TRANSFORMATION FROM TOTAL-FIELD MAGNETIC ANOMALY TO THE PROJECTION OF THE ANOMALOUS VECTOR ONTO THE NORMAL GEOMAGNETIC FIELD BASED ON AN OPTIMIZATION METHOD

The total-field magnetic anomaly Delta T is approximated as the component T-ap of the anomalous vector T-a along the direction of the normal geomagnetic field. It is widely used in magnetic data processing and interpretation practices as a routine if T-a is relatively small. But in highly magnetic environments, the distinction between Delta T and T-ap is often too large to be ignored. We carefully investigate the difference between Delta T and T-ap and find that it will increase rapidly in the trend of the quadratic function as T-a strengthens. We also test the effects of approximation on the component transformation and reduction to the pole on a synthetic single-sphere model. As expected, the error caused by inaccurate information will propagate into subsequent data processing procedures and adversely affect the results. Therefore, we have developed an optimization strategy based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm to transform the total-field anomaly into T-ap. First, we have constructed an objective function after transforming T-ap into T-a through the component transformation in the frequency domain. Then, using Delta T as the initial value of T-ap, T-ap is calculated iteratively by the L-BFGS algorithm. To test the validity of the optimization algorithm, T-ap is transformed for noise-free and noise-corrupted models and models with a background field. The synthetics indicate that the transformed T-ap is almost the same as the model T-ap, whose maximum error is approximately one-hundredth (30 nT) of the difference (8000 nT) between the modeled Delta T and T-ap. The synthetics and field data example from the Yangshan Iron Mine, Fujian Province, southern China, also indicate that the data transformation and forward-modeling results can benefit from the direct use of transformed T-ap instead of Delta T.