International Journal of Earth Sciences (Geologische Rundschau)
New astronomical and revised 40Ar/39Ar ages for the Eocene maar lake of Messel (Germany)
by
Olaf K. Lenz1, Volker Wilde, Dieter F. Mertz, and Walter Riegel
1Technische Universität Darmstadt, Institute of Applied Geosciences, Applied Sedimentology, Schnittspahnstrasse 9, 64287 Darmstadt, Germany,
E-mail: , Phone:+49(0)6151/162271, Fax:+49(0)6151166539
Supplementary material (SM)
Calculation of phase shifts
Based on the synchronization of the eccentricity amplitude modulations of the palynological record with the La2010a and La2010d solutions, it is possible to calculate phase shifts for all eccentricity cycles that can be detected within the filtered short eccentricity signals. The phase angles were calculated by applying a simple formula:
φ° = 360° x f x Δt - (φ = phase angle (deg), f = frequency, Δt = time delay)
For the calculation of the eccentricity Δt–values, the age of the maximum deflection of every cycle of the eccentricity amplitude modulation within the 640 kyr record was recorded from the La2010a and La2010d solutions. The corresponding cycles and the maximum deflections in the amplitude modulations of the individual clusters were also identified and the time differences to the maximum deflections of the La2010a and d solutions calculated (Supplementary data: SM-Tab. 1, 2).
The La2010a/d solutions show that the period respectively the frequency between two cycles is not a constant, because the cycle length fluctuates between 70 and 160 kyr during the time interval between 48.5 and 47 Ma (Supplementary data: SM-Figs.1, 2). Therefore, the average period value for eccentricity (~100 kyr) is not appropriate for the correct calculation of phase angles. Accordingly, the frequency calculation has been adjusted for each cycle by the cycle length provided by the La2010a/d solutions for eccentricity. Subsequently, several phase wheels were constructed, which display the phase angle of every cycle (Text-Figs. 7, 8).
Due to inconsistencies in preparation of the samples and counting, slight variations in the percentages of palynomorphs are possible. Therefore, it is assumed that this can shift the maximum deflection of a cycle within the amplitude modulation by ±1 sample, which leads to a phase error estimation.
Based on the time interval of 1.4 kyr between two samples, an average eccentricity cycle (100 kyr) is composed of 71.4 samples. The phase error of the maximum deflection (±1 sample) is thus for eccentricity ±5°in average. Due to the varying periods and frequencies, for every cycle the phase error calculation has been adjusted by the exact cycle length (Supplementary data: SM Tab. 1, 2).
SM - Figure1:La2010 a solution - Ages of positive anomalies of short eccentricitycyclesand respective cycle lengths for the time interval 48.5 – 47.0 Ma (data available on La2010a data for eccentricity: file La2010a_ecc3L.dat; Laskar et al., 2011).
SM - Figure2:La2010 d solution - Ages of positive anomalies of short eccentricitycyclesand respective cycle lengths for the time interval 48.5 – 47.0 Ma (data available on La2010d data for eccentricity: file La2010d_ecc3L.dat; Laskar et al., 2011).
A / B / C / D / E / F / GOption 1 / e14 / 47.042 / 607.6 / 47.0325 / -9.5 / -34.2 / ±5.0
e13 / 47.142 / 503.5 / 47.1366 / -5.4 / -18.8 / ±4.8
