A statistical theory of seamount magnetism

Abstract

The standard least squares estimation of the average magnetization of a seamount is generally regarded as unsatisfactory. The reason for its poor performance is, I assert, due to the strong correlation and uneven magnitudes of the unfitted noise component of the magnetic anomaly. Least squares estimation depends for its efficiency and freedom from bias upon the statistical independence and common distribution of the random contamination. The primary contributor to the unfitted field is the part due to nonuniformity of the magnetic material within the seamount. If the magnetic heterogeneities are modeled as a random stationary vector field of known functional form, it is possible to calculate the covariance matrix of the magnetic field noise. Then, to the extent that the statistical description of the magnetic sources is valid, the correlation can be properly accounted for in the least squares procedure by weighting the observations to form an equilibrated set with random components that are independent and identically distributed. The main use of the average magnetization vector is in the determination of the associated paleopole position: I show how the least squares estimates of the magnetization vector and its uncertainty are mapped into a confidence region for the pole position. Application of this theory to a young seamount in the South Pacific is highly satisfactory. The model stationary vector field chosen for the magnetization is one with isotropic directional behavior and a very short length scale of correlation. It is found that the equilibrated residuals are far less correlated than those of the conventional procedure and the misfits are uniformly distributed throughout the equilibrated data. The estimated paleopole position is within a few degrees of the north geographic pole, which is the expected location because the seamount is geologically young. Traditional least squares fitting gave a pole at latitude 60°N. The 95% confidence zone associated with the paleopole position has semiaxes measuring 16° by 13°, and thus the uncertainty is not much larger than those of standard paleomagnetic work.