Optimal models of the extended standard anelastic solid type (Section 2.4) fitted simultaneously to the variations of modulus and dissipation with oscillation period for the lowest differential pressure Pd of 5 MPa. Values of selected parameters were refined by the Levenberg–Marquardt scheme for iterative non-linear least-squares fitting to minimize the objective function |${\chi ^2} = \,\,\chi _M^2 + \chi _{{Q^{ - 1}}}^2$|. Values in parentheses indicate the uncertainties in the last digit of the refined value, whereas parameter values in square brackets were held constant. ‘Background + peak’ models are denoted ‘bg + pk’, whereas peak-only models are denoted ‘pk’.
| Parameter, unit . | Glycerine saturation . | Glycerine and water saturation . | |||
|---|---|---|---|---|---|
| . | G & QG−1 . | E & QE−1 . | G & QG−1 . | E & QE−1(adj) . | K & QK−1 . |
| . | pk . | pk . | bg + pk . | bg + pk . | bg + pk . |
| N, (M, logQM−1) pairs | 9 | 9 | 18 | 18 | 11 |
| Pd, MPa | 5 | 5 | 5 | 5 | 5 |
| GU/EU/KU, GPa | 14.7(3) | 28.8(4) | 11.9(2) | 26.0(3) | 16.6(3) |
| ΔB | (0) | (0) | (0.6) | 1.1(3) | 2.1(6) |
| α | (0.25) | 0.39(6) | 0.36(8) | ||
| log(τLR, s) | (−5.0) | (−5.0) | (−5.0) | ||
| log(τHR, s) | (5.0) | (5.0) | (5.0) | ||
| ΔP | 0.86(5) | 0.35(3) | 0.48(2) | 0.45(2) | 1.11(5) |
| log(τPR, s) | 1.2(4) | 1.8(1) | −2.20(6) | −1.26(3) | −0.89(2) |
| σ | (6) | 1.7(2) | (3) | 1.42(7) | 0.55(10) |
| χ2M | 0.29 | 0.9 | 156.2 | 212.7 | 325.0 |
| |$\chi _{{Q^{ - 1}}}^2$| | 2.95 | 19.0 | 32.5 | 92.1 | 215.8 |
| χ2T | 3.24 | 19.9 | 188.7 | 304.8 | 540.8 |
| (χ2T/2 N)1/2 | 0.42 | 1.05 | 2.29 | 2.91 | 4.96 |
| Parameter, unit . | Glycerine saturation . | Glycerine and water saturation . | |||
|---|---|---|---|---|---|
| . | G & QG−1 . | E & QE−1 . | G & QG−1 . | E & QE−1(adj) . | K & QK−1 . |
| . | pk . | pk . | bg + pk . | bg + pk . | bg + pk . |
| N, (M, logQM−1) pairs | 9 | 9 | 18 | 18 | 11 |
| Pd, MPa | 5 | 5 | 5 | 5 | 5 |
| GU/EU/KU, GPa | 14.7(3) | 28.8(4) | 11.9(2) | 26.0(3) | 16.6(3) |
| ΔB | (0) | (0) | (0.6) | 1.1(3) | 2.1(6) |
| α | (0.25) | 0.39(6) | 0.36(8) | ||
| log(τLR, s) | (−5.0) | (−5.0) | (−5.0) | ||
| log(τHR, s) | (5.0) | (5.0) | (5.0) | ||
| ΔP | 0.86(5) | 0.35(3) | 0.48(2) | 0.45(2) | 1.11(5) |
| log(τPR, s) | 1.2(4) | 1.8(1) | −2.20(6) | −1.26(3) | −0.89(2) |
| σ | (6) | 1.7(2) | (3) | 1.42(7) | 0.55(10) |
| χ2M | 0.29 | 0.9 | 156.2 | 212.7 | 325.0 |
| |$\chi _{{Q^{ - 1}}}^2$| | 2.95 | 19.0 | 32.5 | 92.1 | 215.8 |
| χ2T | 3.24 | 19.9 | 188.7 | 304.8 | 540.8 |
| (χ2T/2 N)1/2 | 0.42 | 1.05 | 2.29 | 2.91 | 4.96 |
Optimal models of the extended standard anelastic solid type (Section 2.4) fitted simultaneously to the variations of modulus and dissipation with oscillation period for the lowest differential pressure Pd of 5 MPa. Values of selected parameters were refined by the Levenberg–Marquardt scheme for iterative non-linear least-squares fitting to minimize the objective function |${\chi ^2} = \,\,\chi _M^2 + \chi _{{Q^{ - 1}}}^2$|. Values in parentheses indicate the uncertainties in the last digit of the refined value, whereas parameter values in square brackets were held constant. ‘Background + peak’ models are denoted ‘bg + pk’, whereas peak-only models are denoted ‘pk’.
