مقايسه تبديل مستقيم و معكوس داده‌هاي الكترومغناطيسي هوابرد حوزه بسامد براي يك مدل زمين لايه‌اي

A comparison between the direct transform and the inversion of AEM data in frequency domain for a layered earth

محاسبات رياضي براي به‌دست آوردن ساختارهاي مقاومت ويژه الكتريكي از داده‌هاي الكترومغناطيسي با در نظر گرفتن زمين به‌صورت سه‌بُعدي بسيار پيچيده هستند. با در نظر گرفتن مدل زمين سه‌بُعدي به‌صورت مدل‌هاي ساده‌تر از يك طرف پيچيدگي محاسبات كمتر مي‌شود و از طرف ديگر بخشي از اطلاعات از دست مي‌رود. اما به‌هرحال براي اينكه فهميده شود كه كداميك از اين فرض‌ها يا مدل‌هاي در نظر گرفته شده به واقعيت نزديك‌تر هستند بايد بين آنها مقايسه‌اي صورت گيرد. در اين مقاله دو فرض براي زمين در نظر گرفته شده است: 1) فرض زمين همگن كه مقاومت ويژه و عمق براساس اين فرض با استفاده از تبديل داده‌ها به‌دست مي‌آيد و 2) فرض زمين لايه‌اي كه مقادير مقاومت ويژه با استفاده از فرايند معكوس‌سازي محاسبه مي‌شوند. نتايج بررسي‌ها روي مدل مصنوعي نشان مي‌دهد كه فرض زمين همگن، در سطح زمين مدل‌هاي نزديك به واقعيت را به‌دست مي‌دهد و در عمق دچار انحراف مي‌شود؛ درحالي‌كه مدل زمين لايه‌اي، هم در سطح و هم در عمق، پاسخ‌هاي بسيار بهتري به‌دست مي‌دهد. مقايسه مقاطع به‌دست آمده از داده‌هاي واقعي هم تاييد مي‌كند كه با فرض زمين به‌صورت لايه‌اي، ساختارهاي بيشتر با قدرت تفكيك بيشتري به‌دست مي‌آيد.

Over the past three decades helicopter-borne electromagnetic (HEM) measurements have been used to reveal the resistivity distribution of the earthʹs subsurface for a variety of applications where knowledge of the electrical properties of the earth is important. HEM systems include a “bird” or sensor containing one or more pairs of transmitting and receiving coils. The separation between the rigidly mounted transmitting and receiving coils of a coil-pair typically lies between 4 and 8 m. The EM bird is towed under the helicopter by a 30–50 m long cable. This distance is optimum to minimize the helicopter effects. The modern HEM systems use a multi-frequency devices operating at 4–6 frequencies ranging from 200 Hz to 200 kHz. The receiving coil measures the voltage induced by the primary ?eld from the transmitting coil and by the secondary ?eld from the earth. As the secondary field is very small compared to the primary field, the primary field is generally bucked out and the ratio between the secondary and primary fields is presented in ppm. If there are good electrical conductors below the measuring line there are electrical current induced give rise to a phase shift between the primary and secondary field. This means that the measured data is a complex quantity having in-phase and quadrature components. There are two classes of interpretation tools to apply to HEM data that provide information to understand geological structures and processes. These are either direct transformation of data into a generalized half-space model at certain data frequencies, or inversion of multi-frequency data sets to prepare a layered (1-D) resistivity model of the earth. In the transform method, the earth is assumed as a homogeneous half-space and then the resistivity of such an earth for each of data- associated to each frequency- is calculated. So, this method has the advantage of yielding a single solution for the given output parameter, and the disadvantage that the output parameters may provide a poorly resolved image of the geology. In the inversion method used here, the earth is divided to some horizontal layers and each layer has its own resistivity and thickness. So, this method has the advantage of yielding a much better resolution for the given output parameter and the disadvantage that this method are slower compared to transform methods. In this paper we compare the results using two methods for synthetic and real HEM data. Results from synthetic data show that the inversion method reveals more real structures than the transform method. On the other hand, because the calculated resistivity from transform method is proportional to the imaginary to real component ratio of secondary field at the same frequency, we can just have the number of resistivity values equal to the number of frequencies. But in inversion methods, we can increase the number of layers and get models with more resolution than models created by transform methods. Besides, because transform methods uses a homogeneous half-space to calculate the resistivity for each frequency, the calculated resistivity is an average resistivity of subsurface structures. However, the results from both methods are comparable at the surface. This is because of the fact that higher frequency EM signals cannot penetrate much into the ground, the resistivities associated with these high frequency secondary signals are about surface layers. Applying the methods on real data confirm that the inversion method creates more reasonable models with better resolution than the models obtained using the transform method. Moreover, the models from inversion method can discriminate a resistive layer beneath the conductive layer much better than the models using transform method. The results from this survey reveal that the inversion method yields better models than the transform method. But if the main aim of the field work is a reconnaissance work, not an exact exploration work, the transform method is proposed because its calculations are much lower than the inversion method.