Pseudo 2D inversion of frequency-domain helicopter-borne electromagnetic data based on damped Occam’s inversion (2D-DOInv) method

In this paper, we examine the applicability of a pseudo two-dimensional (2D) inversion technique, called 2D-DOInv, on a layered earth model, to a frequency-domain helicopter-borne electromagnetic (FDHEM) dataset. In this scheme, a one-dimensional (1D) inversion is modified with 2D Occam’s smoothness constraints between 1D models of adjacent sites in addition to the vertical smoothing. By incorporating the vertical and horizontal weighting factors in the regularization matrix, we obtain more stable solution and geologically more realistic results. Unlike 1D Occam’s inversion, in the 2DDOInv algorithm, the data of all stations along a flight line are simultaneously inverted by minimizing a common objective function. In this inversion algorithm, we are able to incorporate the inequality constraints. The inversion scheme can be parallelized using multiple processors in a single computer. To validate the algorithm, we consider synthetic responses generated over known 2D targets, a buried valley structure and a two-layer earth containing heterogeneous overburden. In comparison to the 1D Occam’s inversion, the 2D-DOInv algorithm estimates pseudo 2D cross section of subsurface resistivity structure, and efficiently reduces the effects of the multidimensional modeling cost and data noise. Finally, this inversion is applied on the real data in Kalat-e-Reshm area of Semnan Province, Iran. The resulting inverted parameters using the proposed algorithm correspond reasonably close to the known geology and to the results from electrical resistivity tomography (ERT) data inversion.

The FDHEM applications are industrially feasible, as long as there is a fairly fast algorithm, yet accurate enough for inversion of a tremendous amount of survey data to model near surface resistivity variations. Currently, the only way to invert such large amounts of data in the field is by utilizing a 1D approximation. The 1D inversion often leads to a series of stitched 1D models that can be misleading, since real data inherently consist information about more than one dimension. Unfortunately, multidimensional modelling has been limited by the computational expense. In this paper, we present a 2D smooth regularized inversion based on a 1D forward modelling with a particular pair of regularization coefficients that simultaneously guarantees the stability and best-fit criteria. All data and 1D models along a flight line are inverted together, giving pseudo 2D sections of the subsurface.

Here, the forward modeling routine is based on the 1D assumption in which the thicknesses of layers are fixed and increase logarithmically with depth. To implement the inversion procedure of 2D-DOInv, the 2D model is discretized with M by N blocks of constant resistivity, where the parameter vector is of length M, the data vector is of length N. In this inversion, the model regularization function is improved to smooth the resistivity model by incorporating separate vertical and horizontal smoothing factors in the regularization matrix R. To further stabilize the inverse problem, we introduce the inequality constraint using the transformation of the model parameter vector. The algorithm can parallelize computations using multiple processors on the same computer to make the inversion scheme very large scale and quick. 1D and 2D damped Occam’s inversions, which are developed in MATLAB environment, are first applied on the synthetic data sets obtained from two 2D models. Compared to the 1D damped Occam’s inversion, 2D-DOInv recovers fairly accurate 2D synthetic models from noisy data. Finally, the 2D-DOInv approach is applied on the field data.

In this paper, we have developed a pseudo 2D inversion in MATLAB environment. This inversion technique, named 2D-DOInv, is used to invert FDHEM data. 2D constrained inversion of both synthetic and field data certainly improves the 1D Occam’s inversion results of quasi-layered earth structures, although the misfit is higher. Even in case of noisy data, we can filter out the influence of the noise using our smooth regularized inversion technique, and enhance the resolution of the subsurface resistivity images. Thus, this technique can suppress both the measurements and the processes errors. For non-layered earth structures, e.g. the two-layer model comprising of a heterogeneous overburden that is common in weathered crystalline terrains; however, the reconstructed 2D pseudo section will be blurred as a result of excessive horizontal smoothing. Through this method in which the horizontal constraint is chosen to be relatively weak in the top layer, 2D-DOInv still improves the inversion results and mitigates 2D/3D effects. The example of measured data sets from a DIGHEM survey carried out over Kalat-e-Reshm area demonstrates the capabilities of the algorithm reasonably. We can see reasonable correlations between the pseudo 2D resistivity models from FDHEM data inversion and ERT 2D resistivity models.