e12 / 47.246 / 434.3 / 47.2058 / -40.2 / -141.8 / ±4.9
e11 / 47.348 / 281.0 / 47.3591 / 11.1 / 44.1 / ±5.5
e10 / 47.439 / 180.6 / 47.4595 / 20.5 / 70.3 / ±4.8
e9 / 47.544 / 72.5 / 47.5676 / 23.6 / 106.1 / ±6.3
Option 2 / e13 / 47.142 / 607.6 / 47.1295 / -12.5 / -43.3 / ±4.8
e12 / 47.246 / 503.5 / 47.2366 / -12.4 / -43.9 / ±4.9
e11 / 47.348 / 434.3 / 47.3028 / -45.2 / -178.8 / ±5.5
e10 / 47.439 / 281.0 / 47.4561 / 17.1 / 58.7 / ±4.8
e9 / 47.544 / 180.6 / 47.5565 / 12.5 / 56.3 / ±6.3
e8 / 47.624 / 72.5 / 47.6646 / 40.6 / 99.3 / ±3.4
Option 3 / e12 / 47.246 / 607.6 / 47.2343 / -11.7 / -41.3 / ±4.9
e11 / 47.348 / 503.5 / 47.3384 / -9.6 / -38.1 / ±5.5
e10 / 47.439 / 434.3 / 47.4076 / -31.4 / -107.5 / ±4.8
e9 / 47.544 / 281.0 / 47.5609 / 16.9 / 76.2 / ±6.3
e8 / 47.624 / 180.6 / 47.6613 / 37.3 / 91.3 / ±3.4
e7 / 47.771 / 72.5 / 47.7694 / -1.6 / -5.7 / ±4.9
Option 4 / e11 / 47.348 / 607.6 / 47.3390 / -9.0 / -35.6 / ±5.5
e10 / 47.439 / 503.5 / 47.4431 / 4.1 / 13.9 / ±4.8
e9 / 47.544 / 434.3 / 47.5123 / -31.7 / -142.6 / ±6.3
e8 / 47.624 / 281.0 / 47.6656 / 41.6 / 101.9 / ±3.4
e7 / 47.771 / 180.6 / 47.7660 / -5.0 / -17.5 / ±4.9
e6 / 47.874 / 72.5 / 47.8741 / 0.1 / 0.3 / ±5.0
Option 5 / e10 / 47.439 / 607.6 / 47.4435 / 4.5 / 15.4 / ±4.8
e9 / 47.544 / 503.5 / 47.5476 / 3.6 / 16.1 / ±6.3
e8 / 47.624 / 434.3 / 47.6168 / -7.2 / -17.6 / ±3.4
e7 / 47.771 / 281.0 / 47.7701 / -0.9 / -3.0 / ±4.9
e6 / 47.874 / 180.6 / 47.8705 / -3.5 / -12.5 / ±5.0
e5 / 47.975 / 72.5 / 47.9786 / 3.6 / 13.3 / ±5.2
Option 6 / e9 / 47.544 / 607.6 / 47.5490 / 5.0 / 22.5 / ±6.3
e8 / 47.624 / 503.5 / 47.6531 / 29.1 / 71.2 / ±3.4
e7 / 47.771 / 434.3 / 47.7223 / -48.7 / -170.2 / ±4.9
e6 / 47.874 / 281.0 / 47.8756 / 1.6 / 5.8 / ±5.0
e5 / 47.975 / 180.6 / 47.9760 / 1.0 / 3.7 / ±5.2
e4 / 48.072 / 72.5 / 48.0841 / 12.1 / 47.0 / ±5.4
Option 7 / e8 / 47.624 / 607.6 / 47.6525 / 28.5 / 69.8 / ±3.4
e7 / 47.771 / 503.5 / 47.7566 / -14.4 / -50.5 / ±4.9
e6 / 47.874 / 434.3 / 47.8258 / -48.2 / -171.7 / ±5.0
e5 / 47.975 / 281.0 / 47.9791 / 4.1 / 15.4 / ±5.2
e4 / 48.072 / 180.6 / 48.0795 / 7.5 / 29.2 / ±5.4
e3 / 48.165 / 72.5 / 48.1876 / 22.6 / 85.6 / ±5.3
Option 8 / e7 / 47.771 / 607.6 / 47.7585 / -12.5 / -43.7 / ±4.9
e6 / 47.874 / 503.5 / 47.8626 / -11.4 / -40.7 / ±5.0
e5 / 47.975 / 434.3 / 47.9318 / -43.2 / -160.3 / ±5.2
e4 / 48.072 / 281.0 / 48.0851 / 13.1 / 51.1 / ±5.4
e3 / 48.165 / 180.6 / 48.1855 / 20.5 / 77.7 / ±5.3
e2 / 48.260 / 72.5 / 48.2936 / 33.6 / 115.1 / ±4.8
SM - Table 1: Phase shift calculation for short eccentricity (La2010a solution, Laskar et al., 2011). A: Orbital cycle (see SM-Figs.1/2); B: Ages of positive anomalies (in Ma); La2010a solution for short eccentricity, file La2010a_eccc3L.dat; Laskar et al., 2011); C: Timing of positive anomalies of amplitude modulation of cluster 8 and of negative anomalies of amplitude modulations of clusters 3, 4, 6, 7 (average value in ka); D: Possible ages of positive/negative anomalies of clusters 3, 4, 6, 7, 8 (based on best synchronization, in Ma); E: Time delay to La2010a solution (in ka); F: Phase shift (in °); Green: in-phase situation, phase shift < (-)45°, Orange: slightly out of phase, phase shift > (-)45°, < (-)90°, Red: out of phase or anti-phase situation, phase shift > (-)90°; G: Phase shift – error estimation (in °)
