rectprismgrav {gravmagsubs}

rectprismgrav

Description

Calculates the graviational attraction of 3-D rectangular prisms. Calculates anomalies of N prisms at M observation stations.

Stations cannot be positioned on the edge of a prism.

Coordinates of stations and prisms are assumed to share a common coordinate system.

Usage

rectprismgrav(xstation, ystation, zstation, xmin, xmax, ymin, ymax,
                         zdeep, zshallow, deltarho, bycell=FALSE)

Arguments

xstation

vector of length M with the x-coordinates of each station, in km, positive east;

ystation

vector of length M with the y-coordinates of each station, in km, positive north;

zstation

vector of length M with the z-coordinates of each station, in km, positive up;

xmin

vector of length N with the minimum x-coordinates of each prism, in km, positive east;

xmax

vector of length N with the maximum x-coordinates of each prism, in km, positive east;

ymin

vector of length N with the minimum y-coordinates of each prism, in km, positive north;

ymax

vector of length N with the maximum y-coordinates of each prism, in km, positive north;

zdeep

vector of length N with the bottom z-coordinates of each prism, in km, positive up;

zshallow

vector of length N with the top z-coordinates of each prism, in km, positive up;

deltarho

vector of length N with the density contrast of each prism, in grams per cubic centimeter (g/cc);

bycell

returns M-by-N matrix with anomaly values generated by individual prisms (default FALSE).

Value

Returns a matrix of length M rows.

If bycell=FALSE, there will be M rows and 1 column, and the element in the i-th row represents the total gravity anomaly generated by all N prisms as observed at the i-th station.

If bycell=TRUE, the matrix will have M rows and N columns, with the element [i,j] representing the anomaly value generated by the j-th prism as observed at the i-th station.

References

• Plouff, D., 1975, Derivation of formulas and FORTRAN programs to compute gravity anomalies of prisms, National Technical Information Service No. PB-243-526, U.S. Department of Commerce, Springfield, VA.
  https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/PB243526.xhtml.

See Also

rectprismmag, gravmagsubs.

Examples

#########################################################
## gravity anomaly of a single prism at a single point ##

# location of the point where the gravity anomaly will be calculated
gravstation <- data.frame(x=0, y=0, z=0)

# the rectangular prism is defined by its six edges
prism1 <- data.frame(xmin=-5, xmax=5,
                     ymin=-5, ymax=5,
                     zmin=-10, zmax=-5)

# density contrast in g/cc
drho <- 0.3

gravanom <- rectprismgrav(gravstation$x, gravstation$y, gravstation$z,
                          prism1$xmin, prism1$xmax,
                          prism1$ymin, prism1$ymax,
                          prism1$zmin, prism1$zmax, drho)

#########################################################