Improving the results of singular value decomposition inversion using direct transformation of frequency-domain HEM data



 Helicopter-borne electromagnetic (HEM) is a fast and high resolution airborne electromagnetic (AEM) method that is frequently used for imaging of the subsurface resistivity structures. This is a versatile and cost effective method, frequently has used in mineral and groundwater exploration and various environmental problems. Modern frequency-domain HEM systems utilize small electromagnetic, magnetic, Global Positioning System (GPS) and laser altimeter sensors which are encapsulated in a “bird”, a cigar-shaped 9 m long tube, which is kept at about 30–40 m above the ground level. Separation between the rigidly mounted transmitter and receiver coils typically lies between 4 and 8 m. The modern HEM systems use a multi-frequency devices operating at 4–6 frequencies, ranging from 200 Hz to 200 kHz. In this method, a sinusoidal current flow through the transmitter coil generates a primary magnetic field at a frequency that is very close to a dipole field at some distance from the transmitter coil. The primary oscillating magnetic field induces eddy currents in the subsurface of the Earth. These currents, in turn, generate a secondary magnetic field, which is related to the Earth resistivity distribution. The receiver coils measure the induced secondary magnetic field with respect to the primary magnetic in parts per million (ppm). Due to the induction process of the Electromagnetic (EM) field, there is a small phase shift between the primary and secondary fields. In practice, the transmitter coil is horizontal (VMD: vertical magnetic dipole) or vertical (HMD: horizontal magnetic dipole) and the receiver coil is oriented in a maximally coupled position, resulting in horizontal coplanar (HCP), vertical coplanar (VCP), or vertical coaxial (VCA) coil systems.
The final results of the frequency domain HEM data are normally presented in the form of resistivity maps in various frequency or depth levels or as resistivity depth sections along the survey lines for interpretation. The vertical resistivity sections are constructed by concatenating the resistivity models for every measuring point along a survey line. Several methods have been developed to prepare these resistivity maps or depth sections. Many techniques have been developed to model the measured HEM data during the recent 35 years. They are classified into two general groups: (1) direct transform of the data into a generalized model such as a half-space, and (2) inversion of the data to a specific model such as a layered Earth, for which a starting model is used, followed by iterative fitting of the data in the least-squares sense.
In the direct transformation approaches (e.g. Sengpiel (1988) and Siemon (2001) centroid depth method), upon the calculation of the centroid depth and apparent resistivity values for each frequency, a vertical pseudo-section of the resistivity is created by concatenating the resistivity-depth  curve (smooth model) for each point of a survey line. In these schemes an approximate resistivity model is quickly acquired without a need of a starting or initial resistivity model. In the iterative inversion methods, however, the EM data are modeled inversely using a starting model to get a precise resistivity model. The final outputs of these inversion techniques are highly dependent on the correct selection of the starting model. One of the most effective and accurate methods is the layered earth inversion using the Levenberg-Marquardt (LM) technique based on the singular value decomposition (SVD). Despite the high capability of this inversion technique, it has not been used for modeling of the HEM data in Iran. Because of this reason, this paper aims to verify the accuracy of the final inversion results of the HEM data using various choice of a starting model. Here the required inversion computer codes were developed in the Matlab software. This inversion routine was tested on noise-free and noise-contaminated synthetic data of layered and 3-D models. The obtained results indicate that the final resolved model is in a great accordance with the true model in each case. In addition a set of real HEM data, in south parts of Damghan city in Semnan Province, has finally been inverted with this program, and its results have been compared with those obtained with the direct transformation methods. Results show that the SVD inversion may go to the wrong path when there is not a good starting model. Results also indicate that if the Sengpiel or Siemon centroid depth resistivity models are used as the starting model of the SVD inversion, the final resistivity models would be superior to the final resistivity models obtained by the staring models, yielded by the other direct transformation methods.