deepening vs escalation

deepening

noun
  • The act of becoming deeper. 

escalation

noun
  • an increase or rise, especially one to counteract a perceived discrepancy 

  • a deliberate or premeditated increase in the violence or geographic scope of a conflict 

  • The reassignment of a difficult customer problem to someone whose job is dedicated to handling such cases. 

How often have the words deepening and escalation occurred in a corpus of books? (source: Google Ngram Viewer )