Amalendu Roy

Ambiguity in geophysical interpretation

The question of uniqueness or otherwise of the various geophysical methods has been looked into from a general point of view. A method is theoretically determinate or indeterminate depending on whether the totality of unknowns is smaller or greater than that of the independent measurables. While all natural field methods fall in the latter category, all applied field methods do not necessarily come under the former. Actual interpretations, however, cannot make any use of the theoretical uniqueness even where it exists and must depend on simplifying but permissible hypotheses based on extraneous information. These hypotheses are found to be surprisingly similar in all geophysical methods.

CONVERGENCE IN DOWNWARD CONTINUATION FOR SOME SIMPLE GEOMETRIES

Laplacian fields can be continued either by the use of Taylor series, or by spectral analysis and synthesis. While the first method is applicable to non‐Laplacian fields as well, the second, as it is presently developed, is not. The convergence properties of downward continuation by these methods have been investigated for some source geometries that frequently occur in nature. The cases treated include gravity, magnetic, electrical, and electromagnetic fields. When the spectral method is used, the boundary between regions of convergence and divergence is always a plane that is parallel to the plane of observation. With the Taylor series method, on the other hand, the boundary is a hyperboloid or a combination of hyperboloids. The position of these boundaries—plane or hyperboloid—depends upon the shape of the anomaly‐causing body. For bodies with corners and edges, the plane passes through the shallowest corner or edge, or there is a hyperboloid apexed at each corner or edge so that the outermost envelope...

A SIMPLE INTEGRAL TRANSFORM AND ITS APPLICATIONS TO SOME PROBLEMS IN GEOPHYSICAL INTERPRETATION

A simple integral transform, defined by f(x)=∫-∞+∞F(x,y)dy, where F(x, y) represents the measured geophysical field and x and y are suitably chosen directions, has been used for formulating convenient interpretation techniques to some geophysical problems that are normally not amenable to easy quantitative interpretation. Some synthetic numerical examples are given.

Downward continuation and its application to electromagnetic data interpretation

The existing methods of downward continuation were developed primarily for the interpretation of gravity and magnetic data, and, therefore, assume the validity of Laplace’s equation. The data collected in electromagnetic surveys, strictly speaking, obey Maxwell’s wave equation. However, in practice, two approximations are frequently made. First, the effects of displacement currents are neglected in view of the fact that the frequencies used are low. Second, the contribution of the country rock to the measured field is assumed to be nil, as its electrical conductivity is usually much smaller than that of the target body. Experience seems to indicate that these two approximations are permissible in general. It will be seen that, under these two approximations, Maxwell’s wave equation degenerates to that of Laplace, and the existing techniques of continuation become applicable to electromagnetic field data as well. This hypothesis has been tested by using continuation to interpret 20 electromagnetic profiles...

RESIDUAL AND SECOND DERIVATIVE OF GRAVITY AND MAGNETIC MAPS

There has been considerable discussion regarding the merits and demerits of the “smoothers” and the “gridders” in preparation of residual and second derivative maps. The controversy is probably unnecessary, as it appears that, basically speaking, the “smoothers” determine or tend to determine the residual, whereas the “gridders” aim at the second derivative. Following are the reasons for this statement.

Resistivity signal partition in layered media

Using a method given by Roy and Apparao (1971), the separate contributions to the measured resistivity sounding curve by the individual layers have been precisely determined for two‐layer and three‐layer (ρ1-ρ2-ρ1) models. The substratum in the former, and the middle ρ2-layer in the latter, constitute the targets in the two models. For the two‐layer model, a resistive substratum causes a positive anomaly by contributing higher than normal to the signal measured on the ground surface, while a conducting substratum gives rise to a “negative” anomaly (resistivity low) by contributing less than its normal share. As the two‐layer anomaly develops fully only at infinitely large spacings, it follows that an infinitely resistive basement contributes infinitely although no current flows through it, while a perfectly conducting basement contributes nothing even though it carries the entire current flow. For the three‐layer model, the anomaly peak or trough (as the case may be) is formed at intermediate spacings and...

On the effect of overburden on electromagnetic anomalies; a review

The effect of a conducting overburden in EM prospecting intuitively is considered to be one of degeneration of anomalies, in the sense that the detection of a target and the determination of its unknown parameters become more difficult or ambiguous when an overburden is present than when it is absent. Recently, however, Negi (1967) and Negi and Raval (1969) have suggested on the basis of theoretical work that, if a certain combination of the parameters involved occurs, a conducting overburden can make a target more detectable than it would be without any overburden. These theoretical results and the existing experimental evidence are examined in this paper for the possible existence of “negative screening,” as this effect has been called. Due to a number of incorrect assumptions made in the theoretical analyses by the authors who predicted negative screening, their conclusions do not seem to be valid. A fundamental objection in the case of the stratified sphere, for instance, pertains to the assumption th...

A graphical method for computing geophone group response

The theory for multiple seismometers or shotholes has been dealt with extensively in the literature (see, for instance, Parr and Mayne, 1955; Savit et al, 1958; White, 1958). In deciding upon a particular pattern, a seismic crew, after having determined the relevant noise characteristics of the area, may follow one of the two paths: (1) the crew may decide on a particular response and may then seek analytically, in a rather involved manner, an optimum geophone group whose response satisfactorily approximates the desired response or (2) the crew may compute the responses of a variety of geophone groups to the predominant noise pulse and accept the one that gives the best overall attenuation. Most seismic crews would choose the second alternative as being simpler and more practical, if less elegant than the first one. Besides, a calculated optimum group almost invariably would require fractional weights for the individual elements that are not practically realizable. Our note describes a very simple graphical procedure for fast computation of array responses that is applicable to a standing sine wave or a pulse and to linear, tapered, equally-spaced, or unequally-spaced arrays. The method is so obvious that it is probably in use already in some organizations; although no published evidence to that effect seems to be available.

New interpretation techniques for telluric and some direct current fields

Since the normal derivative of the telluric potential at the ground surface is zero, the odd terms in the Taylor expansion disappear, resulting in a simple technique of computing the downward continued potentials. The top of the nonconducting basement is a flow surface and can, therefore, be determined by sketching in curves orthogonal to the (continued) equipotential lines in suitably chosen sections. A model tank example is given. The applicability of the method of continuation to the interpretation of self potential data is also illustrated. A discussion of the derivatives, two limiting formulas, and a method for calculating telluric anomalies are included.

To: “Radius of Investigation in dc resistivity well logging” by A. Roy and R. L. Dhar, GEOPHYSICS, v. 36, no. 4, p. 754–760.

Due to inadequate precision in computation with small values of radius r, the radial investigation characteristic (RIC) curves in the above paper are incorrect for values of r less than about 0.15. Fortunately, this has not affected the positions of the maxima which determined the radii of investigation in that paper.