampling interval was expected for the determinations. In order to minimize the error, the most appropriate sampling interval should be chosenUp to the present time, the HT has been used extensively only in magnetic and seismic studies. But in the aforementioned studies, it has been used mostly as a Fourier Transform (FT). Taner (1979), in his study, obtained the HT through convolution by using a normalized Hilbert time-domain operator truncated to 61 points The Hilbert Transform (HT) is a mathematical transform function which shifts the phase of a signal as much as π/2 without changing its amplitude. With this definition HT is a linear system, which transforms odd and even functions, with equal amplitude to each other in space or frequency field. Since HT is a linear set, the system should have an input signal, a transfer function and an output function. The HT can be applied to the Fourier Transform (FT) and convolution methods.. In this study, the model parameters of which were unsolved so far, self-potential (SP) methods were determined with HT using convolution and FT methods and the results were compared. In this study, Structural parameters were determined directly from the geophysical anomalies using analytical functions of the complex gradients and the Hilbert Transforms can be applied to reach the above-mentioned situation. The Hilbert Transforms, which can be carried out in two different ways using the Fourier Transform and convolution methods, were used to provide the convolution method between the complex gradients of the anomaly. Structural parameters (electric dipole moment, polarization angle and depth) were then determined from the solutions of the constructed equations. This method was used for two models, a sphere and a horizontal cylinder, with synthetic data without any random noise. The results of this study are as follow: (1) The parameters were determined exactly for the theoretical models using the HT method. Especially, the location of the structure, which had not been determined before, was obtained precisely and directly from the anomaly for the self-potential method. (2) Before the interpretation of the field data with the HT method, the anomaly should be refined from noise. If this procedure has not been carried out, pseudo roots could be formed in the complex gradients of anomaly.
    Keywords: Complex gradients, Hilbert transforms, self, potential, convolution
  • Sarmad Ghader, Farhang Ahmadi Givi, Hakim Golshahy Page 35
    Usually, simplified models, such as shallow water model, are used to describe atmospheric and oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. This model is applied to a fluid layer of constant density in which the horizontal scale of the flow is much greater than the layer depth. However, the dynamics of a two-dimensional shallow water model is less general than three-dimensional general circulation models but is preferred because of its greater mathematical and computational simplicity. Taking intrinsic complexity of fluids, recently, numerical researches have been focused on highly accurate methods. Especially, for large grid spacing numerical simulation, the use of highly accurate methods have become urgent. This trend led to an interest in compact finite difference methods. The compact finite-difference schemes are simple and powerful ways to reach the objectives of high accuracy and low computational cost. Compared with the traditional explicit finite-difference schemes of the same-order, compact schemes have proved to be significantly more accurate along with the benefits of using smaller stencil sizes, which can be essential in treating nonperiodic boundary conditions. Application of some families of the compact schemes to the spatial differencing in some idealized models of the atmosphere and oceans shows that compact finite difference schemes can be considered as a promising method for the numerical simulation of geophysical fluid dynamics problems. In this research work, the sixth-order combined compact (CCD6) finite difference method was applied to the spatial differencing of f-plane shallow-water equations in vorticity, divergence and height forms (on a Randall's Z grid). The second-order centered (E2S), fourth-order compact (C4S) and sixth-order super compact (SCD6) finite difference methods were also used for spatial differencing of the shallow water equations and the results were compared to the ones from a pseudo-spectral (PS) method. A perturbed unstable zonal jet was considered as the initial condition for numerical simulation in which it breaks up into smaller vortices and becomes very complex. The shallow water equations are integrated in time using a three-level semi-implicit formulation. To control the build-up of small-scale activities and thus potential for numerical nonlinear instability, the non-dissipative vorticity equation was made dissipative by adding a hyperdiffusion term. The global distribution of mass between isolevels of the potential vorticity, called mass error, was used to assess numerical accuracy. The CCD6 generated the least mass error among finite difference methods used in this research. By taking the PS method as a reference, the qualitative and quantitative comparison of the results of the CCD6, SCD6, C4S and E2S, indicated the high accuracy of the sixth-order combined compact finite difference method.
