Assessment of the Effect of Instrumental and Discretization Errors on Derivative‐based Potential‐field Geophysical Methods

Abstract

Geophysical field measurements are subject to errors, which consequently comprise part of the data and subsequently they are propagated through processing techniques. Some of these errors can be controlled and eliminated, but others such as the errors introduced by the measuring instrument cannot be avoided. Moreover, the field data are collected as discrete samples, a procedure that introduces errors by itself. These two types of error are examined in the present study regarding their propagation and influence in estimating derivatives and subsequently functions of derivatives, such as the complex attributes. For this reason we consider magnetic anomalies (signals) of typical buried structures that are common in archaeological prospection, such as concealed ditches. In order to have analytical expressions for the magnetic anomaly signal, the structures are simulated by polygonal bodies. The magnetic anomaly signals are subsequently discretized and anomaly derivatives as well as complex attributes are computed using numerical methods. These discrete function values are compared with the corresponding values obtained from the analytical solutions in order to assess the discretization errors involved. Similarly, calculations are repeated after contaminating the signals with Gaussian noise in an attempt to simulate the effect of instrumental error. A parametric study of these two error sources is performed, showing that they have a contradictory effect: larger sampling intervals increase, as expected, the numerical divergence of ideal data (no noise) from their analytical form. On the other hand, for realistic data (with random noise) the increase of the measuring step decreases the effect of instrument error. The combined influence of both sources of errors shows that the various derivative‐based measures exhibit a minimum of the introduced total error for different combinations of discretization and measurement errors. The quantitative study of the combined error provides useful suggestions on the best way that magnetic surveys should be carried out when the use of derivatives is employed for the final data interpretation. Copyright © 2012 John Wiley & Sons, Ltd.