Creating a list column with Powershell for a blog site using existing site columns

When I get the fields property for a blog list, it returns empty.

$SiteURL = "Blog site URL here"

$web = Get-SPWeb $SiteURL

foreach($field in $web.Fields)
{

  Write-Host $field
}

But when I go to site columns in site settings I see many fields with the source being the parent site.

Can someone help me with adding an existing site column to the Post list of a Blog site ?

Thanks