Pop the popcorn, season it with a drizzle of olive oil and salt, and set aside.
In a bowl, combine the tomato juice, lemon juice, fennel, cucumber, onion, celery, salt and pepper, to taste. Place it in the refrigerator to chill.
In a 10-inch skillet over high heat, warm 2 tablespoons olive oil. Season the halibut with salt and pepper, to taste. Add the halibut to the pan and cook, without stirring, until the halibut is browned on 1 side, about 2 to 3 minutes. Stir the halibut briefly and cook for 30 seconds longer. Remove the halibut with a slotted spoon. Add remaining 1 tablespoon olive oil to the pan. When the oil is hot, add the garlic and cook until light brown, stirring. Add the jalapeno and cook for 15 seconds, stirring. Add the shrimp and season with salt and pepper. Stir and cook until barely done, about 1 1/2 minutes. Add the clam juice and wine; bring the mixture to a boil and cook for about 30 seconds. Remove the shrimp from the pan. Continue until the liquid is reduced by half. Return the halibut and shrimp to the pan and stir to coat them with the liquid. Remove the pan from the heat and allow the mixture to cool.
When you are ready to serve, stir the tomatoes, fennel fronds, parsley, basil, and vinegar into the chilled tomato juice and vegetables. Spoon the tomato mixture into bowls and top with the cooled seafood mixture. Garnish with a handful of popcorn.