Which document is used to authorize the operation of trains over broken rail when no other routes are available?

The correct choice is Form D line 13, as this document specifically serves the purpose of authorizing train movements in situations where there may be hazardous conditions, such as broken rail, when no other routes are available. This form is critical in ensuring safety while allowing necessary operations to continue, as it outlines specific instructions and restrictions that must be adhered to during the train's passage over the designated area.

Other documents, like Form D line 4, may serve different functions related to train operations, but they do not encompass the specific context of authorizing train movement over broken rail under such circumstances. Standard Operating Procedures offer broad guidelines for operational practices but lack the specificity needed in emergencies involving track conditions. The Maintenance Log documents the maintenance history of tracks and equipment, but it does not have the authority to permit a train's operation over compromised infrastructure. Thus, Form D line 13 is the appropriate choice to ensure a safe and controlled response in a critical situation.