James Macnae

Evaluating EM waveforms by singular‐value decomposition of exponential basis functions

Exponential basis functions preconvolved with the system waveform are used to convert measured transient decays to an ideal frequency-domain response that can be modeled more easily than arbitrary waveform data. Singular-value decomposition (SVD) of the basis functions are used to assess which specific EM waveform provides superior resolution of a range of exponential time constants that can be related to earth conductivities. The pulse shape, pulse length, transient sampling scheme, noise levels, and primary field removal used in practical EM systems all affect the resolution of time constants. Step response systems are more diagnostic of long time constants, and hence good conductors, than impulse response systems. The limited bandwidth of airborne EM systems compared with ground systems is improved when the response is sampled during the transmitter on time and gives better resolution of short time constants or fast decays.

Bathymetry and seafloor mapping via one dimensional inversion and conductivity depth imaging of AEM

This study examines the application of airborne electromagnetic (AEM) methodologies to bathymetry in shallow seawater and to map seafloor conductivity. Conductivity versus depth sections have been generated from a recent helicopter-borne DIGHEMV survey (operating vertical coaxial and horizontal coplanar transmitter-receiver coil geometries) of lower Port Jackson, Sydney Harbour. The sea depth ranges from about 1 to 30 m. Acoustic bathymetric soundings and marine seismic survey data provide the true seawater layer thickness and estimates of depth to bedrock respectively over most of the EM survey region. This complementary data can be used to evaluate the accuracy of airborne electromagnetic bathymetry. The efficacy of 1D conductivity inversion and rapid conductivity-depth imaging was investigated for shallow seawater overlaying marine sand sediments and sandstone. The inversion constructs layered conductivities which satisfy the AEM data to an accuracy consistent with the observational uncertainties. Inverted frequencies ranged from 328 to 55300 Hz. Resolution of the sea depth gave good agreement with known bathymetry (within about 10% or better) when inversion was unconstrained. Approximate conductivity-depth images obtained using program “EM Flow” gave similar agreement. Both inversion methods clearly identify the location and burial depth of higher resistivity regions associated with shallow marine sandstone bedrock. In addition to measuring water depths to about 30 m, this study has shown that the AEM DIGHEM technique provides a capability for remote sensing of seabed properties and offers the potential to detect areas of shallow bedrock and differentiate between consolidated and unconsolidated sediment in areas of seawater deeper than 25 m.

Doubling the effective skin depth with a local source

The depth at which the amplitude of the frequency‐domain electromagnetic fields due to dipole and square loop sources over a homogeneous half‐space fall to 1/e of their value at the surface is compared to the conventional plane‐wave skin depth. The skin depth due to a local source depends on the transmitter frequency, half‐space conductivity, transmitter altitude, and transmitter‐receiver offset, and may range from a fraction of to more than twice the plane‐wave skin depth. Unlike the plane‐wave skin depth, the “local‐source skin depth” is different for electric and magnetic fields, and may be nonunique for some transmitter geometries and field components. For all transmitter geometries, however, the local‐source skin depth approaches the plane‐wave skin depth as the transmitter altitude and/or receiver offset increase. The concept of the local‐source skin depth has direct application to survey design and data interpretation. A theoretical example demonstrates that it is possible to predict, for a given s...

Comments on the electromagnetic “smoke ring” concept

The electromagnetic (EM) fields in a one‐dimensional (1-D) earth due to a dipole or loop transmitter have been studied by a number of authors, including Lewis and Lee (1978), Pridmore (1978), Nabighian (1979), and Hoversten and Morrison (1982). Nabighian (1979) aptly described the time‐domain‐induced current system in a homogeneous half‐space as resembling a “smoke ring” blown by the transmitter, which moves outwards and downwards and diminishes in amplitude with increasing time after the transmitter is turned off. In a homogeneous half‐space, the physical electric field maximum moves outward from the transmitter loop edge at an angle of approximately 30° with the surface. Hoversten and Morrison (1982) show how the direction of propagation of the time‐domain electric field maximum is affected by conductivity structure. In the case of a highly conductive overburden over a resistive basement, the electric field maximum travels essentially horizontally away from the transmitter, and is effectively trapped in...

Modeling of the EM inductive-limit surface currents

The inductive limit of an electromagnetic (EM) response, which is the early time or infinite‐frequency response, may be quickly and efficiently calculated when compared to the effort and time required to calculate a full 3-D EM model. This can be achieved through matrix solution of a simple set of simultaneous conditions that any primary magnetic field must not penetrate the target body. In airborne EM (AEM) data acquisition, hundreds of local anomalies may need to be interpreted each day of flying, and the inductive limit modeling algorithm provides a useful and very fast model for realistic target geometries. In particular, it allows typical single‐peaked field anomalies in the vertical component of fixed‐wing AEM systems to be fitted, using a multi‐faceted solid body. Thin‐plate models, which are commonly used, produce “M-shaped” responses rarely seen in field data.

Inversion of Airborne EM Data Using Thin-plate Models

Summary An inversion program for interpreting airborne electromagnetic (AEM) data using one or more thin plates in a conductive host with an overburden has been developed. Three parameters describe the two-layer earth, and another eight each target, specifically the x-position, y-position, depth of burial, strike length, depth extent, strike angle, dip angle, and conductance. The forward modeling is based on Weidelts integral-differential formula. The inversion algorithm is based on the second-order damped non-linear least squares method. The required Jacobian matrix is calculated from numerical differences by forward computations. In the first pass of processing AEM data, an efficient conductivity-depth image (CDI) algorithm is used to pick up local anomalies. Once a local anomaly is picked, the thinplate inversion program developed in this study can be applied in a subsequent step, which potentially will provide accurate information about the source of the anomaly. This procedure has been successfully applied to invert AEM data from Lisheen, Ireland, where a massive sulphide deposit containing Zn, Pb, and Fe, is located at depth of approximately 200m.

2.5D Conductivity Inversion of Airborne EM Data

We present an inversion method for generating a twodimensional electrical conductivity model from airborne electromagnetic measurements either in the frequency or time domain. The inversion process is classified as 2.5D, since the two-dimensional conductivity model is excited by a threedimensional dipolar field. The forward model computation is based on an isoparametric finite-element formulation with quadratic basis and test functions. A direct frontal solution method is used to solve for the along-strike components of magnetic and electric fields in the Fourier domain. The sensitivity matrix computation is based on an adjoint equation method which requires one additional source computation for each receiver position. It is shown that the forward model and sensitivity matrix computation for an entire line of say N positions can be computed in (1 + 0.1 N) times the time required for a single source forward model. A damped eigenparameter approach is utilised to regularise the inversion process, rather than forcing adherence to a priori geological constraints. A test with a set of synthetic AEM data with 3% Gaussian noise demonstrates the viability of this inversion program.