# Dictionary:Continuation

Jump to navigation
Jump to search

{{#category_index:C|continuation}}
Determining a field over one surface from measurements of the field over another surface (specifically, at another elevation). The field at the elevation *z*, *F*(*x*,*y*,*z*), can be found from the field on the surface, *F*(*x* ', *y* ',0). Where the surfaces are horizontal and no sources intervene, the **upward-continuation** relation (an application of Green's theorem) is

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle F(x,y,z)=\frac{\left|z\right|}{2\pi}\iint \frac{F(x',y',0}{R^3}dx' dy' }**.

An interchange of the two fields in this equation gives the **downward-continuation** relation. See *downward continuation* and Peters (1949), Telford et al. (1990, §2.6.7 and 3.7.5), and Pawlowski (1995).