INTRODUCTION
Carbonates that grow over years to thousands of years, such as corals or stalagmites, are valuable archives of climate change. Radiocarbon (14C) analysis of these archives in particular is used as a tracer for studying carbon cycle dynamics and paleoclimate (Genty and Massault Reference Genty and Massault1997; Mangini et al. Reference Mangini, Lomitschka, Eichstädter, Frank, Vogler, Bonani, Hajdas and Patzold1998). However, the 14C analysis in these samples suffers from three major drawbacks. First, establishing a time series of 14C requires laborious and time-consuming sample extraction by drilling and further chemical preparation for conversion to CO2 and eventually the preparation of the graphite sample for AMS analysis. Second, the discrete sampling technique generally bears the risk of potentially overlooking valuable information between neighboring sampling points. Third, a standard AMS analysis still requires 5–10 mg of carbonate for graphitization and 0.5–1 mg of carbonate for gas measurement, which poses a strong constraint on the analysis of very small (i.e. mg-sized) samples such as otoliths (Andrews et al. Reference Andrews, Yeman, Welte, Hattendorf, Wacker and Christl2019).
Recently, a novel online sampling and analysis method has been introduced combining laser ablation with accelerator mass spectrometry (LA-AMS) to overcome the above limitations (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Fohlmeister, Breitenbach, Robinson, Andrews, Freiwald, Farmer, Yeman, Synal and Günther2016a; Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). LA-AMS allows to produce spatially resolved 14C profiles of carbonate records covering up to several centimeters within a few hours of measurement. Up to 5 mg of CaCO3 are consumed per hour reaching a precision of 1% for modern samples. The background measured on 14C free marble of F14C = 0.011 ± 0.002 is low and reference carbonate material is well reproduced (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). This method is based on using a focused laser beam for the sampling of the carbonate: A pulsed laser beam with sufficient energy density can evaporate the material from the sample surface, whereby a mixture of particles and gas is produced. The gas, consisting of mainly CO, CO2 (and O2), can directly be flushed into an AMS system equipped with a gas ion source (Ruff et al. Reference Ruff, Wacker, Gäggeler, Suter, Synal and Szidat2007; Synal et al. Reference Synal, Stocker and Suter2007). By constantly moving the sample under the laser, a continuous carbon flow is guaranteed. The AMS data acquisition, however, has a minimum integration time leading to a quasi-continuous 14C profile. This means that a single data point always represents a certain spatial range on the sample that is given by the integration time and the velocity at which the sample is moved under the laser.
While LA AMS offers great advantages in producing highly resolved 14C records, the data evaluation involved with this approach needs careful considerations as during the measurement quasi-continuous 14C profiles are produced rather than distinct point estimates (e.g. from a micro-drilled carbonate sample). The main effects considered here are (numbers in Figure 1):
-
1. Laser-beam width. When combining several AMS data points (typically provided as 10 s averages over the continuous analysis) neighboring subsamples overlap spatially with a width that is equal to the laser width dL.
-
2. Washout. The gas produced by a laser pulse mixes with that of preceding and subsequent pulses. Consequently, a delayed and smoothened 14C/12C ratio is determined in the AMS.
-
3. Target memory. Since the start of gas ion source AMS in the 1980s the problem of a target memory is known (Bronk Ramsey and Hedges Reference Bronk Ramsey and Hedges1987). While for the standard 14C AMS analysis (gas or graphite) one AMS target is assigned to a single sample with a given (constant) 14C concentration, during LA-AMS a continuous flow with changing 14C concentration is produced and measured using the same AMS gas target. This means that gas target memory effects have to be considered.
Figure 1 Schematic view of the LA-AMS system. CO and CO2 are produced by LA in the ablation volume (left box) and then transported via a glass capillary to the ion source of the AMS (right box) passing two consecutive filters. A valve allows switching between the cell head and a He line for flushing the capillary to the ion source. The mixing effects are marked with red numbers: 1—laser-beam width, 2—washout, 3—target memory. (Please see electronic version for color figures).
The aim of this work is to present and discuss these three main effects and to develop a new data reduction strategy optimized for LA-AMS.