| Parameter, unit . | Glycerine saturation . | Glycerine and water saturation . | |||
|---|---|---|---|---|---|
| . | G & QG−1 . | E & QE−1 . | G & QG−1 . | E & QE−1(adj) . | K & QK−1 . |
| . | pk . | pk . | bg + pk . | bg + pk . | bg + pk . |
| N, (M, logQM−1) pairs | 9 | 9 | 18 | 18 | 11 |
| Pd, MPa | 5 | 5 | 5 | 5 | 5 |
| GU/EU/KU, GPa | 14.7(3) | 28.8(4) | 11.9(2) | 26.0(3) | 16.6(3) |
| ΔB | (0) | (0) | (0.6) | 1.1(3) | 2.1(6) |
| α | (0.25) | 0.39(6) | 0.36(8) | ||
| log(τLR, s) | (−5.0) | (−5.0) | (−5.0) | ||
| log(τHR, s) | (5.0) | (5.0) | (5.0) | ||
| ΔP | 0.86(5) | 0.35(3) | 0.48(2) | 0.45(2) | 1.11(5) |
| log(τPR, s) | 1.2(4) | 1.8(1) | −2.20(6) | −1.26(3) | −0.89(2) |
| σ | (6) | 1.7(2) | (3) | 1.42(7) | 0.55(10) |
| χ2M | 0.29 | 0.9 | 156.2 | 212.7 | 325.0 |
| |$\chi _{{Q^{ - 1}}}^2$| | 2.95 | 19.0 | 32.5 | 92.1 | 215.8 |
| χ2T | 3.24 | 19.9 | 188.7 | 304.8 | 540.8 |
| (χ2T/2 N)1/2 | 0.42 | 1.05 | 2.29 | 2.91 | 4.96 |
| Parameter, unit . | Glycerine saturation . | Glycerine and water saturation . | |||
|---|---|---|---|---|---|
| . | G & QG−1 . | E & QE−1 . | G & QG−1 . | E & QE−1(adj) . | K & QK−1 . |
| . | pk . | pk . | bg + pk . | bg + pk . | bg + pk . |
| N, (M, logQM−1) pairs | 9 | 9 | 18 | 18 | 11 |
| Pd, MPa | 5 | 5 | 5 | 5 | 5 |
| GU/EU/KU, GPa | 14.7(3) | 28.8(4) | 11.9(2) | 26.0(3) | 16.6(3) |
| ΔB | (0) | (0) | (0.6) | 1.1(3) | 2.1(6) |
| α | (0.25) | 0.39(6) | 0.36(8) | ||
| log(τLR, s) | (−5.0) | (−5.0) | (−5.0) | ||
| log(τHR, s) | (5.0) | (5.0) | (5.0) | ||
| ΔP | 0.86(5) | 0.35(3) | 0.48(2) | 0.45(2) | 1.11(5) |
| log(τPR, s) | 1.2(4) | 1.8(1) | −2.20(6) | −1.26(3) | −0.89(2) |
| σ | (6) | 1.7(2) | (3) | 1.42(7) | 0.55(10) |
| χ2M | 0.29 | 0.9 | 156.2 | 212.7 | 325.0 |
| |$\chi _{{Q^{ - 1}}}^2$| | 2.95 | 19.0 | 32.5 | 92.1 | 215.8 |
| χ2T | 3.24 | 19.9 | 188.7 | 304.8 | 540.8 |
| (χ2T/2 N)1/2 | 0.42 | 1.05 | 2.29 | 2.91 | 4.96 |
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