Correlation-Based Automatic Localisation Taper

Builds an npar x nobs localisation taper directly from the ensemble, with no parameter / observation coordinates required. This is the iterative-ensemble-smoother-native localisation of Luo & Bhakta (2020): spurious sample correlations between a parameter and an observation (an artefact of finite ensemble size) are damped, while genuine correlations that stand above an estimated noise floor are retained.

Usage

correlation_localisation(
  par_diff,
  obs_diff,
  threshold = -1,
  taper = "hard",
  n_shuffle = 1L,
  quantile = 0.95
)

Arguments

par_diff

Matrix (npar x nreal). Parameter anomalies.

obs_diff

Matrix (nobs x nreal). Observation anomalies.

threshold

Numeric. Noise floor on \(|\rho|\). Negative (default -1) triggers automatic estimation by permutation.

taper

Character. "hard" (indicator) or "soft" (linear ramp above the floor).

n_shuffle

Integer. Number of permutation replicates for the automatic floor (default 1; each replicate yields npar * nobs spurious samples). Ignored when threshold >= 0.

quantile

Numeric in (0, 1). Quantile of the spurious-correlation distribution used as the floor (default 0.95). Ignored when threshold >= 0.

Value

A list with rho (the npar x nobs taper), threshold (the floor used), n_active (count of entries with non-zero weight), and frac_active (that count over npar * nobs).

Details

The sample correlation \(\rho_{ij}\) between parameter-anomaly row \(i\) and observation-anomaly row \(j\) is compared against a noise floor \(\theta\). When threshold < 0 the floor is estimated by destroying the parameter-observation link — the realisation order of the observation anomalies is randomly permuted, independently per replicate, and the floor is taken as a high quantile (default 0.95) of the resulting spurious \(|\rho|\) values. The permutation uses R's RNG, so the estimate is reproducible under set.seed().

Two tapers are offered. "hard" keeps correlations above the floor unchanged (weight 1) and zeroes the rest. "soft" applies a smooth, monotone ramp \(w_{ij} = \mathrm{clip}((|\rho_{ij}| - \theta) / (1 - \theta), 0, 1)\), which downweights near-floor correlations rather than thresholding them sharply.

References

Luo, X. & Bhakta, T. (2020). Automatic and adaptive localization for ensemble-based history matching. Journal of Petroleum Science and Engineering, 184, 106559.

Examples

set.seed(1L)
npar <- 8L; nobs <- 5L; nreal <- 40L
pd <- matrix(rnorm(npar * nreal), npar, nreal)
# Make parameter 1 genuinely correlated with observation 1.
od <- matrix(rnorm(nobs * nreal), nobs, nreal)
od[1L, ] <- od[1L, ] + 2 * pd[1L, ]
loc <- correlation_localisation(pd, od)
loc$threshold
#> [1] 0.2559031
loc$rho[1L, 1L]
#> [1] 1