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fixed formula for mm1
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src/gstools/cokriging/base.py

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@@ -28,7 +28,7 @@ class CollocatedCokriging(Krige):
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Both variants assume the cross-covariance follows:
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.. math::
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C_{YZ}(h) = \\rho_{YZ}(0) \\cdot \\sqrt{C_Z(h) \\cdot C_Y(h)}
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C_{YZ}(h) = \frac{C_{YZ}(0)}{C_Z(0)} \cdot C_Z(h)
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where :math:`\\rho_{YZ}(0)` is the cross-correlation at zero lag. This assumption
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requires that primary and secondary variables have similar spatial

src/gstools/cokriging/methods.py

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@@ -27,15 +27,15 @@ class SimpleCollocated(CollocatedCokriging):
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Assumes the cross-covariance follows the Markov Model I:
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.. math::
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C_{YZ}(h) = \\rho_{YZ}(0) \\cdot \\sqrt{C_Z(h) \\cdot C_Y(h)}
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C_{YZ}(h) = \frac{C_{YZ}(0)}{C_Z(0)} \cdot C_Z(h)
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where :math:`\\rho_Y(h) = \\rho_Z(h)`, meaning both variables share the same
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spatial correlation structure. This requires similar spatial correlation
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patterns between primary and secondary variables.
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**Known Limitation:**
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MM1 can produce variance inflation :math:`\\sigma^2_{\\text{SCCK}} > \\sigma^2_{\\text{SK}}`
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Simple collocated cokriging can produce variance inflation :math:`\\sigma^2_{\\text{SCCK}} > \\sigma^2_{\\text{SK}}`
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in some cases. For accurate variance estimation, use :any:`IntrinsicCollocated` instead.
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**Estimator:**
@@ -187,7 +187,7 @@ class IntrinsicCollocated(CollocatedCokriging):
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Like :any:`SimpleCollocated`, assumes the cross-covariance follows:
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.. math::
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C_{YZ}(h) = \\rho_{YZ}(0) \\cdot \\sqrt{C_Z(h) \\cdot C_Y(h)}
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C_{YZ}(h) = \frac{C_{YZ}(0)}{C_Z(0)} \cdot C_Z(h)
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**Advantage over SimpleCollocated:**
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