    Keywords: Combined compact method, numerical accuracy, finite difference, semiimplicit
  • Ehsan Pegah, Abdolrahim Javaherian, Davood Nowroozi Page 50
    In oil exploration, because of the anisotropy of the earth, the velocity of the waves in horizontal nd vertical directions are not uniform; however, with a good accuracy in exploration procedures, e can assume that in a layer, velocity changes are limited as a results of slow variations in ensity as well as the elastic properties of the layers in these horizontal directions. In general, ariations of the above mentioned parameters inhorizontal directions are much slower than in ertical ones. For this reason, the acquisition area is often divided into smaller areas; horizontal variations are neglected while the same vertical velocity distributions are applied in any sub-area. There are basically two methods in calculation of the bin size and migration aperture in a 3-D seismic survey design. The first method is based on using a constant velocity model which is not compatible with real conditions. In this model, we assume that the medium between the surface of the earth and the target layer is replaced with supposed layer and ascribe a constant amount velocity to this layer that is equal to the average velocity in medium between the surface and the target layer. The second method uses the model wherein the velocity changes with depth and therefore a linear velocity model is assumed which is more compatible with reality in comparison with the previous method. Whereas the linear velocity method can include all important wave propagation effects, it involves a certain circular logic. This method, involves building a detailed subsurface velocity model and uses ray tracing or other simulation techniques to customize the survey for the local subsurface. In Ahwaz Oil Field, the main target was Asmari Formation and the deep target was Fahlian Formation. The 3-D seismic survey design of Ahwaz Oil Field was performed on the main target located in the depth of 2900 m and the deep target located in the depth of 5000 m from the mean sea level. Ground level was about 15 to 40 m higher than the sea level in this area. By considering the check shot, VSP and sonic log data from 14 well logs, the image area was divided into 14 parts, so that the variations of the horizontal velocity could be neglected in each part and the constant contribution for the vertical velocity could be used. Finally, using the velocity values at the desired vertical depth to the reflection point (target depth), the dip angles of the target horizon (dip of reflector at the reflection Point) and the maximum frequency reflected from the main target, we were able to calculate the bin size and migration aperture in each part. At last, we could select a value for the bin size in this project. In this study, we examined the parameters of the velocity-dependent 3-D seismic survey design. These parameters included the bin size and migration aperture. Conventional formula for the bin size and migration aperture for Ahwaz Oil Field was carried out based on the linear model between the velocity and depth. As an intermediate between constant velocity and interval velocity model, we have given expressions valid for a linear velocity function. By using the linear velocity model, the design parameters incorporated first-order ray bending. Hence, this method was adjusted to the reality and led to better results compared to a constant velocity model. Linear V(z) is an attractive approximation for three reasons. First, this kind of velocity variation captures the first-order effect of the pressure and the temperature increases with depth. It does not require detailed knowledge of the subsurface velocities. Second, analytical expressions are available for the ray path geometry and travel times in such a medium. Third, the linear V(z) propagation allows turning waves which have potential for imaging dips beyond 90 degrees. Migration aperture is overestimated by constant velocity calculations, whereas the bin size is underestimated and this results in an increase in costs. On the other hand, calculations based on a linear velocity model require a less migration aperture and a larger bin size. The bin size and migration aperture are two sensitive economy parameters. Hence, using a larger bin size and a smaller migration aperture obtained from a linear velocity model, the cost of a 3-D seismic survey design will be decreased.
