Three-dimensional inversion of borehole, time-domain, electromagnetic data for highly conductive ore-bodies.

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1 Three-dimensional inversion of borehole, time-domain, electromagnetic data for highly conductive ore-bodies. Nigel Phillips, Doug Oldenburg, Eldad Haber, Roman Shekhtman. UBC-Geophysical Inversion Facility Dept. of Earth and Ocean Science University of British Columbia, Vancouver, B.C. Small, deep, highly conductive ore-bodies can present several challenges in applying time-domain EM inversion methods. These challenges can include: large conductivity contrasts, and the associated long time constants; the proximity of the receiver locations to large conductivity contrasts; and the level of resolution needed to define the ore-body. We present the application of time-domain inversion to borehole UTEM data collected at Nickel Rim South, Ontario and demonstrate methods developed to accommodate the difficult scenarios encountered. The methods are first tested on synthetic models prior to inverting field data. As such, we also address the importance of noise estimation in the field data. We would like to acknowledge Falconbridge Ltd. for providing the data which allows us to drive the application of inversion technology through real world examples. Background Nickel Rim South (NRS) is a contact deposit located on the edge of the Sudbury Igneous Complex. Comprised of conductive nickel-rich sulphides (~1000 S/m), the deposit is relatively small and deep, and hosted on the contact between sub-layer norite and footwall breccia, both of which are resistive ( Ohm-m). The UTEM survey used to collect this data comprised of a 1.1km by 1.8 km surface transmitter with 4Hz, three-component db/dt data collected down hole (Figure 1). Six holes were used for this study totaling 900 data locations collected in proximity to, and within conductors. The data were un-normalized from the UTEM conventions to be in db/dt units of T/s for a transmitting current of 1 Ampere, and rotated to be orthogonal with the spatial axes used in the modeling. In order to model this data we use a program called EH3DTDinv to invert timevarying electric and magnetic fields in three-dimensions. This code has been developed by UBC-GIF over the last few years. The code solves Maxwell s equations in time and space for the whole volume at all times using a finite volume, staggered grid spatial discretization, and a backward Euler discretization for time. Optimization is performed using a Quasi-Newton method.

2 Tx 2 km Rx s 3 km Figure 1: Survey layout comprising of a large surface transmitter and receivers located in 6 bore-holes. Assigning Errors The optimization problem we solve contains many unknowns, so in order to produce a result within a reasonable amount of time (1-2 days) we limit the number of cells in the model. As a result, the cell size is sometimes larger than it should be for the high conductivities we are trying to model at the early times in the waveform. This is the case with the NRS data set, so we perform synthetic experiments to see how well we can model the electromagnetic fields with a given spatial discretization. With the same survey parameters as the field data set we forward model a conductive block to emulate the fields we would expect from the NRS deposit. This is done twice; once with a very fine cell discretization using cells small enough that are appropriate for the large conductivities, and again with the cell discretization that we use in the inversion. The results (Figure 2) show that we cannot expect to model the fields well when the data are collected within a conductor but can be much more accurately reproduced when the data are collected more than 50m away. This provides us with an estimate of how well we should be fitting the data in an inversion for a given spatial discretization. As a result appropriate errors can be assigned to the data in addition to other sources of estimated noise in the data.

3 2e-8 BH data through conductor 5m cells 20m cells 2e-8 BH data near conductor 5m cells 20m cells dbx/dt [T/s] -5e-9-5e Depth [m] Depth [m] Figure 2: Comparison of synthetic borehole UTEM data using different cell discretization sizes, 5m in black and 20m in blue. The left plot shows that data passing through a conductive block are not as accurately reproduced when a coarse discretization is used. The image on the right shows that much more accurate fields can be modeled with larger cells when the data are collected 50m away from the conductor. Improving the inversions Two methods have been developed to improve both the accuracy and efficiency of the inversion when applied to high conductivity contrast problems such as NRS: corrective sources and extended waveforms. First, from the synthetic experiment above we can see a need to reduce the cell size in order to increase the modeling accuracy. This will also increase the resolution of the inversion if the survey parameters allow. For this we use a method of corrective sources where we finely discretize around a core region of interest where the data is located thus allowing for smaller cell sizes and obviating discretization around the transmitter. In practice fields are first forward modeled on a large volume using a background conductivity model and used to set up initial field conditions for the inversion within the core volume. The source term now becomes currents on the boundary of the detailed core volume. Secondly, because we are dealing with such large conductivities and therefore time-constants that are much larger (1-10 sec) that the time period (1/4 sec) of the waveform, we choose to model several waveforms in order to set up the steady-state conditions in which the data are actually recorded in the field. In order to do this without modeling many time-steps for each inversion iteration (which would slow the optimization process) we use a method of extended waveforms. The method splits up the waveform time-steps into those modeled before and those modeled during the data measurement (Figure 3). Fields modeled at time-steps before the data are measured can be calculated from the previous iteration if we assume the fields haven t changed much in a single time-step. This division of time-steps is exploited by using separate processors to calculate the two groups of time-steps. This results in accelerated inversions with modeling times being reduced from 5 days to 20 hours.

4 1 Current [A] Data time [s] Figure 3: A multi-cycle waveform is used to set up steady-state conditions and the method of extended waveforms is used to split up the waveform into two parts: time-steps before the data is considered being measured (dashed) and time-steps during the data collection (solid). Inversion of field data Application of the methods above to the inversion of the NRS field data have resulted in a conductivity model that gives a good representation of the deposit (Figure 4). The predicted data fit the observed data more appropriately as the modeling is more accurate and realistic conductivities of 100 S/m have been recovered. Conclusion We have demonstrated the capability to successfully invert multi-borehole time-domain EM data for a single transmitter and the application of methods to account for high conductivities such as those encountered at Nickel Rim South. It is important to understand the data in terms of normalizations and reduction applied to the data as well as understanding sources of noise in the data. An appropriate level of data misfit for an inversion can be determined by analysis of the discretization used. In addition it is important to understand the background geologic/conductivity structure, especially when using corrective source methods in order to reduce cell size and improve modeling accuracy. Three-dimensional time-domain EM inversion has a large potential for detection and delineation of targets in geologically complicated environments characterized by high conductivities. We would like to acknowledge Daryl Ball and Kevin Stevens of Falconbridge Limited for their help in this study.

5 Figure 4: Conductivity inversion model of the Nickel Rim South deposit. 10m cells are used and a 100 S/m isosurface is shown.