عنوان پایان‌نامه
وارون سازی تصادفی سه بعدی داده های گرانی با استفاده از کوکریجینگ
- رشته تحصیلی
- ژئوفیزیک-گرانی سنجی
- مقطع تحصیلی
- کارشناسی ارشد
- محل دفاع
- کتابخانه مرکزی -تالار اطلاع رسانی شماره ثبت: 76843;کتابخانه موسسه ژئوفیزیک شماره ثبت: 1302;کتابخانه مرکزی -تالار اطلاع رسانی شماره ثبت: 76843;کتابخانه موسسه ژئوفیزیک شماره ثبت: 1302
- تاریخ دفاع
- ۰۴ خرداد ۱۳۹۵
- دانشجو
- منصوره خالقی یله گنبدی
- استاد راهنما
- وحید ابراهیم زاده اردستانی
- چکیده
- مدل سازی مرحله ای از تفسیر داده های گرانی به شمار می آید که هدف تعیین شکل دوبعدی یا سه بعدی توده زیرسطحی به همراه تباین چگالی آن باشد. اما با توجه به اینکه وارون گرانی‌سنجی از نوع مسائل بد وضع است، در حل این مسایل با عدم یکتایی و عدم پایداری جواب مواجهیم. امروزه استراتژی های زیادی برای رفع مساله عدم یکتایی و ناپایداری جواب ها وجود دارد. در هر یک از این روش ها با اعمال قید در روابط وارون سازی، یا از طریق منظم سازی تعداد پاسخ ها را محدود و آن ها را پایدار می کنند. به همین منظور در این تحقیق یک روش وارون سازی سه بعدی بر اساس دانش زمین آمار با استفاده از الگوریتم تصادفی تحت عنوان کوکریجینگ ارائه می شود. یکی از مزیت های اصلی روش کوکریجینگ این است که می توان از آن در مواقعی که داده چگالی کمی در اختیار است و یا داده چگالی نداریم تنها با استفاده از داده های گرانی توده های زیرسطحی را مدل کنیم. الگوریتم روش کوکریجینگ به زبان برنامه نویسی Matlab توسط نگارنده نوشته شده و نتایج روش از طریق این کدها روی داده های مصنوعی (بدون نوفه و با نوفه) و داده های واقعی مربوط به سایت معدن منگنز صفو و نیز سایت دهنو آزمایش شده است. نتایج حاصل با نتایج مربوط به حفاری و سایر روش های ژئوفیزیکی همخوانی و تطابق قابل توجهی دارند.
- Abstract
- In this paper the 3D inversion of gravity data for determination of models of subsurface density distribution using a geostatistics method of Co-kriging is considered. Co-kriging is a mathematical interpolation and extrapolation tool that uses the spatial correlation between the secondary variables and a primary variable to improve the estimation of the primary variable at un-sampled locations. The Co-kriging method gives weights to data so as to minimize the estimation variance (the Co-kriging variance). In this paper, the primary variable is density, (estimated by ?*) and the secondary variable is gravity g. For determination of kernel matrix the subsurface under the survey area is divided into large number of rectangular blocks of known sizes and positions. The unknown density contrasts within each prism define the parameters to be estimated. In addition, the weighting matrix also has been used in order to prevent mass shrinkage to the surface. Preconditioned Conjugate Gradients method is used for inversion. The computer program is written in MATLAB and tested on synthetic data produced by a cube. The results indicate that the geometry and density of the reconstructed model are close to those of the original model. The gravity data acquired over the Safo mining camp in the north-west of Iran, which is well-known for manganese ores, are used as a real modeling case. The results show a density distribution in the subsurface from about 5 to 35-40 m in depth, which are close to those obtained by bore-hole drilling on the site. Introduction In gravity inversion we have two problems: non-uniqueness and non-stability of solutions. The first happen for two reason. The first reason is known as the theoretical ambiguity of the unknown nature of potential theory. The second reason is known as algebraic uncertainty is considered, when it comes to the number of parameters is greater than the number of observations at ground level. A second problem is caused by two reasons, first because of bad condition (ill-condition) kernel matrix and the second due to the presence of noise in the data. For finding an answer that it is unique and has the necessary stability, we must add constraints in the objective function and then we must minimize the new objective function that replaced the initial objective function. Methodology and Approaches For determination of kernel matrix the subsurface under the survey area is divided into large number of rectangular blocks of known sizes and positions. The unknown density contrasts within each prism define the parameters to be estimated. This kind of parameterization is flexible for the reconstruction of the subsurface model, but requires more unknown model parameters than observations (here N << M, where N is the number of data and M is the number of model parameters). Because of this type of inversion is stochastic, the objective function involve the gravity covariance matrix and the density covariance matrix for uncertainty in the data and the uncertainty in parameters respectively. In this study, The necessary gravity, density, and gravity-density covariance matrices are estimated using the observed gravity data. Then the densities are Co-kriged using the gravity data as the secondary variable. The co-variances Cgg and Cg? are not stationary even on a horizontal plane due to the limited lateral extension of the underlying density model. The non-stationary nature of the gravity-gravity and gravity-density co-variances presents a problem for statistical inference. Thus, traditional estimators such as variograms cannot be used directly, and the model parameters for density covariance must, themselves, be estimated by inversion. We used the V-V plot approach which enables immediate generalization to the non-stationary case. Results and Conclusions By applying the method on a single cube in states of without and with random noise, good results achieved in the density and depth of the cube. By applying the method on actual data in manganese mine site (Sfv) was observed that the results in terms of depth and density in good agreement with data obtained from drilling and other geophysical methods implemented in the region. Also the underground shape was recovered well.
