Landslides are generally associated with a trigger, such as an earthquake, a rapid snowmelt or a large storm. The landslide event can include a single landslide or many thousands. The frequency-area (or volume) distribution of a landslide event quantifies the number of landslides that occur at different sizes. We examine three well-documented landslide events, from Italy, Guatemala and the USA, each with a different triggering mechanism, and find that the landslide areas for all three are well approximated by the same three-parameter inverse-gamma distribution. For small landslide areas this distribution has an exponential 'roll-over' and for medium and large landslide areas decays as a power-law with exponent −2·40. One implication of this landslide distribution is that the mean area of landslides in the distribution is independent of the size of the event. We also introduce a landslide-event magnitude scale m L = log(N LT ), with N LT the total number of landslides associated with a trigger. If a landslide-event inventory is incomplete (i.e. smaller landslides are not included), the partial inventory can be compared with our landslide probability distribution, and the corresponding landslide-event magnitude inferred. This technique can be applied to inventories of historical landslides, inferring the total number of landslides that occurred over geologic time, and how many of these have been erased by erosion, vegetation, and human activity. We have also considered three rockfall-dominated inventories, and find that the frequency-size distributions differ substantially from those associated with other landslide types. We suggest that our proposed frequency-size distribution for landslides (excluding rockfalls) will be useful in quantifying the severity of landslide events and the contribution of landslides to erosion.

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organised criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. These include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection and magnetic field generation. Many advances have been made in the field since the first edition was published. In this edition coverage of self-organised criticality is expanded and statistics and time series are included to provide a broad background for the reader. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics. Problems are included for the reader to solve.

Mantle Convection in the Earth and Planets is a comprehensive synthesis of all aspects of mantle convection within the Earth, the terrestrial planets, the Moon, and the Galilean satellites of Jupiter. The book includes up-to-date discussions of the latest research developments that have revolutionized our understanding of the Earth and the planets. It is suitable as a text for graduate courses in geophysics and planetary physics, and as a supplementary reference for use at the undergraduate level. It is also an invaluable review for researchers in the broad fields of the Earth and planetary sciences including seismologists, tectonophysicists, geodesists, mineral physicists, volcanologists, geochemists, geologists, mineralogists, petrologists, paleomagnetists, planetary geologists, and meteoriticists. The book features a comprehensive index, an extensive reference list, numerous illustrations (many in color) and major questions that focus the discussion and suggest avenues of future research.

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If the number‐size distribution of objects satisfies the condition N ∼ r−D, then a fractal is defined with a fractal dimension D. In many cases, fragmentation results in a fractal distribution. This is taken as evidence that the fragmentation mechanism is scale invariant. Fragments produced by weathering, explosions, and impacts often satisfy a fractal distribution condition over a wide range of scales. Most correlations for number versus size for meteorites, asteroids, and interstellar grains also satisfy the fractal condition. Fractal behavior implies scale invariance; the renormalization group approach is often applicable to scale invariant processes. Two models are considered for a renormalization group approach to fragmentation; the models yield a fractal behavior but give different values for the fractal dimension. These results indicate that the fractal dimension is a measure of the fragility of the fragmented material.