4625 & 4776 Errors on DC

I am seeing Event ID errors 4625 & 4776 in the security logs on the Domain Controllers. Our Intranet DC have a one way trust with our DMZ DCs (DMZ trusts Intranet). On the Intranet DCs the errors show failed login due to "Unknown user name or bad password" for the machine account. The DMZ DC is failing login on the Intranet DC.



Log Name:     Security
Source:       Microsoft-Windows-Security-Auditing
Date:         10/2/2015 11:15:52 AM
Event ID:      4625
Task Category: Logon
Level:        Information
Keywords:     Audit Failure
User:         N/A
Computer:     Intranet_DC
Description:
An account failed to log on.

Subject:
                Security ID:                             NULL SID
                Account Name:                      -
                Account Domain:                   -
                Logon ID:                               0x0

Logon Type:                                          3

Account For Which Logon Failed:
                Security ID:                             NULL SID
                Account Name:                      DMZ_DC$
                Account Domain:                   DMZ

Failure Information:
                Failure Reason:                     Unknown user name or bad password.
                Status:                                     0xc000006d
                Sub Status:                             0xc000006a

Process Information:
                Caller Process ID: 0x0
                Caller Process Name:           -

Network Information:
                Workstation Name:               DMZ_DC
                Source Network Address:     XXX.XXX.XXX.XXX
                Source Port:                           60261

Detailed Authentication Information:
                Logon Process:                     NtLmSsp
                Authentication Package:       NTLM
                Transited Services:               -
                Package Name (NTLM only):               -
                Key Length:                            0

This event is generated when a logon request fails. It is generated on the computer where access was attempted.

The Subject fields indicate the account on the local system which requested the logon. This is most commonly a service such as the Server service, or a local process such as Winlogon.exe or Services.exe.

The Logon Type field indicates the kind of logon that was requested. The most common types are 2 (interactive) and 3 (network).

The Process Information fields indicate which account and process on the system requested the logon.

The Network Information fields indicate where a remote logon request originated. Workstation name is not always available and may be left blank in some cases.

The authentication information fields provide detailed information about this specific logon request.
                - Transited services indicate which intermediate services have participated in this logon request.
                - Package name indicates which sub-protocol was used among the NTLM protocols.
                - Key length indicates the length of the generated session key. This will be 0 if no session key was requested.

Event:
Log Name: Security
Source: Microsoft Windows security
Event ID: 4625
Level: Information
User: N/A
OpCode: Info
Task Category: Logon
Keywords: Audit Failure
Computer: Intranet_DC

------------------------------------------------------------------------------------

The computer attempted to validate the credentials for an account.

Authentication Package:       MICROSOFT_AUTHENTICATION_PACKAGE_V1_0
Logon Account:     DMZ_DC$
Source Workstation:             DMZ_DC
Error Code:            0xc000006a

Event:
Log Name: Security
Source: Microsoft Windows security
Event ID: 4776
Level: Information
User: N/A
OpCode: Info
Task Category: Credential Validation
Keywords: Audit Failure
Computer: Intranet_DC