subroutine verder(grid,nx,ny,dx,dy,norder,store) c c Subroutine VERDER calculates the vertical derivative of c gridded potential field data using the following steps: c (1) Fourier transform the field, (2) multiply by the vertical c derivative filter, and (3) inverse Fourier transform the c product. Field values are specified on a rectangular grid c with x and y axes directed north and east, respectively; c north is arbitrary. Z axis is down. Requires subroutines c FOURN and KVALUE. c c Input parameters: c nx - number of elements in the south-to-north direction. c ny - number of elements in the west-to-east direction. c (NOTE: both nx and ny must be a power of two.) c grid - a singly dimensioned real array containing the c two-dimensional potential field. Elements should c be in order of west to east, then south to north (i.e., c element 1 is southwest corner, element ny is c southeast corner, element (nx-1)*ny+1 is northwest c corner, and element ny*nx is northeast corner. c store - a singly dimensioned real array used internally. c It should be dimensioned at least 2*nx*ny in the c calling program. c dx - sample interval in the x direction, units irrelevant. c dy - sample interval in the y direction, units irrelevant. c norder - the order of the vertical derivative. c c Output parameters: c grid - upon output, grid contains the vertical derivative of c the potential field with same orientation as above. c dimension grid(nx*ny),store(2*nx*ny),nn(2) complex cgrid,cmplx real kx,ky,k data pi/3.14159265/ index(i,j,ncol)=(j-1)*ncol+i nn(1)=ny nn(2)=nx ndim=2 dkx=2.*pi/(nx*dx) dky=2.*pi/(ny*dy) do 10 j=1,nx do 10 i=1,ny ij=index(i,j,ny) store(2*ij-1)=grid(ij) 10 store(2*ij)=0. call fourn(store,nn,ndim,-1) do 20 j=1,nx do 20 i=1,ny ij=index(i,j,ny) call kvalue(i,j,nx,ny,dkx,dky,kx,ky) k=sqrt(kx**2+ky**2) cgrid=cmplx(store(2*ij-1),store(2*ij)) cgrid=cgrid*k**norder store(2*ij-1)=real(cgrid) 20 store(2*ij)=aimag(cgrid) call fourn(store,nn,ndim,+1) do 30 j=1,nx do 30 i=1,ny ij=index(i,j,ny) 30 grid(ij)=store(2*ij-1)/(nx*ny) return end