A 58-year-old man from Mumbai presents with acute onset swelling, pain, and warmth in the right lower limb over the past 24 hours. He had undergone total knee replacement 10 days ago. On examination, the right calf is swollen (3 cm difference in circumference compared to left), tender, and warm. Homan's sign is positive. D-dimer is elevated at 1.2 μg/mL (normal <0.5). Compression ultrasound shows a hypoechoic, non-compressible thrombus in the popliteal vein extending into the distal femoral vein. What is the most appropriate initial management?