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Heuristically and Laterally Constrained Inversions (HLCI) of VTEM data Karl Kwan Geotech Ltd. Alexander Prikhodko Geotech.

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Presentation on theme: "Heuristically and Laterally Constrained Inversions (HLCI) of VTEM data Karl Kwan Geotech Ltd. Alexander Prikhodko Geotech."— Presentation transcript:

1 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.

2 Outlines Introduction VTEM full waveform System LCI Method HLCI/Airbeo(CSIRO/AMIRA) Method HLCI of Synthetic Data HLCI of Real Data Conclusions

3 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.

4 New VTEM System with “full waveform”, streaming, calibrated and de-convolved data EM Transmitter Loop diameter, m26 Number of turns4 Effective loop area, m Base Frequency, Hz25 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 WaveformBi-polar Trapezoid Nominal transmitter loop clearance, m 30 EM Receiver ComponentsVertical (Z) and horizontal (X) Coil diameter, m1.2(Z); 0.32(X) Effective Area, m 2 113(Z); 20(X) Off-time range, msec – 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 30 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 antennainstalled on EM bird Gyroscopic Inclinometer installed on EM bird Real-Time navigation GPS antennaThe second antenna installed on helicopter tail

5 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: 1.A continuous system response calibration; 2.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.

6  1,1 d 1,1  1,2 d 1,2  1,n 1 st station Basement  i,1 d i,1  i,2 d i,2  i,n i th station Basement Each model for each station has n layer resistivities, (n-1) layer depths or layer thicknesses. 1D Layered Earth (sedimentary environments) ~3 m ….. How to create 1D models with smooth lateral variations? 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. A couple of implications for small footprints: 1.Some geological cases can be considered locally 1D, globally non-1D, i.e. top of kimberlites; 2. sensitivities set to 0 outside the footprint, saving memory and time; this had been exploited in 3D AEM inversion already! (Cox et al, 2010)

7 LCI Method 1 Subsurface: divided into a large number of 1D models Constraints: carry information on geologic variability Output: layered model 2D sections with smooth lateral variations Depth Model 1 Model 2 Model 3 from Auken et al, EAGE presentation.

8 LCI Algorithm (Auken 2004) Schematic representation: G is the Jacobian matrix, data variances in C obs R is the roughening matrix, constraint variances in C c m prior is the a priori model, constraint variances in C prior e is error vectors Spatially dependent constraints, R  and R d, to tie adjacent models

9 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 (Newman 2 ) using digital filters of Christensen 3.  Locally 1D, but with lateral constraints, LCI produces geologically consistent pseudo 2D sections; therefore LCI can be called a pseudo 2D method.

10 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.

11 Airbeo (CSIRO/AMIRA) Features  Inversion algorithm based on Jupp and Vozoff 5, 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!) 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.

12 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 – 5 th International Conference on Airborne Electromagnetics, Finland” by Marc A. Vallee and Richard S. Smith.

13  1,1 c 1,1  1,2 c 1,2  1,n Model Basement  i,1 c i,1  i,2 c i,2  i,n Model i Basement  i,1 c n,1  i,2 c n,2  i,n Model n Basement Each station has its own initial model. In the initial models, the layer depths c ij 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. Initial Model 1 Initial Model i Initial Model n HLCI – Phase II

14 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. LCI HLCI 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.

15 HLCI of Synthetic Data I 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. TESTING

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

17 HLCI of Noisy Radarb Data 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). Phase I Phase II 200m TESTING

18 HLCI of Synthetic Data II 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. TESTING

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

20 HLCI of Noisy Radarb Data Phase I Phase II 100m TESTING

21 HLCI of Real Data Spiritwood Valley Aquifer, Manitoba Location of Spiritwood Valley Aquifer (from Oldenborger et al, 2010) VTEM L1010

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

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

24 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

25 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.

26 Acknowledgements Our thanks to: Airbeo, CSIRO/AMIRA and its creator, Dr. Art Raiche. Andrea Viezzoli, HydroGeophysics Group, UofAarhus

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