استفاده از روش کوادراتیک در مدلسازی وارون دوبعدی داده‌های گرانی به منظور ارائه یک مدل بهبودیافته

وارون‌سازی داده‌های گرانی یکی از مهم‌ترین گام‌ها در تفسیر این داده‌ها است. هدف از این کار تخمین توزیع چگالی مدل ناشناخته زیر سطحی از طریق داده‌های اندازه‌گیری شده در سطح زمین است. مشکل اصلی در وارون‌سازی داده‌های حاصل از عملیات گرانی‌سنجی، عدم یکتایی جواب ناشی از وارون‌سازی داده‌های ژئوفیزیکی است. وارون‌سازی خطی داده‌های گرانی‌سنجی مسئله‌ای کم تعیین شده و بد حالت است. تعیین پارامتر منظم‌سازی بهینه در وارون‌سازی داده‌های گرانی از اهمیت فراوانی برخوردار است. یکی از این روش‌ها، روش اعتبارسنجی متقاطع تعمیم‌یافته (gcv) است. در این پژوهش از روش برنامه‌نویسی درجه دو (روش کوادراتیک) به عنوان یک روش بهینه‌سازی استفاده شده است. این روش دارای سه الگوریتم، منطقه اعتماد، نقطه داخلی و مجموعه فعال است. این سه الگوریتم از نظر مدت زمان اجرای وارون‌سازی و همچنین میزان پایداری هر یک از این الگوریتم‌ها در مقابل نوفه بررسی خواهند شد. به منظور اعتبارسنجی روش ارائه شده، از داده‌های گرانی حاصل از دو مدل مصنوعی و داده‌های گرانی ذخیره سولفیدی سن‌نیکلاس واقع در کشور مکزیک استفاده شد.

The Using of a Quadratic Method in the 2D Inverse Modeling of Gravity Data to Achieve an Improved Model

SummaryThe inversion of gravity data is one of the most important steps in the interpretation of these data. The purpose of this work is to estimate the distribution of the unknown subsurface model by the measured data on the ground. The main problem in the inversion of the data obtained from the operation of the gravity survey is the nonuniqueness response due to the inversion of geophysical data. Linear inversion of gravity data is an underdetermined and badcondition. It is important to determine the optimal regularization parameter for the inversion of gravity data. One of these methods is the Generalized CrossValidation (GCV). In this research, the quadratic method has been used as an optimization method. IntroductionInversion of gravity data is one of the most important steps in the interpretation of practical gravity data. The goal of inversion is to estimate the density distribution of an unknown subsurface model from a set of known gravity observations measured on the surface. Inversion of gravity data is an underdetermined and illposed problem. In addition, the nonuniqueness of the solution is the main issue of the inversion. One way to achieve a suitable model result in the inversion is to carry out the inversion with smoothness and smallness constraints. The solution can then be obtained by minimization of an objective function that consists of a misfit function and one of Tikhonov regularization functions. The regularization parameter makes a tradeoff between misfit and regularization function. The determination of an optimal regularization parameter is highly important in gravity data inversion. There are different methods for automatic estimation of the regularization parameter in inversion. The GCV method is one of the most popular methods for choosing optimal regularization parameters in the inversion of gravity data. Methodology and ApproachesIn this paper, we use the quadratic method to minimize the Tikhonov objective function. Also, in order to obtain the regularization parameter of the generalized crossvalidation (GCV) method. The GCV method has been adapted for the solution of inverse problems. The basic idea for GCV is that a good solution to the inverse problem is one that is not unduly sensitive to any particular datum. In this method, the optimal regularization parameter minimizes the GCV function. We have developed an algorithm for 2D inversion of gravity data that uses the GCV method for choosing optimal regularization parameter, and then, the inverse problem is solved by the quadratic algorithm. To evaluate the reliability of the introduced method, the gravity data of a synthetic model contaminated by 5 percent random noise have been inverted using the developed method. Finally, The introduced algorithm has been used for 2D inversion of gravity data from San Nicolas massive sulfide deposit. The results are consistent with geological information. Results and ConclusionsIn this paper, the GCV method has been developed for choosing the optimal regularization parameter in 2D constrained inversion of gravity data using the quadratic algorithm. Data from the synthetic model have been inverted using the introduced algorithm and acceptable results have been obtained. The geometrical parameters of the synthetic model have been obtained from the inversion process with acceptable accuracy. After validation of the algorithm performance on the synthetic model, it has been applied for 2D inversion of gravity data from San Nicolas massive sulfide deposit. The results of geological information in the area confirm the results of the 2D inversion.