    Keywords: Bin size, migration aperture, linear velocity model, constant velocity model, Asmari Formation, Fahlian Formation
  • Mehdi Sadeghi, Amin Roshandel Kahoo, Hamid Reza Siahkoohi, Alireza Heydarian Page 62
    pectral decomposition of time series has a significant role in seismic data processing nd interpretations. Since the earth acts as a low-pass filter, it changes the frequency ontent of the passing seismic waves. Conventional methods of representing signals in a ime domain and frequency domain cannot show the time information and the frequency nformation simultaneously. Time-frequency transforms an upgraded spectral ecomposition to a new step and can show time and frequency information imultaneously. ime-frequency transforms generate a high volume of spectral components, which ontain useful information about the reservoir and can be decomposed into single requency volumes. These single frequency volumes can overload the limited space of a omputer hard disk and are not easy for an interpreter to investigate them individually; herefore, it is important to use methods to decrease the volume without losing nformation. The frequency slices are thus separated from these volumes and used for an nterpretation. n this study, three different methods were used to represent a buried channel. In the irst method, the numbers of the single frequency slices were investigated, variations of he frequency amplitudes in the slices were observed, and an expert interpreter could btain some information about the channel content and lateral variation. Since different requencies contain different types of information (low frequencies are sensible to hannel content and high frequencies are sensible to channel boundaries), none of the lices were able to show all information simultaneously. In the next two methods using a olor stacking method, the RGB plots were constructed which, due to the different requency content, resulted in more information than the frequency slice representation method. An RGB image, sometimes referred to as a true color image, is an image that defines red, green, and blue color components for each individual pixel and has an intensity between 0 and 1. In this study, RGB plots were constructed in two different manners, RGB plots based on conventional RGB plot methods and RGB plots using basis functions. In the conventional method, three different frequency slices were mapped against the red, green and blue components. Although this method obviates some drawbacks of the single frequency plots, it uses only three slices and practically ignores a big part of information. Using basis functions and defining windows, the interpreter was able to introduce some frequency intervals and plot them against the primary components and use the total bandwidth or its major part. Three simple raised cosine functions having different frequency centers and different periods were chosen. The image quality strongly depended on these two parameters. Longer window widths will introduce longer frequency widths into every primary component and resulted in smoother color combinations for images and very short periods had the same results as the conventional RGB plot method. Different centers showed different details. Low frequency centers showed channel content properties, and high frequency centers showed channel boundaries and fine branches.In this study, the spectral decomposition was first performed on land seismic data from an oil field in Iran using a short time Fourier (STFT) transform and an S transform. Then three demonstration methods were applied for channel detection. Finally it was shown that how RGB color stacking method represented buried channels in more precise images and how a basis function based RGB represents better results than the conventional RGB method.
    Keywords: Buried channels, spectral decomposition, color stack, short time Fourier transform, S transform, single frequency slices
  • Mohammad Reza Sepahvand, Farzam Yaminifard, Gholam Javan Doloie Page 73
    The Zagros mountain belt is approximately 1500 km long, 250–400 km wide, and runs from eastern Turkey, where it connects to the North and East Anatolian faults, to Oman Gulf, where it dies out at Makran subduction zone. The Zagros Mountains were formed by closure of the Neotethys Ocean and collision of Central Iran and Arabia plates. GPS studies estimate a convergence rate of 22 mm/yr between Arabian and Eurasian plates and the Zagros accommodates about 6.5 ± 2 mm/yr of the overall shortening in Iran. However this rate is not constant along the Zagros and increases from 4.5 mm/yr in the northwest to 9 mm/yr in the southeast. Changes in the rate and direction of convergence across the Zagros cause changes in its strike and diversity of the deformation mechanism. The Main Recent Fault (MRF) and the Main Zagros Reverse Fault (MZRF) are located in the northwest and northeast of the Zagros collision zone, respectively, in a suture zone between central Iran and the Arabian plate. Based on GPS and seismology studies, the MZRF is presently inactive. On the contrary, as evidenced by high seismicity and the occurrence of earthquakes with magnitudes as large as 7, like 1909 Doroud Earthquake, the MRF is one the major active strike-slip faults in the Middle East. Geological studies on the MRF fault have identified the fault segmentation and the existence of pull-apart basins. The Main Recent Fault strikes NW–SE and can be traced as a narrow, linear series of fault segments from near the Turkey–Iran border at 37N for over 800 km to the SE. Based on strain partitioning theory, the strike-slip MRF fault is a response to a horizontal component of oblique convergence between Arabian and Eurasian plates and Zagros’s reverse fold belt accommodates the vertical component of this convergence. Seismological studies based on the teleseismic data have limited the location accuracy because they rely on global velocity models. Therefore, microearthquake local studies complement the teleseismic information because they locate seismic events with an accuracy of a few kilometers which is an order of magnitude better than teleseismic locations. The 2006 Silakhur earthquake with a magnitude of 6.1 and its aftershocks recorded by a local seismic network provide a unique opportunity for a high resolution study of the Doroud section of the MRF. The results of the aftershock analysis are presented in this paper. After occurring March 31, 2006 Silakhur Earthquake, Mw 6.1, a temporary seismic network including 10 stations was installed by International Institute of the Earthquake Engineering and Seismology for nearly two months. An aftershock analysis revealed a wide zone of the aftershocks trending southeast northwest. Another trend in east-west direction was deduced from the epicentral distribution of the aftershocks in the west of the Boroujerd. Depth distribution of the aftershocks showed that the majority of the aftershocks located in 4-11 km depth range, verified the brittle crust uppermost layer in this part of the Zagros. Depth profile showed the northeast trending of the aftershocks. The spatial distribution of the b value showed low values in the northern part of the aftershock zone that its reason could be the higher stress concentration in this region relative to the southern part.
