Step 1: Understand what "depth of investigation" means for a logging tool:
Depth of investigation refers to how far into the formation, away from the borehole wall, a logging tool can effectively sense and measure formation properties. Tools with a larger volume of investigation read deeper into the undisturbed formation, beyond the invaded zone near the borehole.
Step 2: Consider the Neutron log:
The neutron log measures the hydrogen index of the formation to estimate porosity. Its depth of investigation is relatively shallow, typically limited to a small radius around the borehole, because neutrons lose energy quickly through collisions with hydrogen atoms close to the source.
Step 3: Consider the Sonic log:
The sonic log measures the travel time of acoustic waves through the formation. It has a moderate depth of investigation, generally shallow to a few inches beyond the borehole wall, since it primarily responds to the rock immediately surrounding the tool.
Step 4: Consider the Density log:
The density log uses gamma ray backscatter to measure bulk density and is also a shallow reading tool, since gamma rays are absorbed quickly and the measurement is dominated by the region very close to the borehole wall.
Step 5: Consider the Resistivity log:
Resistivity logging tools, especially deep induction and deep laterolog tools, are specifically designed with long spacing between transmitter and receiver electrodes or coils to read well beyond the invaded zone into the true, undisturbed formation. This gives resistivity tools a much greater depth of investigation compared to neutron, sonic, or density tools.
Step 6: Compare and select the correct method:
Among the four options, resistivity logging provides the deepest, most extensive investigation into the marine formation, making it the correct answer.
Final Answer:
\[ \boxed{\text{Resistivity}} \]