The deposition of sediment where there is a steep drop-off into shallow, flat land can create an alluvial fan. An alluvial fan is a triangular-shaped deposit of sand, gravel, and small sediments.
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A slow change to the earth's surface would be the formation of mountain ranges over millions of years due to the shifting of tectonic plates under the earth. Also, another slow change could be considered erosion or weathering. Two rapid changes could be landslides and earthquakes.