    Keywords: Aftershock, Silakhur, Zagros, b value, temporary seismological network
  • Meysam Zareie, Amin Roshandel, Hamid Reza Siahkoohi, Mehdi Sadeghi Page 85
    Time representation was the first way to describe a signal, and later on the frequency representation was introduced as another important way to describe a signal for its physical significance. Due to the non-stationary property of seismic data, time-frequency transform has to be used to analyze it. During the last decade, spectral decomposition techniques have proven to be an excellent tool to describe thin beds associated with channel sands, alluvial fans, and the like. However, with the traditional spectral decomposition method based on the short time Fourier Transform, it is difficult to acquire the accurate time-frequency spectrum for non-stationary seismic signals. Recently, the emergence of seismic attribute co-rendering, principal component analysis, cluster analysis, and neural networks has partially solved the problem, but the extraction of spectral attributes from spectral-decomposition tightly linked to the geology has more advantages over other approaches. Popular time–frequency methods have some disadvantages. A good time resolution requires a short window and a good frequency resolution require a narrow-band filter, i.e. a long window, but unfortunately, these two cannot be simultaneously realized. The Wigner-Ville Distribution (WVD) of a signal is the Fourier Transform of the signal’s time-dependent auto-correlation function, a quadratic expression which is bilinear in the signal. As a result, the cross-terms appear in the locations of the resulting time-frequency spectra that either interfere with the interpretation of auto-terms or for which we can provide no physical interpretation. Due to the existence of cross-terms, WVD is not often used. Reduction of the cross-terms is achieved by manipulating the ambiguity function as a mask that reduces the cross-terms while preserving the time and frequency resolution of WVD. The short-time Fourier Transform (STFT) spectrogram, which is the squared modulus of the STFT, is a smoothed version of WVD. An STFT spectrogram is a 2-D convolution of the signal WVD and the utilized window function. In this paper, we introduce a Deconvolutive Short-Time Fourier Transform (DSTFT) spectrogram method, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram. Compared to the STFT spectrogram, the spectrogram obtained by this method shows a significant improvement in the time-frequency resolution. In this study, we extract two attributes namely the peak frequency and the peak amplitude, based on the Deconvolutive Short- Time Fourier Transform. The maximum frequency attribute is directly related to the thickness of the thin-bed, like channel, and the maximum amplitude attribute also responds to the thin-bed. We use instantaneous seismic attributes: maximum instantaneous frequencies and their associated amplitudes, as a tool to detect seismic geomorphologic bodies and to identify thin layers. Then we use attributes extracted by Deconvolutive Short Time Fourier Transform to detect the burial channel in both synthetic and real 3D seismic data. Usually, the center of the channel is recognized by the lower maximum frequency and when the thickness of the channel gets thinner away from the center of the channel, the maximum frequency increases correspondingly. Therefore, this attribute could clearly describe the distribution of channel both vertically and horizontally. Results of this study on the synthetic and real seismic data examples illustrate the good performance of the DSTFT spectrogram compared with other traditional time-frequency representations.
