The large bandwidth combined with ultra-massive multiple-input multiple-output (UM-MIMO) arrays enables terahertz (THz) systems to achieve terabits-per-second throughput. The THz systems are expected to operate in the near, intermediate, as well as the far-field. As such, channel estimation strategies suitable for the near, intermediate, or far-field have been introduced in the literature. In this work, we propose a cross-field, i.e., able to operate in near, intermediate, and far-field, compressive channel estimation strategy. For an array-of-subarrays (AoSA) architecture, the proposed method compares the received signals across the arrays to determine whether a near, intermediate, or far-field channel estimation approach will be appropriate. Subsequently, compressed estimation is performed in which the proximity of multiple subarrays (SAs) at the transmitter and receiver is exploited to reduce computational complexity and increase estimation accuracy. Numerical results show that the proposed method can enhance channel estimation accuracy and complexity at all distances of interest.