No abstract

Broad areas of anomalously shallow seafloor surround regions of active or recently active hot spot volcanism. The cause of these midplate swells has been modeled both as elevated temperatures in a convecting layer and as thermal expansion within the conducting portion of the lithosphere. According to the former explanation, we would expect the low-density material compensating the swell to lie beneath the conducting lid, whereas the latter model allows compensation at shallower depths. We present a technique based on the application of linear filters for determining the compensation depth of midplate swells given observations of topography and geoid or gravity anomalies. Our method does not require an a priori estimate of swell height or width, nor does it assume complete spatial or spectral separation between the swell topography and the signal from the hot spot volcanoes, which are compensated by flexure of the oceanic Moho. Rather, we exploit the difference in the predicted sign and amplitude of the Moho deflection beneath elevated topography produced by loading above versus loading below the elastic plate in order to separate the two effects. An application of these linear filters to residual topography and geoid data from the region surrounding the Hawaiian hot spot yields a compensation depth of 70 + 10 km, within the lower lithosphere. 13,91513,916 MCNUTT AND SHURE: COMPENSATION DEPTH OF THE HAWAIIAN SWELL sea

The traditional least squares method for modeling seamount magnetism is often unsatisfactory because the models fail to reproduce the observations accurately. We describe an alternative approach permitting a more complex internal structure, guaranteed to generate an external field in close agreement with the observed anomaly. Potential field inverse problems like this one are fundamentally incapable of a unique solution, and some criterion is mandatory for picking a plausible representative from the infinite‐dimensional space of models all satisfying the data. Most of the candidates are unacceptable geologically because they contain huge magnetic intensities or rapid variations of magnetization on fine scales. To avoid such undesirable attributes, we construct the simplest type of model: the one closest to a uniform solution as measured by the norm in a specially chosen Hilbert space of magnetization functions found by a procedure called seminorm minimization. Because our solution is the most nearly uniform one we can say with certainty that any other magnetization satisfying the data must be at least as complex as ours. The theory accounts for the complicated shape of seamounts, representing the body by a covering of triangular facets. We show that the special choice of Hilbert space allows the necessary volume integrals to be reduced to surface integrals over the seamount surface, and we present numerical techniques for their evaluation. Exact agreement with the magnetic data cannot be expected because of the error of approximating the shape and because the measured fields contain noise of crustal, ionospheric, and magnetospheric origin. We examine the potential size of the various error terms and find that those caused by approximation of the shape are generally much smaller than the rest. The mean magnetization is a vector that can in principle be discovered from exact knowledge of the external field of the seamount; this vector is of primary importance for paleomagnetic work. We study the question of how large the uncertainty in the mean vector may be, based on actual noise, as opposed to exact, data; the uncertainty can be limited only by further assumptions about the internal magnetization. We choose to bound the rms intensity. In an application to a young seamount in the Louisville Ridge chain we find that remarkably little nonuniformity is required to obtain excellent agreement with the observed anomaly while the uniform magnetization gives a poor fit. The paleopole position of ordinary least squares solution lies over 30° away from the geographic north, but the pole derived from our seminorm minimizing model is very near the north pole as it should be. A calculation of the sensitivity of the mean magnetization vector to the location of the magnetic observations shows that the data on the perimeter of the survey were given the greatest weight and suggests that enlargement of the survey area might further improve the reliability of the results.

We present/a preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements using the method of harmonic splines. This model (PHS (80) for preliminary harmonic splines) is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of 10 nT to account for crustal and external fields as well as noise in the measurement procedure). Therefore PHS (80) is more suitable for studies of the core than models derived with the traditional least squares approach (e.g., GSFC (9/80)). We compare characteristics of the harmonic spline spectrum, topology of the core field and especially the null-flux curves (loci where the radial field is zero) and the flux through patches bounded by such curves. PHS (80) is less complex than GSFC (9/80) and is therefore more representative of that part of the core field that the data constrain. INTRODUCTIONModels for the internal part of the earth's magnetic field for epoch 1980 have been derived using least squares analysis techniques [e.g., . The internal part itself has two major constituents. The larger portion by far arises from electric currents flowing in the highly conducting core; magnetized crustal rocks are the second most important internal source. The separation of the two sources has, until now, been attempted by designating some degree L in the spherical harmonic representation of the field's potential as the cutoff for the core contributions. Unfortunately, there is no physical reason for truncation at any specific degree. In the past the cutoff was chosen to include only statistically significant coefficients or, more recently, where spectral evidence [Langel and indicates that crustal fields dominate core fields. The task is analogous to low-pass filtering a noisy time series: it is not assumed that the original signal is devoid of energy at high frequencies, but the filter is used to isolate the part of the spectrum that can be reliably extracted from the observed signal. The spherical geometry and the requirement of a harmonic representation make it impossible to apply standard filter design theory directly to our problem. Nonetheless, it seems reasonable to assume that the undesirable characteristics of filters with an extremely sharp cutoff (particularly ringing in the filtered series) would carry over. Truncation of the spherical harmonic series corresponds to the sharpest possible kind of low-pass filter. We avoid truncation by using a different approach, that of harmonic splines (see Shure et al., [1982], hereafter referred to as SPB, and Parker and Shure [1982]). A field model is constructed that is as smooth as possible at the core (in a precisely defined sense) and that is consistent with the observations when the crustal contribution is regarded as noise.With the harmonic spline approach we have constructed a preliminary model of the core field based upon 4180 measurements carefully selected from the Magsat data base. In this paper we ...