    Keywords: Time, frequency transform, spectrogram, resolution, deconvolutive short time Fourier transform, 2D convolution, seismic attributes, burial channels
  • Vahid Maleki, Zaher Hossein Shomali, M. Reza Hatami Page 96
    Major earthquakes are often associated with large earthquakes which have a magnitude smaller than the main shock known as aftershocks. The occurrence of aftershocks with different magnitudes and times is a random process and therefore in the area affected by the main shock, it can cause greater damage than the main shock, and hence they are very important. Study of aftershocks can be useful to get information from tectonic activites and causative faults. Many studies have considered the aftershocks of large earthquakes, such as Omori (1894), Otsu (1961) and kisslinger (1996). Among the aftershock studies, the exact relocation of the main earthquake and its aftershocks help us find the causative fault and the releasing energy associated with that fault. Many studies have used relocation methods to examine the aftershocks. Some of these methods are Hong et al (2008), Hugh et al (2009) and Zhao et al (2011). Due to the complexity of the earth sub-layers and the three-dimensional structure of the crustal velocity and also the seismic wave path from the source to stations, there is a nonlinear relationship between the arrival time of seismic waves at the stations and the hypocenter of the earthquake. In order to simplify the earthquake location problem solving, most methods and programs use linearized relationships. Most of these methods and algorithms are based on the Geiger’s principles (Geiger, 1912). Using the linearized relationships reduces the accuracy of earthquake location due to losing the higher terms of Taylor series. It may also lead to failure in determining the location of earthquakes using a suboptimal network, e.g. where the earthquake is located outside the seismic network. Thurber (1985) showed that when the depth of an earthquake was smaller than the closest distance to the station, determining the focal depth was not possible in linearized methods. Furthermore, using higher terms of Taylor series is required to calculate higher degree derivatives, which are very complex and sometimes impossible, using a three-dimensional velocity model. In order to avoid calculating the partial derivatives, Tarantola and Valette (1982) presented a method that determines the location of earthquakes with fully non-linear relationships with no need to calculate the partial derivatives. The basic theory of nonlinear probabilistic method to determine the location of the earthquakes was introduced by Tarantola and Valette (1982) and Tarantola (1987). In this study, we used a nonlinear probabilistic method based on Tarantula and Valette theory and NonLinLoc program (Lomax et al, 2000) to relocate the earthquakes. The Rigan earthquake with Mn = 6.5 occurred on Dec 20, 2010 in the Southeastern region of Iran. After this earthquake, a lot of aftershocks occurred in this area which in some cases the magnitude of aftershocks was in order of the main shock. The largest aftershock with a magnitude Mn = 6.0 occurred after 37 days which itself included a lot of aftershocks. To improve the quality of data, in this study we combined the arrival time data from the Iranian Seismological Center (IRSC) stations and the data from the International Institute of Seismology and Earthquake Engineering (IIEES). Due to the lack of proper station coverage in the southeastern region of Mohammad Abad Rigan, we added IIEES stations data in this area which greatly helped us increase the station coverage. Regarding the lack of a proper regional velocity model in the Eastern and the Southeastern regions of Iran, we used Tatar et al (2003) local velocity model and determined the depth of Moho based on Dehghani and Makris (1983) study in an order of 55 km. In this study, we used Omori’s law to specify the energy release in the media and occurrence of aftershocks chronologically.We found that a large number of aftershocks have occurred in two different time windows near the two large earthquakes; in this regard, we divided the data based on these two time windows. The first time window contained the main shock with Mn = 6.5 and aftershocks until the occurrence of second earthquake with Mn = 6.0. The second time window contained the second earthquake Mn = 6.0 and its aftershocks.In order to get good results, we considered those earthquakes recorded at least by five stations. Finally, we could relocate 222 aftershocks out of 296 aftershocks associated with Rigan area. The relocation results of the earthquakes showed that the two main earthquakes and their aftershocks were distributed in the epicenter and the focal depth separated completely. They also showed two different fault trends. Relocated aftershocks in the first time window showed a fault trend parallel to Kahurak Fault, and aftershocks with Mn > 4 in the second time window showed a fault trend parallel to Kahurak fault.
