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**Heuristically and Laterally Constrained Inversions**

(HLCI) of VTEM data Karl Kwan Geotech Ltd. Alexander Prikhodko Geotech Ltd. Andrei Bagrianski Geotech Ltd. Zihao Han Geotech Ltd.

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**Outlines Introduction VTEM full waveform System LCI Method**

HLCI/Airbeo(CSIRO/AMIRA) Method HLCI of Synthetic Data HLCI of Real Data Conclusions

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Introduction New VTEM system with “full waveform”, streaming, calibrated and de-convolved can acquire quality early time data (~20 sec after TX turn-off), thus improving shallow imaging capability for hydrological and environmental investigations over sedimentary (layered earth) areas, and kimberlite exploration. Clients want Laterally Constrained Inversions (LCI), or LCI-type inversions of the VTEM data. Geotech has developed a Heuristically and Laterally Constrained Inversion (HLCI) inversion; some of the results will be presented here.

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**with “full waveform”, streaming, calibrated and de-convolved data**

New VTEM System with “full waveform”, streaming, calibrated and de-convolved data EM Transmitter Loop diameter, m 26 Number of turns 4 Effective loop area, m2 2123 Base Frequency, Hz 25 or 30 Peak current, A (depends on width pulse) Dipole Moment, NIA 400, ,000 (depends on width pulse) Current pulse width, msec Programmable up to 7.5 Waveform Bi-polar Trapezoid Nominal transmitter loop clearance, m 30 EM Receiver Components Vertical (Z) and horizontal (X) Coil diameter, m 1.2(Z); 0.32(X) Effective Area, m2 113(Z); 20(X) Off-time range, msec 0.018 – 10.0, sampled in 44 time gates Recorded EM Data vertical and horizontal components of dB/dt and B-field Nominal EM Receiver terrain clearance, m Magnetometer (Horizontal Gradiometer) Sensors 2 split-beam caesium vapour Geometrics Horizontal sensors separation 12.5 m Magnetic sensitivity, nT 0.02 (0.001 base) Receiving magnetic data Total field; cross-line, in-line and full horizontal gradients. Nominal Magnetic sensors terrain clearance, m 40 m Bird position and attitude GPS antenna installed on EM bird Gyroscopic Inclinometer Real-Time navigation The second antenna installed on helicopter tail

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Cont… In an effort to improve shallow imaging capability, Geotech has developed a “full waveform” VTEM system, which provides streaming data with Post processing which includes: A continuous system response calibration; Parasitic and drift corrections using ideal waveform deconvolution. This results in an increased system bandwidth, and early time data (~20 sec) after TX turn-off.

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**1D Layered Earth (sedimentary environments)**

The footprint of VTEM systems is a small spot (~ m in diameter) on earth. Depending on speed, normal EM data sampling interval is about 3 meters. Data collected at each station (soundings) over sedimentary areas can be 1D inverted for layer thickness and resistivity. Inverted 1D models change from station to station. 1,1 d1,1 1,2 d1,2 1,n 1st station . Basement i,1 di,1 i,2 di,2 i,n ith station . Basement Each model for each station has n layer resistivities, (n-1) layer depths or layer thicknesses. ~3 m ….. A couple of implications for small footprints: Some geological cases can be considered locally 1D, globally non-1D, i.e. top of kimberlites; sensitivities set to 0 outside the footprint, saving memory and time; this had been exploited in 3D AEM inversion already! (Cox et al, 2010) How to create 1D models with smooth lateral variations?

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**LCI Method1 Subsurface: divided into a large number of 1D models**

Constraints: carry information on geologic variability Output: layered model 2D sections with smooth lateral variations Model 1 Model 2 Model 3 Depth from Auken et al, EAGE presentation.

