تخمين عمق به روش جديد اويلر RDAS و مقايسۀ آن با نتايج مدل‌سازي؛ مطالعۀ موردي: داده‌هاي گراني معدن هماتيت

Depth estimation using the new method of Euler RDAS and comparison with modelling results, Case Study: gravity data of hematite mine

تخمين عمق ساختارهاي زمين‌شناسي يكي از مهم‌ترين اهداف مطالعات ژئوفيزيكي است. واهماميخت اويلر (اويلر استاندارد) يكي از روش‌هاي معروف و پركاربرد در تخمين عمق است. بر پايۀ اويلر استاندارد روش‌هاي متنوعي براي كاهش خطاي تخمين عمق معرفي شده است. در اين پژوهش از روش جديدي به نام اويلر RDAS استفاده شده است. اين روش با استفاده از اويلر استاندارد به دست مي‌آيد و بر پايۀ گراديان اول قائم و مشتقات سيگنال تحليلي استوار است. بررسي داده‌هاي گراني مصنوعي نشان مي‌دهد كه اويلر RDAS، در تخمين عمق اين داده‌ها، خطاي كمتري از اويلر استاندارد دارد. همچنين از اين دو روش براي تخمين عمق داده‌هاي گراني ناشي از تودۀ هماتيت، واقع در استان كرمان، استفاده شده است. جواب‌هاي اويلر RDAS در مقايسه با اويلر استاندارد انطباق بيشتري با مرز آنومالي‌ها دارد و همچنين براي هر آنومالي، جواب‌ها در بازۀ قائم كوچك‌تري قرار دارند كه مي‌تواند ملاكي براي دقيق‌تر بودن جواب‌هاي اويلر RDAS باشد. براي بررسي بيشتر با استفاده از وارون‌سازي به روش كاماچو داده‌هاي گراني معدن هماتيت مدل‌سازي شده است. افزون بر اين، نتايج مدل‌سازي با نتايج تخمين عمق اويلر مقايسه شده است. در اين مقايسه 10 نقطه برروي آنومالي‌ها مشخص شده و عمق دقيق آنومالي‌ها براي اين نقاط نشان داده شده است. خطاي ميانگين مجذور مربعات بين جواب‌هاي اويلر و مدل‌سازي محاسبه شده است. اين خطا، بين اويلر RDAS و مدل‌سازي، كمترين مقدار است كه نشان مي‌دهد جواب‌هاي اويلر RDAS به جواب‌هاي مدل‌سازي نزديك است. بنابراين مي‌توان گفت جواب‌هاي اويلر RDAS و مدل‌سازي از اويلر استاندارد دقيق‌تر است.

Depth estimation of geological structures is one of the most important objectives in geophysical studies. Euler deconvolution (standard Euler) is a well-known method in the depth estimation. Based on standard Euler, various methods are introduced to reduce error of the depth estimation. In this study we have used a new method called Euler RDAS. This method is based on the standard Euler. In this method derivatives of analytic signal and first vertical are used in Euler equation. Applying derivatives of analytic signal for depth estimation is better than the analytic signal. There is no problem of choosing structural index in this method which increases accuracy in the depth estimation. To examine the performance of this method, depths of several synthetic models are estimated and their results are compared to that of the standard Euler. In all models, results of the RDAS Euler shows fewer errors in high depth model in comparison to that of the standard Euler. This method was tested on synthetic data with noise. RDAS Euler sensitive to noise due to usage of high-degree derivatives is less than the standard Euler. Study shows that if the noise in the data is reduced by methods such as filter upward, it can provide an appropriate estimate of the depth. In this study, the depth of gravity anomalies caused by the masses of hematite located in Kerman, has estimated using standard Euler and RDAS Euler. Upward continued by 3 m has been used for reducing noise in this data. There are 3 possible hematite masses in residual map of the study area. The minimum of high depth anomalies indicates masses of hematite, which is calculated using RDAS Euler and was about 5 meters and a maximum of high depth is about 20 meters. The minimum depth obtained using standard Euler for this anomaly is about 5 meters and the maximum depth is about 40 meters. Responses of RDAS Euler is more compatible that of standard Euler with the boundary anomalies and has smaller vertical interval which can be a criterion for more precise solutions of the RDAS Euler. For further examination, the gravity data of hematite mine is used with inverse modeling of Camacho method. Minimum and maximum upper depths obtained for these anomalies are 5 to 35 meters, respectively. In addition, the modeling results is compared with the results of depth estimation of Euler. To this, 10 points in the anomalies area are pointed and the calculated depth of these points using standard Euler, RDAS Euler and modeling are shown. Root mean square error (RMS) between Euler’s and modeling results is calculated. In comparison of the results in different methods, which are not standard, results of two methods that have the lowest RMS error is considered as the selection criteria. RMS for standard Euler with MATLAB code, Geosoft, and RDAS Euler are equal to 11.43, 8.5, and 2.66 respectively. The results of two methods among these three methods which are used to estimate the depth of hematite masses are close hence they can be more reliable results. Therefore, due to fewer errors of RMS of RDAS Euler and modelling results are more accurate than that of the standard Euler.