    Keywords: Relocation, Nonlinear method, Aftershock, Rigan attributes, burial channels
  • Malihe Sadat Kazemi Page 112
    Seismic velocities in rocks are used as indicators of their petrophysical properties. Vp/Vs has been used for many purposes, such as a lithology indicator, degree of consolidation, identifying pore fluid, and predicting velocities. The velocity ratio (Vp/Vs) usually depends on porosity, degree of consolidation, pore geometry and other factors. Vp/Vs is used as a lithology indicator for hydrocarbon detection. This ratio decreases with gas saturation. The Vp/Vs crossplot is used to identify fluid type based on the fact that shear wave velocity is more sensitive than the P-wave velocity due to the fluid effect. Two multicomponent measurements are important for gas exploration. These include Vp/Vs ratio and anisotropy behavior (Rojas, 2005). The results from laboratory and dipole sonic log data analysis showed that lithology has a significant influence on Vp/Vs ratio. Castagna, et. al. (1985) presented some empirical relation between P- and S-wave velocities. Wang (2000) developed an empirical equation that predicts S-wave velocity using the bulk density of the saturated rocks, the pore fluid modulus and the P-wave velocity. Brocher (2005) reviewed the existing Vs as a function of Vp, and proposedseveral new empirical relations based on a wide-variety of common rock types. When there is no shear wave log for a well, we must estimate Vs from Vp with correlation relations. Shear wave velocity associated with compressional wave velocity can provide accurate results for geophysical study of a reservoir. These studies have important role in reservoir characterization such as lithology determination, identifying pore fluid type, and geophysical interpretation. Vp/Vs is sensitive to gas in most clastic rocks and will often show a decrease due to its presence. Besides, shear wave velocities are much more sensitive to fractures than the P-wave velocity. Dipole sonic tools such as DSI are designed to excite both compressional and flexural energy in the borehole and are thus able to directly measure both compressional and shear wave speeds in all type of formations. A dipole source excites the borehole flexural mode that provide a means to determine shear wave velocities. Wave velocities and attenuation are two important properties that provide information about the saturation of the reservoir rocks. In general, by going deeper, the formation becomes harder and more rigid, with both Vp and Vs increasing and Q factor becoming higher. Generally, a high attenuation corresponds to a low velocity and a high Vp/Vs. The attenuation effects are directly related to the quality factors QP and QS as well as the QP/QS ratio. QP is noticeably affected by the presence of hydrocarbons. The ratio of the quality factors (QP/QS) is large in wet rocks and small in the gas zones. In this study, the log data for two wells from the South Pars gas field and the analysis of DSI in one of the wells are used to develop relationships between Vp and Vs. However, in order to apply the relations obtained between elastic properties of the rocks and petrophysical properties, it turns out to be necessary to calculate the elastic properties from seismic data, such as Vp/Vs. When there is no shear wave log for a well, we have to estimate Vs from Vp with correlation relations. In a well (well I) relationships between Vp and Vs near the walls of a borehole for Kangan (K1 and K2) and Dalan (K3 and K4) Formations of South Pars field are determined. The P- versus S-wave velocity crossplot for all layers, show very good correlations. Correlation relations between Vp and Vs could be used for two other wells (II and III) in which Vs was obtained with Castagna’s relation. The Q factors are obtained in the wells II and III as well.S-wave velocity estimation based on Vp could be used for regions wherein we have no core sample and DSI data. Also, the relations between Vp and Vs for other parts of this field are obtained by estimation of S-wave velocity. Finally, the relation between P- and S- wave velocities are obtained from DSI in comparison with Castagna’s relation. A good relation between Vp/Vs and QP/QS is then found based on the Vs used from DSI.
    Keywords: Vp, Vs ratio, DSI, correlation relations, Castagna relation, Q factor, QP, QS ratio