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**LCI Algorithm (Auken 2004) Schematic representation:**

G is the Jacobian matrix, data variances in Cobs R is the roughening matrix, constraint variances in Cc mprior is the a priori model, constraint variances in Cprior e is error vectors Spatially dependent constraints, R and Rd , to tie adjacent models

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LCI Features Models, constraints and a priori information are inverted simultaneously. Densely sampled airborne TEM data are pre-processed and averaged before LCI (reducing cultural interferences). Long lines are divided into many small sections. Forward Calculations: Frequency Domain Hankel transform and inverse Fourier transform (Newman2) using digital filters of Christensen3. Locally 1D, but with lateral constraints, LCI produces geologically consistent pseudo 2D sections; therefore LCI can be called a pseudo 2D method.

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**HLCI/Airbeo (CSIRO/AMIRA)4**

CSIRO, which stands for Commonwealth Scientific and Industrial Research Organization, has conducted mathematical and algorithm research to develop practical geophysical software tools for mineral exploration industry. Project P223F created a suite of software for airborne and ground electromagnetic (EM) systems (time and frequency domain) . One of programs, Airbeo allows users to invert AEM data for layered earth models. Principal investigator of Airbeo was Dr Art Raiche. Sponsors of P223F were BHP Billiton, Fugro, Vale Inco, Newmont, Barrick, De Beers and others. At the end of the project P223F, sponsors agreed that the source codes should be released into the public domain. (2008) We modified Airbeo, v4.7.0, , for Heuristically and Laterally Constrained Inversion (HLCI), a LCI-type inversion algorithm programmatically built entirely on the Geosoft Oasis Montaj platform.

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**Airbeo (CSIRO/AMIRA) Features**

Inversion algorithm based on Jupp and Vozoff5, using Generalized Singular Value Decomposition (SVD) Truncation and Marquardt Methods of iterative inversion, i.e. damped eigen-parameter method. Forward Modelling: Frequency Domain Hankel transform and inverse Fourier transform (Newman) using digital filters of Christensen; identical to those used by LCI. Models can be constrained in several ways; one of them is to constrain layer resistivities and/or depths/thicknesses. For a 5-layer model, the constraint array for fixing layer depths looks like: (this is THE feature we want to exploit!) 1 Constraints array for 5-layer model, first n entries are for layer resistivities and last (n-1) entries are for layer depths. 0 means free and 1 means fixed.

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**HLCI Algorithm Phase I (step 1):**

Airbeo 1D inversions for VTEM data of an entire line, using one initial model. Each 1D inversion will terminate when the RMS error cannot be reduced further. Selection of an initial model is critical. Allow different iterations for each station, i.e. number of iterations not restricted. No pre-filtering or averaging of VTEM data. However, data de-selection by user is allowed. Deriving lateral constraints (step 2): Apply spatially dependent (distance based) statistical mean filtering, with user-defined filter width (heuristically: experimenting the best solution for next step), to layer depths derived from Phase I along survey line direction (laterally). The filtered layer depths, which has minimum structure in the lateral sense, will be used in the initial models for Phase II inversions. A priori information, such as drillhole resistivity logs, can be incorporated here to better define the constraints. Phase II (step 3): Airbeo 1D inversions with layer depths/thicknesses constrained. Each model has its own initial model with layer depths/thicknesses derived in step 2 and layer resistivities computed in Phase I. Only layer resistivities are free to vary. A LCI method of inverting time-domain airborne data, based on modified Airbeo, was presented at “AEM2008 – 5th International Conference on Airborne Electromagnetics, Finland” by Marc A. Vallee and Richard S. Smith.

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HLCI – Phase II 1,1 c1,1 1,2 c1,2 1,n Model 1 . Basement i,1 cn,1 i,2 cn,2 i,n Model n . Basement i,1 ci,1 i,2 ci,2 i,n Model i . Basement Initial Model 1 Initial Model n Initial Model i Each station has its own initial model. In the initial models, the layer depths cij are constrained (fixed), while the layer resistivities, computed from Phase I, are free to vary. Final layer resistivities may require filtering in order to have laterally smooth layer resistivities.

