Recovering 1D conductivity from AEM data using Occam inversion

Over the past three decades helicopter-borne electromagnetic (HEM) measurements have been used to reveal the resistivity distribution of the earth's subsurface for a variety of applications. 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. Because the distance between transmitter and receiver coils in the bird is much smaller than the altitude of the bird (typically more than 30 m), we can use magnetic dipole approximation for the transmitter coil. This approximation allows the ease of primary and secondary magnetic field calculations. The EM bird is towed under the helicopter to minimize the helicopter effects. The modern HEM systems use 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 field 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 will be electrical currents induced and 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 for use to better 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. Transform methods have 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. On the other hand, inversion methods have the advantage of yielding a much better resolution for the given output parameter and the disadvantage that these methods are slower compared to transform methods. Inversion methods for the interpretation of HEM data for a layered earth are being employed more commonly for helicopter-borne surveys as the data quality is improved and as both the number of frequencies and computer speed are increased. A considerable number of papers exist on the inversion methods used to model the resistivity of a layered earth. These algorithms are useful in conditions where resistivity is locally uniform in the horizontal direction over distances comparable to the footprint of the transmitter. However, if the scale length of the structural variation is small, then differences between the 1-D and 3-D responses will be a problem for the 1-D inversion. The violation of the 1-D assumption may make the recovered models unreliable for interpretation in particular areas of the survey. However, due to the limited extent of the HEM footprint which is less than 200 m in general, one-dimensional inversion of HEM data is often sufficient to explain the data in areas where the subsurface resistivity distribution varies relatively slowly in a lateral direction.
Here, we use simultaneously a number of frequencies in the transmitter. So it is convenient to use “EM sounding” in this work because each of these magnetic fields can penetrate to the associated depths of the ground.
The inversion of EM sounding data does not yield a unique solution but a single model to interpret the observation is sought. Here we use Occam’s inversion which yields a model as simple as possible. To obtain such models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is solved explicitly for the desired model rather than for a model correction. To obtain the best solution, we make an objective function which is composed of the norm of model as well as the norm of data differences, and then we minimize this objective function.
Applying the Occam’s inversion on synthetic data, created over some 1D models with multiple sequences of resistive and conductive layers, shows that this method works well and the predicted models can be good approximations of synthetic models. The quality of results depends on the number of frequencies used. The more frequencies used, the better the results. Besides, as the value of frequencies increase, the penetrations of EM waves decrease and vice versa. So, removing a frequency of low value can affect the results in the higher depths, as is shown in the last two figures.
Besides, the method does not need a priori information about subsurface structure. All the results are obtained without a primary model. This shows that the method is stable to recover conductivities. On the other hand, results reveal that the method can detect a resistive layer beneath the conductive one whilst the EM methods are more sensitive to conductors than resistors.