Size-Frequency Distribution

Definition

The size-frequency distribution is a statistical representation of the relative abundance of different-sized objects within a population or sample. It is commonly used in the context of impact craters to understand the distribution and frequency of crater sizes on planetary surfaces.

5 Must Know Facts For Your Next Test

1. The size-frequency distribution of impact craters on a planetary surface follows a power law, with smaller craters being more abundant than larger ones.
2. The slope of the size-frequency distribution curve provides information about the impactor population and the cratering process on the surface.
3. Crater scaling laws are used to estimate the size of the impactor that created a crater based on the crater's diameter.
4. The size-frequency distribution can be used to estimate the age of a planetary surface by comparing it to the expected distribution for a known crater production function.
5. Crater saturation occurs when the surface is so densely cratered that new craters begin to overlap and destroy older ones, leading to a constant crater density over time.

Review Questions

• Explain how the size-frequency distribution of impact craters on a planetary surface is related to the impactor population and cratering process.
  • The size-frequency distribution of impact craters on a planetary surface follows a power law, where smaller craters are more abundant than larger ones. This relationship is a result of the impactor population, which is typically dominated by smaller objects, and the cratering process, where the size of the crater scales with the size and velocity of the impactor. The slope of the size-frequency distribution curve provides information about the impactor population and the cratering process, as it reflects the relative abundance of different-sized impactors and the efficiency of the cratering process.
• Describe how crater scaling laws are used to estimate the size of the impactor that created a specific impact crater.
  • Crater scaling laws are empirical relationships that describe the size of an impact crater as a function of the impactor size, velocity, and other parameters. By measuring the diameter of an impact crater and applying the appropriate crater scaling law, it is possible to estimate the size of the impactor that created the crater. This information can be used to infer the characteristics of the impactor population and the cratering process on the planetary surface.
• Analyze how the size-frequency distribution of impact craters can be used to estimate the age of a planetary surface.
  • The size-frequency distribution of impact craters on a planetary surface can be used to estimate the age of the surface by comparing it to the expected distribution for a known crater production function. Older surfaces will have a higher density of craters and a more evolved size-frequency distribution, with fewer small craters due to the cumulative destruction of smaller craters over time. By matching the observed size-frequency distribution to the expected distribution for a given age and crater production function, it is possible to estimate the age of the planetary surface. This technique is commonly used in planetary geology to understand the history and evolution of planetary surfaces.

Related terms

Power Law: A mathematical function that describes the relationship between the size and frequency of objects, where the frequency is inversely proportional to a power of the size.

Crater Scaling Laws: Empirical relationships that describe the size of an impact crater as a function of the impactor size, velocity, and other parameters.

Crater Saturation: The state where the surface of a planetary body is covered with so many impact craters that new craters begin to overlap and destroy older ones, leading to a constant crater density over time.