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Summary of Significant Accounting Policies - Reconciliation of Numerators and Denominators used in Computing Basic and Diluted Net Income Per Share (Detail) - USD ($)
 3 Months Ended
Mar. 31, 2024
Mar. 31, 2023
Accounting Policies [Abstract]    
Net income (loss) attributable to Odyssey Marine Exploration, Inc. $ 3,498,024 $ 22,307,687
Basic net income (loss) available to stockholders 3,498,024 22,307,687
Fair value change in debt instruments (1,617,819) 0
Fair value change in warrants (6,798,430) 0
Interest expense related to convertible debt 0 3,562
Diluted net income (loss) available to stockholders $ (4,918,225) $ 22,311,249
Denominator:    
Weighted average common shares outstanding – Basic 20,425,934 19,666,459
Dilutive effect of options 0 4,399
Dilutive effect of restricted stock awards 0 170,681
Dilutive effect of warrants 1,909,565 0
Dilutive effect of convertible instruments 4,322,601 37,005
Weighted average common shares outstanding – Diluted 26,658,100 19,878,544
Net (loss) income per share – basic $ 0.17 $ 1.13
Net (loss) income per share – diluted $ (0.18) $ 1.12