I don't travel from disaster to disaster, but am prepared to do so if necessary. (for example, folks from my local team did go to NYC to provide debriefings for the folks working at the WTC site in 10/01 as well as since that time.)
There's enough going on locally to keep teams busy though.
My particular training is through an organization called the
International Critical Incident Stress Foundation which provides training in one particular debriefing model. I've had multiple hours of classes through that organization, although there are several other models used, including something called "Nova" and another which is offered through the Red Cross.
The primary focus of the ICISF is to work with emergency services providers of all kinds ... police, firefighters, EMTS/paramedics, and so forth, who have been exposed to what is considered a 'critical incident' ... basically a call or event that is SOO bad that folks have trouble dealing with memories, images, or reminders of that event. A critical incident can be a big one ... like the Oklahoma City Bombing, or it can be a 'lesser' event, such as a call involving the death of a child, a death of a member of the squad, esp. line of duty death, multiple fatality accidents, that kind of thing. The purpose of debriefing is to make it less likely that individuals will be less likely to develop PTSD, reduce the risk and amount of burnout, keep people functional in the field.
In addition to the ICISF training specifically related to post traumatic stress and their debriefing process, I have a Master's Degree in Clinical Psychology. As I've mentioned elsewhere here, I'm a mental health commitment officer and crisis intervention specialist. (The debriefing stuff is volunteer, by the way. most of the ICISF debriefers are PEERS ... they are firefighters, dispatchers, police officers, and EMT/paramedics who have been exposed to the process and sought the training ... there are actually fewer pure mental health folks involved.)
And yes, there ARE people who debrief me. In addition to the informal debriefing that ordinarily occurs after a debriefing session (which can involve multiple people and last several hours) there's also a specific process called 'Debriefing the Debriefers' ... it's recognized that you can't help someone else when you yourself are getting crispy around the edges.