The inversion of magnetic anomalies in terms of an irregular layer of magnetized material is studied, and an efficient procedure for constructing solutions is developed. Even when magnetic orientation and layer thickness are known, the solution is not unique because of the existence of a magnetization (called the magnetic annihilator) that produces no observable magnetic field. We consider an example of near‐bottom marine data and discuss methods for overcoming the problem of nonuniqueness.

Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by , is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can IntroductionMeasurements of gravity over large-scale topographic features such as mountain ranges typically show negative Bouguer anomalies that have an inverse correlation with the Prescnl address: Department o f Environmental Sciences, Univcrsity of Lancaster, Lancaster, England. 432 R . J. Banks, R . L. Parker and S. P. Huestis elevation. The recognition of this relationship led to the development of the concept of isostasy; that the excess mass above sea level represented by topographic features is compensated by a deficiency of mass below sea level. The hypothesis can be given a more specific formulation in one of two ways: either in terms of the equality of mass of material in equal prisms above the 'level of compensation', or in terms of the equality of hydrostatic pressure over a 'level' surface within the earth. The second is a more flexible condition, in that it can be applied to both local and regional compensation models, and only requires that stresses within the earth are hydrostatic below some depth.The Bouguer gravity anomalies associated with topographic features contain information about the distribution of compensating mass, even though they do not determine it uniquely. If plausible limits can be placed on the maximum density differences involved, for instance, bounds can be established on the depth of the compensating mass (Parker 1975). More powerful constraints on the distribution of compensation are possible if a mechanical model of the compensation process can be specified.The earliest, and still the most commonly used, isostatic models are those of Pratt and Airy. They have tended t o dominate geophysical thinking about the processes by which isostasy is achieved, and about the definition and computation of isostatic gravity anomalies. Both are local compensation models: a topographic load is assumed to be supported only by the hydrostatic pressure at a point on the surface of compensation directly beneath it, or conversely, the compensating density at any point within the earth is determined only by the topographic elevation directly above it. The classic picture of local compensation is of a set of rigid blocks floating in a denser liquid, entirely independent of one another, and free to move vertically so as to achieve individual hydrostatic equilibrium. In the Pratt model, the blocks have different densities, the value of the density determining the elevation; in the Airy model, the blocks are of equal density, but diffe...

A near‐bottom magnetic survey was conducted over the Brunhes/Matuyama reversal boundary near the East Pacific Rise crest at 21° N. Magnetic measurements were made on a level plane approximately 200 m above the sea floor using the Marine Physical Laboratory's deep‐tow vehicle, with precise transponder navigation. Track density was high both parallel and perpendicular to the magnetic lineations in order to study fine scale deviations from two‐dimensionality. The magnetic field on a gridded map was inverted to obtain the crustal magnetization distribution (including the effects of topography) by extension of the Fourier technique of Parker and Huestis [1974]. Linearity of sources parallel to the spreading center was not assumed, nor was upward continuation necessary in this treatment. We found that the polarity transition boundary is extremely straight and sharp and is very close to two‐dimensional even on a scale of hundreds of meters. Deviations from two‐dimensionality, however, occur within the magnetized blocks away from the transition zone. The polarity transition width is narrow, only 1000 m to 1400 m throughout the study area. This suggests a zone of crustal emplacement which is only 600–1000 m wide at the spreading center, which is in excellent agreement with geologic observations in the area. Comparisons are made with a two‐dimensional treatment of the same data from profiles (i.e., assuming linearity of sources). These studies also document a long‐wavelength (≈ 60 km) sinuosity in the trend of the magnetic anomalies. This sinuosity is the result of offsets of the spreading center which are not transform faults but which involve a component of strike slip motion subparallel to the spreading center.

Near-bottom magnetic data over six oceanic ridge segments in the East Pacific are inverted, giving magnetization solutions with alternate positive and negative bands which correspond to geomagnetic field reversals. We estimate the average half-width of the crustal formation zone to be 2-3 km, based on the transition widths between these bands. The solutions show a narrow region of high magnetization centred directly over the centre of spreading, superimposed on a more gradual decrease of magnetization amplitudes with age. Both features are attributed to weathering of highly magnetized pillow lavas. We demonstrate that the short wavelength ( < 3 km) anomalies are largely due to topography. Distances to reversal boundaries give distance us age curves for each ridge which show that spreading changes occur as sudden accelerations typically separated by several million years of very constant motion. These rate changes are probably accompanied by shifts in the locations of poles of relative motion, which are necessary in a system of more than two interacting plates. Palaeomagnetic data and reversal boundary locations from near-bottom and surface data are combined to give spreading half-rates and a refined time scale for the past 6 My. Widespread spreading rate variations occurred at 2-3 MyBP and about 5 MyBP, possibly as a response to large scale changes in the plate pattern.

S U M M A R YWhen marine magnetic-anomaly data are used to construct geomagnetic polarity timescales, the usual assumption of a smooth spreading-rate function at one seafloor spreading ridge forces much more erratic rate functions at other ridges. To eliminate this problem, we propose a formalism for the timescale problem that penalizes non-smooth spreading behaviour equally for all ridges. Specifically, we establish a non-linear Lagrange multiplier optimization problem for finding the timescale that (1) agrees with known chron ages and with anomaly-interval distance data from multiple ridges and (2) allows the rate functions for each ridge to be as nearly constant as possible, according to a cumulative penalty function. The method is applied to a synthetic data set reconstructed from the timescale and rate functions for seven ridges, derived by Cande & Kent (1992) under the assumption of smooth spreading in the South Atlantic. We find that only modest changes in the timescale (less than 5 per cent for each reversal) are needed if no one ridge is singled out for the preferential assumption of smoothness. Future implementation of this non-prejudicial treatment of spreading-rate data from multiple ridges to large anomaly-distance data sets should lead to the next incremental improvement to the pre-Quaternary geomagnetic polarity timescale, as well as allow a more accurate assessment of global and local changes in seafloor spreading rates over time.