OR/13/003 Technical background
Beamish, D. 2013. The construction of a merged EM (conductivity) database using Tellus and Tellus Border airborne geophysical data. (Land Use, Planning and Development Programme). British Geological Survey Internal Report, OR/13/003. |
Data sets
The EM data used here are from contractor supplied final data files available through GSNI and GSI. Processing reports that accompany the data are also available from the 2 organisations. In EM data terms, the change from a 2 frequency system used in 2005 to a 4 frequency system used in 2006 (and thereafter) provides an added complication to merging the 4 primary data sets. The method used previously is described in the final processing report (Beamish et al., 2006^{[1]}; http://nora.nerc.ac.uk/7427/1/IR06136.pdf). EM data from two common frequencies (3125/3005 Hz) and (14 368/11 962 Hz) were used to construct low frequency (LF, 3125/3005 Hz) and high frequency (HF,14 368/11 962 Hz) estimates of the half-space apparent conductivities/resistivities uniformly across the combined survey area. The procedures used also supplied uniform/merged estimates of the coupling ratios at each frequency. This was made possible by 2 control lines (LINES 1214 and 1215) repeated by both the 2005 and 2006 surveys and passing over the large water body of Lough Neagh. The use of a large body of water ensured that flying altitudes of the two control survey lines were well-maintained.
The primary EM survey data comprise complex coupling ratios referred to as P (real or in-phase, in ppm) and Q (imaginary or in-quadrature, in ppm) at each frequency. These data, along with altitude (ALT), may then used to construct a half-space conductivity model. The P, Q data display a high degree of sensitivity to altitude (Beamish, 2002a^{[2]}, b^{[3]}; Beamish and Leväniemi, 2010^{[4]}) and unless identical altitudes are maintained in overlap zones between surveys, the ability to merge P, Q, ALT data is compromised. The apparent conductivity data obtained by transform modelling of the P, Q data has no dependence on altitude and so these data can be simply merged across surveys. Although it is possible to consider merging conductivity models for the four frequency sets provided across 3 of the surveys, this procedure would, necessarily, omit the large and central area of the TEL-05 survey. In the first instance the production of merged conductivity data sets for all 4 surveys is undertaken at low frequency (LF, referred to as 3 kHz) and at high frequency (HF, referred to as 12–14 kHz).
Half-space conductivity transforms
The apparent conductivity, or resistivity, data supplied by the contractors are generated by modern adaptations of a simple transform procedure (Fraser, 1978^{[5]}) that uses the P, Q data at each frequency but not the altitude. The transform also returns an apparent depth (AD) parameter (see Beamish, 2002a^{[2]}). A detailed, previously unpublished description of the transform procedure used by the JAC is included in Appendix 1. A similar procedure has been used to deliver apparent conductivities in the TB survey data.
Each specific AEM system has a limited conductivity aperture defined by system parameters and the signal/noise of the P, Q data acquired and processed. These are discussed in Appendix 1. In order to provide a valid estimate of apparent conductivity, each P, Q measurement must be greater than zero and also greater than the noise level of the measurement. Since different assignments of low value threshold values may be used in the processing of different survey data, the ability to merge different data sets across areas having low resistivity (say >1 000 ohm.m) may not be accurate.
Following the discussion in Appendix 1, we here set a low value threshold of P,Q = 20 ppm for low frequency data (0.9 and 3 kHz) and P, Q = 30 ppm for higher frequency data (12–14 and 25 kHz). These are estimates of the typical ‘best’ accuracy that can be achieved in the processing of the acquired P, Q coupling ratios. As an example, Figure 3 shows the P, Q values at and below the threshold values for the delivered (levelled) TB data at low frequency (0.9 kHz) and at higher frequency (12 kHz).
As is clearly demonstrated, the numbers below the threshold limit typically increase with decreasing frequency. In practice all the data points shown are defined as inadequate and are simply set to the artificial threshold of P, Q = 20 ppm or P, Q = 30 ppm. This aspect of the data behaviour and processing control is often overlooked when examining final images of half-space conductivities.
The transform procedure, while reliable, provides conservative estimates of apparent conductivity using a digital look-up algorithm (Appendix 1 and Beamish, 2002b^{[3]}). An alternative inversion procedure, used to model the P, Q, ALT data supplied by the contractors is now described.
Half space conductivity inversion
The non-linear, least-squares half-space inversion described by Beamish (2002a)^{[2]} is used here. The inversion uses the P, Q, ALT data at each frequency and considers a model of a thin-resistive zone above a uniform half-space. The resistivity of the at-surface layer is fixed at 100 000 ohm.m but the thickness is allowed to vary. The ability of the thickness parameter (THK) to accommodate incorrect (underestimated) radar altimeter data due to canopy effects was demonstrated by Beamish (2002b)^{[3]}. The second parameter returned by the inversion is the conductivity of the half-space. The inversion minimises the difference between the observed data (P, Q) and the response of the model. The result is a ‘best-fitting’ model with an error estimate describing how well the response of the model has been fitted to the observed data.
Due to the small numbers of observations used in the inversion (i.e. 2), an L1 norm (based on the sum of differences) rather than an L2 norm (based on the sum of squared differences) misfit parameter is used. Here the L1 norm percentage error is defined as:
- L1 (%) = 100 Σ_{i}│ O_{i}–C_{i} │ / C_{i} …(1)
where the summation index (i) extends from 1 (P) to 2(Q). Oi is the i’th observation (an in-phase or in-quadrature coupling ratio) and Ci is the corresponding calculated value. L1 norms are typically greater than L2 norms (e.g. an rms misfit) by a factor of 10. This definition of misfit is used throughout. The L1 misfit term is referred to as the ERR (error) parameter of the inversion.
The error term is particularly useful since it allows inconsistent half-space conductivity model estimates to be rejected. Subsequent to the inversion, an estimate of centroid depth i.e. the mean depth of the induced in-phase current can also be provided. Following Siemon (2001)^{[6]}, who used estimated apparent resistivity and apparent depth (AD), we here would calculate the centroid depth (Cd) as
- C_{d} = THK + δ/2 …(2)
where δ is the standard EM plane-wave skin-depth (in m) depending on the apparent conductivity (obtained by the inversion) and frequency. Essentially we have replaced the original apparent depth estimate (AD) which can take on both positive and negative values with the THK parameter returned by the inversion and which is strictly positive.
References
- ↑ BEAMISH, D, CUSS, R J, and LAHTI, M. 2006. The Tellus airborne geophysical survey of northern Ireland: final processing report. British Geological Survey Technical Report IR/06/136. A report prepared for the DETI, Belfast.
- ↑ ^{2.0} ^{2.1} ^{2.2} BEAMISH, D. 2002a. An assessment of inversion methods for AEM data applied to environmental studies. Journal of Applied Geophysics, 51, 75–96.
- ↑ ^{3.0} ^{3.1} ^{3.2} BEAMISH, D. 2002b. The canopy effect in airborne EM. Geophysics, 67, 1720–1728
- ↑ BEAMISH, D, and LEVÄNIEMI, H. 2010. The canopy effect in AEM revisited: investigations using laser and radar altimetry. Near Surface Geophysics, 8, 103–115.
- ↑ FRASER, D C. 1978, Resistivity mapping with an airborne multicoil electromagnetic system: Geophysics, 43, 144–172.
- ↑ SIEMON, B. 2001. Improved and new resistivity-depth profiles for helicopter electromagnetic data. Journal of Applied Geophysics, 46, 65–76.