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Different geophysical surveys have a specific sensitivity to geological targets, determined by the physical nature of the observed geophysical field, the design of the data acquisition system, and the configuration and type of the source of the recorded data. The sensitivity is usually limited to some part of the examined geological formation, located relatively close to the sensors. This paper introduces a concept of controlled sensitivity, which enables the sensitivity of a geophysical data to be increased within a specific target area of a geological formation. In particular, this method can be used to increase the sensitivity of the data with the depth. The developed approach is demonstrated with a numerical study of the sensitivity of marine Towed Streamer Electro-Magnetic (TSEM) surveys. However, a general mathematical formulation of the method, presented in this paper, makes it possible to apply the developed technique to a wide variety of geophysical data.