calibrate_nls: calibrate_nls
In khaors/rves: R package for the interpretation of Vertical Electric Soundings

Description Usage Arguments Value Author(s) References See Also Examples

Function to estimate the real resistivities and thicknesses using the nonlinear least-squares approach proposed by Roy(1999).

1	calibrate_nls(ves, par0, iterations = 30, ireport = 10, trace = TRUE)

`ves`	A ves object
`par0`	A numeric vector with the values of the layer resistivities and thicknesses
`iterations`	Number of iterations
`ireport`	Number of iterations to report results on the console
`trace`	A logical flag to indicate if the optimization information must be traced

A list with the following entries:

par: A numeric vector with the values of the layer resistivities and thicknesses
value: The value or the RSS (Residual sum of squares)
rel.error: The value of the relative error (in percentage)
cal.error: A matrix with the RSS and relative error at each iteration
residual: A vector with the residuals (original scale)
var.residual: The variance of the residuals (log transformed scale)
hessian: First order approximation of the Hessian matrix. This is calculated using the Jacobian matrix.
cov.matrix: Covariance matrix of the estimated parameters calculated as the inverse of the hessian matrix.
corr.matrix: Correlation matrix of the estimated parameters.

Oscar Garcia-Cabrejo khaors@gmail.com

Roy, I. An efficient non-linear least-squares 1D inversion scheme for resistivity and IP sounding data. 1999. Geophysical Prospecting, 47, 4, 527-550.

Other calibration functions: calibrate_ilsqp, calibrate_joint_nls, calibrate_seq_joint_nls, calibrate_step_nls, calibrate_step, calibrate_svd, calibrate, log_mnad_resistivity, log_mxad_resistivity, log_rss_resistivity, mnad_resistivity, mxad_resistivity, relative_error_resitivity, rss_resistivity

# Example 1
data(ves_data1)
ab2 <- ves_data1$ab2
apprho <- ves_data1$apprho
sev1a <- ves(id= "VES1", ab2 = ab2, apprho = apprho)
# Let's fit a four layer model
rho <- c(40, 70, 30, 20)
thick <- c(2, 10, 50, 500)
par0 <- c(rho, thick)
res.nls1 <- calibrate_nls(sev1a, par0, iterations = 30, ireport = 5, trace = FALSE)
sev1a$rhopar <- res.nls1$rho
sev1a$thickpar <- res.nls1$thickness
sev1a$interpreted <- TRUE
plot(sev1a, type = "ves")
# Example 2
data(ves_data2)
ab2 <- ves_data2$ab2
apprho <- ves_data2$apprho
sev2a <- ves(id = "TD76", ab2 = ab2, apprho = apprho)
rho <- c(20, 50, 100, 10)
thick <- c(10, 20, 500, 100)
par0 <- c(rho, thick)
res.nls2 <- calibrate_nls(sev2a, par0, iterations = 30, ireport = 5, trace = FALSE)
sev2a$rhopar <- res.nls2$rho
sev2a$thickpar <- res.nls2$thickness
sev2a$interpreted <- TRUE
plot(sev2a, type = "ves")