Cross domain account logon events

Hi,

Our organisation has two domains with a 2 way trust established between the two, lets call them domain A and domain B.

We have users in domain A who often use domain resources in domain B, however, we do not have auditing of resource usage configured via group policy.

I need to find a way of tracing which users in domain A have used resources in domain B.

I know that logon events for users in domain A will be logged in the DC in domain A that authenticated them, however, will any events be logged on any DCs in domain B if the user accesses resources in this domain, without auditing enabled of course?

Any advice is greatly appreciated.

Thanks