The answer is b: counting the craters in surrounding plains.
Explanation for each option:
a. Measuring the thickness of lava flows on their sides: This method can provide information about the volume and extent of lava flows, but it does not directly indicate the age of the most recent eruption.
b. Counting the craters in surrounding plains: This is a common method used in planetary geology to estimate the age of a surface. The number of impact craters can be used to determine the relative age of a surface, as older surfaces tend to have more craters. This method is often used to estimate the age of volcanic activity on Mars, including the Tharsis volcanoes.
c. Measuring the intensity of infrared radiation emitted by them: While infrared measurements can provide information about the temperature and composition of volcanic surfaces, they do not directly indicate the age of the most recent eruption.
d. Measuring the changes in sulfur compound concentrations in the planet's atmosphere: Changes in atmospheric sulfur compounds could indicate volcanic activity, but they do not provide a direct method for dating the most recent eruption.
In summary, counting the craters in surrounding plains is the most relevant method for determining the most recent time the Tharsis volcanoes on Mars have erupted.
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