Application of the two-layer (Weaver) model requires difficult evaluations of 12 analytical expressions. Each has real and imaginary components. Even after these computa-
tions, it is clear that for some seabed areas, it is an over simplication of the environment to use the two-layer concept as a "global" model with which to describe ELFE propaga tion effects. Extending the model to take account of three or more uniform conducting layers would markedly increase in its complexity.
The same observation would apply if it were planned to extend the model to take account of sloping seabeds. Such a change would provide an improved theoretical basis for considering l ong-range ELFE detections. However, it would likewise greatly increase the complexity of the model.
Nevertheless , these experiments have demonstrated that there are shallow-water areas in which ELFE propagation can be accurately described by the two-layer (Weaver) model, provided it is applied on a pointwise basis, with range-varying values of seabed conductivity. Many of the requirements for the electromagnetic ranging of vessels will be s atisfied by using the Weaver model in this way.
A question may arise as to why the inner area of the grid in Fig . 15 is unsurveyed. Such a situation arose because the multifrequency ELFE dipoles were towed by a vessel that was also undergoing electromagnetic ranging. The electric field detectors were thus required to simulta neously provide undistorted records of both the vessel Signatures and the ELFE transmissions. Such records could not be obtained at close ranges. Moreover, the presence near the sensors of a conductive body (the ship hull) several scores of meters in length and of several meters draft was believed to influence ELFE propagation in that vicinity . The two-layer model cannot be readily extended to include such boundary conditions.
With the benefit of experience and additional resources, another approach would be to augment conductivity surveys at a test site using sensor spacings and dipole lengths of about 1 m. Ideally, the ELFE sources would be towed by a small work boat with a hull of nonconducting material .
Several advantages would accrue from such practices. First, assume that a short HED source can be successfully ranged using the method in Eq. (4) to provide an accurate calibration of its dipole moment I. This factor can then be exploited to carry out conductivity surveys over the inner areas represented by the cropped grid. In this instance, the real root that characterises the conductivity value «()2) o f seabed can be found by using similar i terative search processes to evaluate the expression:
� >- 1
:�
.� u :J "0 c 8 -10 -300 -200 UNCLASSIFIEDRANGINGS OF ELFE SOURCES OVER SHORT RANGES
-100 o 1 00 200 200 Easting (m) 300 300 -100 o 1 00 Northing (m) -300 -200
Fig. 15 -Cropped mesh grid indicating the coverage of characteristic seabed conductivity values between measurement points and the electric field sensors at the center of the grid
� E � >- � 4 g 2 -0 c 8 0 -300 -200 -100 -300 1 00 1 00 200 Northing (m) Easting (m) 300 300
Fig. 16 -Contour levels between 0.5 and 4 .0 S.m·' (in steps of 0.5 S.m·') for the characteristic
seabed conductivity values at the World's End test site
UNCLASSIFIED
UNCLASSIFIED
684 RUMBALL AND KA Y
in which I E;' I is as defined, I
I
E;:M I is the signal from anBED source as measured along the radial axis of the
electric field sensors, and w is the angular frequency of the
BED transmission. Equation (5) is a reordering of Eq . (34) in Ref. 1 . Such an approach may reduce the earlier loss of accuracy in measuring the seabed conductivity over tJle inner area of the cropped grid.
In attempting to apply the global, two-layer modeJl at the World's End test site (and others), it has been found necessary to use range-varying values of seabed conductivi ty to describe ELFE propagation through media that are nonisotropic. The tests described in this article are not sufficiently sensitive to ascertain whether there are other propagation dependencies of the media that are not being detected. For instance, in some circumstances, it may be important to ascertain if there are frequency-related or polarisation-related properties of the seabed that need to be considered for modeling applications.
Reference was made earlier to the single value of permeability that is used to characterize each of the two isotropic conducting layers (of the Weaver model) . This simplification is appropriate in many areas off the east coast of New Zealand. The material that comprises the upper layers of the seabed has a relative permeability of approxi mately 1 .0 .
Such a condition does not apply over large tracts off the country's west coast. M aterial in the seabed often has a significant magnetite content. Other simulations have reveaJed a clear deficiency in the ability of the Weaver model to predict subsurface ELFE propagation in such regions.
All of the above points support the notion that ad vanced studies of ELFE propagation over short ranges and in shallow-water conditions may be better carried out with finite element models. Such models provide for the inclu sion of more detailed boundary conditions, which inclUde more accurate descriptions of conductivity, permittivity , and permeability parameters. Multiple Sea bed layers of differing thicknesses and gradients can also be considered within the finite element models.