griddataLSC can be used interpolate data using least squares collocation.It offers the choice of 6 covariance functions; 1. the 3-D logarithmic covariance function2. the 2-D exponential covariance function3. the 2-D Reilly covariance function4. the 2-D triangular covariance function5. the 2-D Gaussian covariance function6. the 2-D second order Markov covariance functionThe covariance function parameters can be specified or they can be fitted to estimated empirical covariance values. ________________________________________________________________________How to use griddataLSC2-D observation data:.............G (x,y)+N(X,Y)_________G(x,y)+N(X,Y)...................................../........../............/........................................................./_G (x_i,y_i)?__/......................................................../.........../............/..................................G(x,y)+N(X,Y)/______/______/G(x,y)+N(X,Y)..............for some observation data G made a locations X,Y with estimated noise variances N (~=0) (for each measurement G) griddataLSC can interpolate G by least squares collocation to locations Xi,Yi using one of the following covariance functions, - the exponential, - Reilly, - triangular, - Gaussian or - Second order Markov model to obtain values Gi, and determine the covariance function parameters C0 and D ; [Gi,C0,D]=griddataLSC('exp',X,Y,G,N,Xi,Yi); for exponential [Gi,C0,D]=griddataLSC('Reilly',X,Y,G,N,Xi,Yi); for Reilly [Gi,C0,D]=griddataLSC('tri',X,Y,G,N,Xi,Yi); for triangular [Gi,C0,D]=griddataLSC('gaus',X,Y,G,N,Xi,Yi); for Gaussian [Gi,C0,D]=griddataLSC('som',X,Y,G,N,Xi,Yi); for Second order Markov to also out put the estimated empirical covariance values the users can specify the following additional output argumentse.g. for exponential[Gi,C0,D,Covariancevalues,CovarianceDistance]=griddataLSC('exp',X,Y,G,N,Xi,Yi); a figure of the empirical covariance values and the fitted model can also be output using the additional input arguments e.g. for exponential[Gi,C0,D,Covariancevalues,CovarianceDistance]=griddataLSC('exp',X,Y,G,N,Xi,Yi,'covfigure'); if C0,D are already known and you want to specify them, usee.g. for exponential [Gi]=griddataLSC('exp',X,Y,G,N,Xi,Yi,C0,D);3-D observation data:..............G (x,y,z)+N(x,y,z)_________G(x,y,z)+N(x,y,z)................................../............/............/........................................................../______/______/........................................................../............/............/.................................G(x,y,z)+N(x,y,z)/______/______/G(x,y,z)+N(x,y,z)...................................._____________............................................................/............/............./.........................................................../_G (x_i,y_i,zi)?_/........................................................../............/............./.........................................................../______/______/.......................................for some observation data G made a locations X,Y and Z with estimated noise variances N (~=0) (for each measurement G) griddataLSC can interpolate G to locations Xi,Yi,Zi using a 3-D logarithmic covariance function fitted to the data emprical covariance values, [Gi,C0,D,T]=griddataLSC('log',X,Y,Z,G,N,Xi,Yi,Zi);to out put the empirical covariance values, use the following additional output arguments [Gi,C0,D,T,Covariancevalues,CovarianceDistance]=griddataLSC('log',X,Y,Z,G,N,Xi,Yi,Zi);to output a figure of the empirical covariance values and the fitted model,use the following additional input arguments [Gi,C0,D,T,Covariancevalues,CovarianceDistance]=griddataLSC('log',X,Y,Z,G,N,Xi,Yi,Zi,'covfigure'); if C0,D,T are already known or the user would like to specify them, then the following can be used [Gi]=griddataLSC('log',X,Y,Z,G,N,Xi,Yi,Zi,C0,D,T);This can be be used to upward/downward continue gravity observations and simultaneously grid the data.
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