SM - Table 2: Phase shift calculation for short eccentricity (La2010d solution, Laskar et al., 2011). A: Orbital cycle (see SM-Figs.1/2); B: Ages of positive anomalies (in Ma); La2010a solution for short eccentricity, file La2010d_eccc3L.dat; Laskar et al., 2011); C: Timing of positive anomalies of amplitude modulation of cluster 8 and of negative anomalies of amplitude modulations of clusters 3, 4, 6, 7 (average value in ka); D: Possible ages of positive/negative anomalies of clusters 3, 4, 6, 7, 8 (based on best synchronization, in Ma); E: Time delay to La2010a solution (in ka); F: Phase shift (in °); Green: in-phase situation, phase shift < (-)45°, Orange: slightly out of phase, phase shift > (-)45°, < (-)90°, Red: out of phase or anti-phase situation, phase shift > (-)90°; G: Phase shift – error estimation (in °)
A / B / C / D / E / F / GOption 1 / e14 / 47.048 / 607.6 / 47.0321 / -15.9 / -58.2 / ±5.1
e13 / 47.146 / 503.5 / 47.1362 / -9.8 / -35.2 / ±5.0
e12 / 47.246 / 434.3 / 47.2054 / -40.5 / -144.4 / ±5.0
e11 / 47.347 / 281.0 / 47.3587 / 11.8 / 46.6 / ±5.5
e10 / 47.438 / 180.6 / 47.4591 / 21.2 / 79.3 / ±5.3
e9 / 47.534 / 72.5 / 47.5672 / 33.2 / 126.0 / ±5.3
Option 2 / e13 / 47.146 / 607.6 / 47.1290 / -17.0 / -61.3 / ±5.0
e12 / 47.246 / 503.5 / 47.2331 / -13.0 / -46.2 / ±5.0
e11 / 47.347 / 434.3 / 47.3023 / -44.7 / -176.8 / ±5.5
e10 / 47.438 / 281.0 / 47.4556 / 17.6 / 66.1 / ±5.3
e9 / 47.534 / 180.6 / 47.5560 / 22.0 / 83.3 / ±5.3
e8 / 47.629 / 72.5 / 47.6641 / 35.1 / 127.5 / ±5.1
Option 3 / e12 / 47.246 / 607.6 / 47.2260 / -20.0 / -71.4 / ±5.0
e11 / 47.347 / 503.5 / 47.3301 / -17.0 / -67.1 / ±5.5
e10 / 47.438 / 434.3 / 47.3993 / -38.7 / -145.2 / ±5.3
e9 / 47.534 / 281.0 / 47.5526 / 18.6 / 70.6 / ±5.3
e8 / 47.629 / 180.6 / 47.6530 / 24.0 / 87.2 / ±5.1
e7 / 47.728 / 72.5 / 47.7611 / 33.1 / 128.0 / ±5.4
Option 4 / e11 / 47.347 / 607.6 / 47.3218 / -25.2 / -99.7 / ±5.5
e10 / 47.438 / 503.5 / 47.4259 / -12.1 / -45.5 / ±5.3
e9 / 47.534 / 434.3 / 47.4951 / -38.9 / -147.4 / ±5.3
e8 / 47.629 / 281.0 / 47.6484 / 19.4 / 70.7 / ±5.1
e7 / 47.728 / 180.6 / 47.7488 / 20.8 / 80.5 / ±5.4
e6 / 47.821 / 72.5 / 47.8569 / 35.9 / 76.9 / ±3.0
Option 5 / e10 / 47.438 / 607.6 / 47.4288 / -9.2 / -34.5 / ±5.3
e9 / 47.534 / 503.5 / 47.5329 / -1.1 / -4.3 / ±5.3
e8 / 47.629 / 434.3 / 47.6021 / -26.9 / -97.7 / ±5.1
e7 / 47.728 / 281.0 / 47.7554 / 27.4 / 106.2 / ±5.4
e6 / 47.821 / 180.6 / 47.8558 / 34.8 / 74.6 / ±3.0
e5 / 47.989 / 72.5 / 47.9639 / -25.1 / -123.9 / ±6,9
Option 6 / e9 / 47.534 / 607.6 / 47.5328 / -1.2 / -4.5 / ±5.3
e8 / 47.629 / 503.5 / 47.6369 / 7.9 / 28.6 / ±5.1
e7 / 47.728 / 434.3 / 47.7061 / -21.9 / -84.7 / ±5.4
e6 / 47.821 / 281.0 / 47.8594 / 38.4 / 82.4 / ±3.0
e5 / 47.989 / 180.6 / 47.9598 / -29.2 / -144.0 / ±6,9
e4 / 48.062 / 72.5 / 48.0679 / 5.9 / 20.0 / ±4,8
Option 7 / e8 / 47.629 / 607.6 / 47.6385 / 9.5 / 34.5 / ±5.1
e7 / 47.728 / 503.5 / 47.7426 / 14.6 / 56.4 / ±5.4
e6 / 47.821 / 434.3 / 47.8118 / -9.2 / -19.7 / ±3.0
e5 / 47.989 / 281.0 / 47.9651 / -23.9 / -117.7 / ±6,9
e4 / 48.062 / 180.6 / 48.0655 / 3.5 / 11.9 / ±4,8
e3 / 48.168 / 72.5 / 48.1736 / 5.6 / 20.7 / ±5.2
Option 8 / e7 / 47.728 / 607.6 / 47.7302 / 2.2 / 8.5 / ±5.4
e6 / 47.821 / 503.5 / 47.8343 / 13.3 / 28.4 / ±3.0
e5 / 47.989 / 434.3 / 47.9035 / -85.5 / -421,6 / ±6,9
e4 / 48.062 / 281.0 / 48.0568 / -5.2 / -17.5 / ±4,8
e3 / 48.168 / 180.6 / 48.1572 / -10.8 / -40.1 / ±5.2
e2 / 48.265 / 72.5 / 48.2653 / 0.3 / 1.0 / ±4.9