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**HLCI and LCI equivalence**

HLCI Phase I and II approximately equivalent to LCI with R=0; HLCI allows different number of iterations per station. HLCI takes deriving lateral constraints, or minimizing the model misfit, out of the formal inversion process. Formal inversions try to minimize = d + m d, m : data and model misfits In HLCI, finding the minimum m is done heuristically by the geophysicist, instead of by formal inversions in LCI. Left is a cartoon showing m for a three-layer model (two layers plus the basement). Two axes are layer depths. LCI uses iterative damped Least-squares (Marquardt) to find the minimum structure in several steps. HLCI finds the same in ONE step heuristically. LCI HLCI

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**HLCI of Synthetic Data I**

TESTING Model and data descriptions: Three-layer model, having a 20m thick overburden of 10 ohm-m resistivity and a 100 ohm-m relative resistive channel of variable thickness over a conductive basement. Middle resistive unit simulates sand and gravel aquifer channel. Data are sampled at 5m intervals, times from – msec. Simulate paleo-channels in hydrological studies.

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**LCI and HLCI Noise Free Data**

TESTING Original Model 200m HGG LCI – layer resistivities fixed. HLCI Noise free forward data were pre-filtered and averaged to 15m sampling interval (from 5m original) for LCI.

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**HLCI of Noisy Radarb Data**

TESTING 200m Phase II Phase I Gaussian noise added to radarb data (standard deviation of 2 m). Phase I inversions show significant lateral variations in layer depths (blue lines). Laterally statistical mean averaged layered depths are computed (pink lines).

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**HLCI of Synthetic Data II**

TESTING Model and data descriptions: Three-layer model with a resistive 500 ohm-m resistivity overburden and a 100 ohm-m relative conductive and truncated layer over a 2000 ohm-m resistive basement (kimberlite simulation). Data are sampled at 5m intervals, times from – msec; Only the first 10 channels have responses above noise level.

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**HLCI of Noise Free Data TESTING 100m**

Data from ms are used; data from later times are below the noise level. 100m HGG LCI HLCI Phase I

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**HLCI of Noisy Radarb Data**

TESTING 100m Phase I Phase II

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**HLCI of Real Data Spiritwood Valley Aquifer, Manitoba**

VTEM L1010 Location of Spiritwood Valley Aquifer (from Oldenborger et al, 2010)

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**Seismic and Ground Electrical data**

P-wave seismic section overlain with the surface electrical resistivity inverted data LCI VTEM (11m) HLCI VTEM (3m)

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**HLCI and LCI Comparison**

L1010 AIRBEO UNCONSTRAINED 1D Phase I (5-Layer Model) HLCI Phase I Displays Noticeable Variations in Layer Resistivity and Thickness (Not Geologic Related) Demonstrating improvements in subsurface Resistivity Imaging using HLCI. LATERALLY-CONSTRAINED (thickness) 1D Phase II Laterally Constrained (Thickness Only) shows Significantly Better Lateral Continuity LATERALLY-CONSTRAINED 1D Phase II (resistivity smoothing) Resistivity smoothing Improves Clarity without Significantly Affecting Geologic Detail AARHUS LATERALLY-CONSTRAINED 1D LCI INVERSION (Same Parameters as Above) Comparison with Industry Standard 1D LCI

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**HLCI CPU Elapsed Time vs No of data**

Computer: HP Z210 Workstation Processors: Intel ® Core ™ GHz, Quad-Core, 64-bit OS, 8.00 GB RAM

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Conclusions A robust and fast HLCI algorithm has been developed for VTEM data, based on modified Airbeo (CSIRO/AMIRA) 1D layered earth inversion code. Synthetic and real data tests show HLCI is capable of delivering layered earth pseudo 2D sections with smooth lateral variations. HLCI delivers results comparable to those from LCI of Aarhus Workbench. HLCI can be easily upgraded to 3D, with layer thickness constrained laterally in both X and Y directions. (providing corrections for static shift in MT) HLCI is applied routinely to “full waveform”, streaming, calibrated and de-convolved VTEM data.

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**Acknowledgements Our thanks to:**

Airbeo, CSIRO/AMIRA and its creator, Dr. Art Raiche. Andrea Viezzoli, HydroGeophysics Group, UofAarhus

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