<P><FONT FACE="Helvetica" SIZE="-1"> Bessel [ Jo (h) ]</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> exp(-h) * cos(dh)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> exp(-h) * Jo(dh)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> exp(-h<SUP>2</SUP>) *cos(dh)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> exp(-h<SUP>2</SUP>) *Jo(dh)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> exp(-h<SUP>2</SUP>) * (1 - dh<SUP>2</SUP>)</FONT></P><BR WP="BR1"><BR WP="BR2"></MULTICOL><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">data:  data [x yvariable]</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x0:  grid coordinates [xiyi]</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">model:  semivariogrammodel</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">a:  semivariogram range</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">d:  model coefficient (differentfrom coefficient b of variogr, same as d in cokri)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">c:  model amplitude</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">A:  g(h<SUB>ik</SUB>) matrix ifalready calculated; if not, ignore that input.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Zp:  kriged data matrix at x0positions</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Sp:  variance of kriged data atx0 positions</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Davis, J.C.  1986.<EM>Statistics and Data Analysis in Geology</EM>, 2nd ed., JohnWiley &amp; Sons, New York, 289 p.</FONT></P><P><FONT FACE="Helvetica"><STRONG>deplie</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Vector to matrixtransformation.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat = deplie (y, nx,ny)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Transformation of a vector yinto a matrix mat of size ny x nx.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y:  row or columnvector</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">nx:  number of columns in matrixmat</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">ny:  number of rows in matrixmat</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U></U></FONT><FONTFACE="Helvetica" SIZE="-1"><U>Output variable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">mat:  matrix</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = [(1:10) (1:10)(1:10)];</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">deplie (y, 10, 3) = 1 2 3 4 5 67 8 9 10</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1 2 3 4 5 6 7 8 9 10</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"> 1 2 3 4 5 6 7 8 9 10</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">kregrid</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica"><STRONG>filresp</STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Barnes' filter response in thewavelength domain.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">R = filresp (c, g)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Barnes' filter response in thewavelength domain is given by:</FONT></P><P><FONT FACE="Times New Roman" SIZE="-1"></FONT><FONT FACE="TimesNew Roman" SIZE="-1"><img src="engli0{image20}.gif" width="137"height="29" align=bottom > </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">where</FONT><FONT FACE="TimesNew Roman" SIZE="-1"> </FONT><FONT FACE="Helvetica" SIZE="-1"><imgsrc="engli0{image21}.gif" width="140" height="29" align=bottom >, cand g are the filter parameters and l is the wavelength.</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><center><imgsrc="engli0{image22}.gif" width="1" height="1"></center></FONT><FONT FACE="Times New Roman" SIZE="-1"><center><imgsrc="engli0{image23}.gif" width="287" height="287"></center></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">f2 =filresp(200,0.6);</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>References</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Barnes, S.L.,1973.  MesoscaleObjective Map Analysis Using Weighted Time Series Observations.NOAA Tech.  Memo.  ERL NSSL-62, 60 p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Maddox, R.A., 1980.  AnObjective Technique for Separating Macroscale and Mesoscale Featuresin Meteorological Data.  Mon.  Wea.  Rev., 108,1108:1121.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG>Seealso</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">barnes, tintore</FONT></P><P><FONT FACE="Helvetica"><STRONG>fitvario / fitvari2 /fun</STRONG></FONT><FONT FACE="Helvetica" SIZE="-1"></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario:  Optimization ofvariogr.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvari2:  Optimization ofvariogr2 (without the Optimization Toolbox).</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fun:  Called from fitvario toestimate variograms.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario (model, data, a)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario (model, data, a,b)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvari2 (model, data, a, b,C)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">f = fun (lam, data)</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Least-square fitting ofsemivariogram model coefficients a, b and C.