Step 1Puree the tomato quarters in a blender in batches. Pour through a sieve into a large pitcher. Discard the seeds. You should have 4 cups tomato juice. Set aside.
Step 2Place the olives, peppers, lemon and lime juice, Worcestershire, horseradish, pepper, Tabasco and salt in a blender and puree until smooth.
Step 3 Add the tomato juice and blend.