Heuristically and Laterally Constrained Inversions (HLCI) of VTEM data

Karl Kwan Geotech Ltd. Karl@geotech.ca

Alexander Prikhodko Geotech Ltd. alexander@geotech.ca

Andrei Bagrianski Geotech Ltd. andrei@geotech.ca

Zihao Han Geotech Ltd. zihao@geotech.ca

Outlines

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

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.

New VTEM Systemwith “full waveform”, streaming, calibrated

and de-convolved dataEM Transmitter

Loop diameter, m 26Number of turns 4Effective loop area, m2

2123

Base Frequency, Hz 25 or 30Peak current, A 250-350 (depends on width pulse)Dipole Moment, NIA 400,000-600,000 (depends on

width pulse)

Current pulse width, msec

Programmable up to 7.5

Waveform Bi-polar TrapezoidNominal transmitter loop clearance, m

30

EM ReceiverComponents 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

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 attitudeGPS antenna installed on EM birdGyroscopic Inclinometer

installed on EM bird

Real-Time navigationGPS antenna The second antenna installed on

helicopter tail

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.

1,1

d1,1

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d1,2

1,n

1st station

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Basement

i,1

di,1

i,2

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i,n

ith station

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Basement

Each model for each station has n layer resistivities,(n-1) layer depths orlayer 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 (~200-300m 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)

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

Depth

Mod

el 1

Mod

el 2

Mod

el 3

from Auken et al, EAGE presentation.

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

c

prior

obs

prior

obs

true

e

e

e

r

m

d

m

R

I

G

c

prior

obs

C00

0C0

00C

C

• Spatially dependent constraints, R and Rd , to tie adjacent models

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.

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, 2007-03-17, for Heuristically and Laterally Constrained Inversion (HLCI), a LCI-type inversion algorithm programmatically built entirely on the Geosoft Oasis Montaj platform.

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!)

0 0 0 0 0 1 1 1 1

Constraints array for 5-layer model, first n entries are for layer resistivitiesand last (n-1) entries are for layer depths. 0 means free and 1 means fixed.

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.

1,1

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Model 1

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Basement

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Model i

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i,1

cn,1

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cn,2

i,n

Model n

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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

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 tominimize = 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.

c

prior

obs

prior

obs

true

e

e

e

r

m

d

m

R

I

G

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 0.021 – 7.036 msec.Simulate paleo-channels in hydrological studies.

TESTING

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

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

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 0.021 – 0.145 msec;Only the first 10 channels have responses above noise level.

TESTING

HLCI of Noise Free Data

Data from 0.021-0.145ms are used; data from later times are below the noise level.

HGG LCI

HLCI Phase I

100m

TESTING

HLCI of Noisy Radarb Data

Phase I Phase II

100m

TESTING

HLCI of Real DataSpiritwood Valley Aquifer, Manitoba

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

VTEML1010

P-wave seismic section overlain with the surface electrical resistivity inverted data

LCI VTEM (11m)

HLCI VTEM (3m)

Seismic and Ground Electrical data

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 IDisplays NoticeableVariations in LayerResistivity and Thickness(Not Geologic Related)

Laterally Constrained(Thickness Only) showsSignificantly BetterLateral Continuity

Resistivity smoothingImproves Clarity withoutSignificantly Affecting Geologic Detail

Comparison withIndustry Standard1D LCI

Demonstratingimprovementsin subsurfaceResistivity Imaging using HLCI.

HLCI CPU Elapsed Time vs No of data

• Computer: HP Z210 Workstation• Processors: Intel ® Core ™ i7-2600 @3.40 GHz, Quad-Core, 64-bit OS, 8.00 GB RAM

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.

Acknowledgements

Our thanks to:

Airbeo, CSIRO/AMIRA and its creator, Dr. Art Raiche.

Andrea Viezzoli, HydroGeophysics Group, UofAarhus