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Geophysical Prospecting: Normalized downward continuation of potential fields within the quasi‐harmonic region

Downward continuation is a useful transformation, mainly used to enhance measured gravity or magnetic field anomalies. It is known to be an unstable transformation that should be strictly used only in the harmonic region, apparently preventing any meaningful application to continuations inside the source volume. Despite these well‐known theoretical and practical limitations it has been used to recover source parameters by different methods, here referred to as normalized full gradient methods. Such methods show that downward continuation may be extended to the source volume, which is assumed to contain one‐point, isolated singularities, which is a quasi‐harmonic region. We modify the normalized full gradient method focusing our attention to the way the downward continuation is normalized. Differently from normalized full gradient methods, we study the effect of the normalization not only on the analytical signal modulus of the downward continued field but also on the downward continuation of the gravity or magnetic fields themselves. With our method, called normalized downward continuation, several statistically meaningful normalizations are considered, some of them yielding improved, more resolved depth estimations for synthetic as well as measured total‐field anomalies. From a statistical point of view, the downward continued field tends to have right‐skewed histograms at shallow depths, while becoming symmetrically distributed at greater depths. This occurs because, as the depth of continuation increases, the intrinsic error propagation of the downward continuation allows the error to dominate with respect to the source‐related signal. For non‐isolated anomalies, consistent results are also obtained but the normalizing factors must be computed within windows centred to the studied anomaly.

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