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">model:  model type (seevariogr)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">data(:,1):  x-axis (distance)(gam(:,1))</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">data(:,2):  y-axis (variance)(gam(:,2))</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">a, b et C:  starting values ofcoefficients a, b and C of variogr</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Output:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The graphical output shows theplot of the semivariance as a function of the distance.Experimental results appear as symbols.  The plain line gives thebest fit for the model chosen.  The optimal values of a, b and C arealso displayed on the graph.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><center><imgsrc="engli0{image24}.gif" width="1" height="1"></center></FONT><FONT FACE="Times New Roman" SIZE="-1"><center><imgsrc="engli0{image25}.gif" width="323" height="277"></center></FONT><FONT FACE="Helvetica"SIZE="-1"><STRONG>Example</STRONG></FONT></P><MULTICOL COLS="2" WIDTH="340" GUTTER="46"><P><FONT FACE="Helvetica" SIZE="-1">r = (0:10)';</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">x = 1 - exp(-r);</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvario(2,[r x],2) </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">fitvari2(2,[rx],2,0,1.5)</FONT></P><BR WP="BR1"><BR WP="BR2"></MULTICOL><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>See also</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">leastsq into the OptimizationToolbox, variogr, variogr2</FONT></P><P><FONT FACE="Helvetica"><STRONG>gam2, gamv2, gamv2uv gam3,gamv3</STRONG></FONT><FONT FACE="Helvetica"SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">MEX-file called from vario2dr,vario2di, var2diuv, vario3dr and vario3di.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, gam, hm, tm, hv, tv] = gam2(nlag, nx, ny, ndir, ixd, iyd, vr, tmin, tmax, nvarg, ivtail,ivhead, ivtype, nvar)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, dis, gam, hm, tm, hv, tv] =gamv2 (nd, x, y, vr, tmin, tmax, nlag, xlag, xltol, ndir, azm, atol,bandw, nvarg, ivtail, ivhead, ivtype, nvar)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, dis, gam, hm, tm, hv, tv] =gamv2uv (nd, x, y, u, v, tmin, tmax, nlag, xlag, xltol, ndir, azm,atol, bandw, nvarg, ivtail, ivhead, ivtype, nvar, option)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, gam, hm, tm, hv, tv] = gam3(nlag, nx, ny, nz, ndir, ixd, iyd, izd, vr, tmin, tmax, nvarg,ivtail, ivhead, ivtype, nvar)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">[np, dis, gam, hm, tm, hv, tv] =gamv3 (nd, x, y, z, vr, tmin, tmax, nlag, xlag, xltol, ndir, azm,atol, bandwh, dip, dtol, bandwd, nvarg, ivtail, ivhead, ivtype,nvar)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">The description of inputs andoutputs is given in vario2dr, vario2di, var2diuv, vario3dr andvario3di.  These functions are MEX-files compiled from sourceFortran codes gam2.for, gamv2.for, gam3.for and gamv3.for of GSLIB(Deutsch et Journel, 1992).</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Reference</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Deutsch, C.  V and A.  G.Journel,1992.<EM> GSLIB:  Geostatistical Software Library and User'sGuide</EM>.  Oxford University Press, Oxford, 340 p.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>See also</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">vario2dr, vario2di, vario3dr,vario3di, var2diuv</FONT></P><P><FONT FACE="Helvetica"><STRONG>kregrid /kregrid3</STRONG></FONT><FONT FACE="Helvetica"SIZE="-1"><STRONG></STRONG></FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Purpose</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Matrix (m x 2) of 2-D gridcoordinates.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Matrix (m x 3) of 3-D gridcoordinates.</FONT></P><P><FONT FACE="Helvetica"SIZE="-1"><STRONG>Synopsis</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = kregrid (x0, dx, xf, y0, dy,yf)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y = kregrid3 (x0, dx, xf, y0,dy, yf, z0, dz, zf)</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><STRONG></STRONG></FONT><FONTFACE="Helvetica" SIZE="-1"><STRONG>Description</STRONG></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Grid (x,y) coordinates arereshape in an m x 2 matrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">Grid (x,y,z) coordinates arereshape in an m x 3 matrix.</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Inputvariables:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">(x0,y0,z0):  (x,y,z) position ofthe lower left corner of the grid</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">(xf, yf, zf):  (x,y,z) positionof the upper right corner of the grid</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">dx:  x grid interval </FONT></P><P><FONT FACE="Helvetica" SIZE="-1">dy:  y grid interval</FONT></P><P><FONT FACE="Helvetica" SIZE="-1">dz:  z grid interval</FONT></P><P><FONT FACE="Helvetica" SIZE="-1"><U>Outputvariable:</U></FONT></P><P><FONT FACE="Helvetica" SIZE="-1">y:  m x 2 or m x 3 matrix ofgrid coordinates</FONT></P><P><FONT FACE="Helvetica"