I'd suggest to use robocopy
for replicating the contents of the subfolders:
$srcBase = 'C:\some\Logs\Application'
$dstBase = 'D:\other\Logs\Application'
Get-ChildItem $srcBase | ? { $_.PSIsContainer } | % {
$dst = "$dstBase\$($_.Name)\Machine1"
& robocopy $_.FullName $dst /e
}