MATERIAL AND METHODS
Instrumental Setup
Since 2014, the LA interface connected to the gas ion source of the MICADAS at ETH (Synal et al. Reference Synal, Stocker and Suter2007; Wacker et al. Reference Wacker, Bonani, Friedrich, Hajdas, Kromer, Němec, Ruff, Suter, Synal and Vockenhuber2010a) has been in use for online 14C analysis of carbonates (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Fohlmeister, Breitenbach, Robinson, Andrews, Freiwald, Farmer, Yeman, Synal and Günther2016a, Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). A pulsed ArF excimer laser (193 nm, 8 ns pulse duration, GAM LASER, Orlando, USA) is focused onto the plane surface of the sample. The LA-AMS setup used in this study was modified from the version described in (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Fohlmeister, Breitenbach, Robinson, Andrews, Freiwald, Farmer, Yeman, Synal and Günther2016a, Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). This comprises that the rectangular spot size of the laser was reduced from 110 × 680 µm2 to 75 × 140 µm2. Furthermore, the fluence on the sample surface was increased, which leads to a higher ablation rate and gaseous carbon production (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Yeman, F. M. Breitenbach, Synal and Günther2017), resulting in a similar carbon flow rate while reaching higher spatial resolution. To move the sample under the laser, it is fixed in a holder that is mounted on an x-y positioning system in a box of two compartments (sample box). The big compartment has a volume of about 700 mL, typically filled with 200–500 mbar He that acts as a carrier gas and contains the positioning system. The small compartment is the ablation volume where the ablation process takes place, shown in Figure 1 (LA box) with a size of 900 µL (modified). For online AMS analysis, only the gaseous proportion of the ablated material is suitable. Exiting the cell, the ablated material passes through two consecutive frits with pore sizes of 2 µm and 0.5 µm (Valco frits, Vici International AG), respectively. The remaining gas mixture of He carrier gas and COX and O2 is then transported into the ion source of the MICADAS via a fused silica capillary (Ø 220 µm, l = 1 m). This gas flow is restricted to less than 3 mL/min to guarantee high vacuum conditions in the ion source. Gas targets used for LA-AMS are the same as for standard gas measurements (Ruff et al. Reference Ruff, Wacker, Gäggeler, Suter, Synal and Szidat2007; Fahrni et al. Reference Fahrni, Wacker, Synal and Szidat2013).
The key parameters influencing the gaseous C production of roughly 6 μg/min are the fluence and frequency of the laser pulse as well as the velocity of the sample moving under the laser (see Table 1). The depth of the laser track is 250 µm at a speed of 10 µm/s and repetition rate of 200 Hz. Even at a minimum speed of 5 µm/s the carbon production is constant, and no signal is lost due to crater depth. Redeposited material is negligible compared to the ablated sample volume.
Table 1 Key factors for carbon production.
Measurement Sequence
The existing LA-AMS setup is in operation at three scanning modes (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Fohlmeister, Breitenbach, Robinson, Andrews, Freiwald, Farmer, Yeman, Synal and Günther2016a)—layer scan, precision scan, and survey scan. With the layer scan, the laser is ideally moving along the growth layers constantly producing a gas mixture of one 14C/12C ratio. This mode is most similar to a regular AMS gas measurement. The precision scan describes a zigzag pattern where the laser scans up and down within growth layers while slowly moving forward across layers of different years of formation indicated by a small displacement dx. This extends the measurement time while crossing only very few growth layers, which increases counting statistics and therefore leads to more precise results. In the third scanning mode, the survey scan, the sample is ideally moved parallel to the growth axis. In the following, only survey scans will be discussed with regard to data evaluation because only in this case the 14C/12C ratio of the ablated sample material is expected to change continuously with measurement time.
LA-AMS measurements follow a standard procedure: First, the ion source of the AMS is tuned using a CO2 gas standard fed into the gas interface system (Ruff et al. Reference Ruff, Wacker, Gäggeler, Suter, Synal and Szidat2007; Wacker et al. Reference Wacker, Fahrni, Hajdas, Molnar, Synal, Szidat and Zhang2013). The measurement sequence then starts with the analysis of a CO2 gas standard (5% CO2 in helium from NIST Ox-II standard) and a gas blank (5% CO2 in helium, Messer Schweiz AG, Lenzburg, Switzerland). Both measurements are later used for blank subtraction and normalization, respectively, following BATS data reduction (Wacker et al. Reference Wacker, Christl and Synal2010b). Next, the LA system is connected to the ion source and a carbonate blank and reference carbonate material are measured to affirm operational quality of the LA-AMS setup (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). After this setup procedure the LA AMS measurements of the unknown samples start. In between samples, the carbonate blank and reference are repeatedly measured as quality and drift control. After each LA AMS sample the cell is evacuated and filled with pure helium gas to minimize crosstalk between consecutive samples. This cell cleaning procedure is repeated three times.
At the MICADAS AMS system, 14C atoms are counted for a minimum time of tC = 10 s, which is referred to as one cycle. During one cycle, the sample is moved between 50 and 5000 µm under the laser (velocities given in Table 1). Consequently, the measured 14C/12C ratio is always a mixture of 14C/12C ratios of the ablated material within one single cycle ultimately defining the limit of the spatial resolution. A single gas target can be used for up to about 100 cycles and such a measurement on one gas target is referred to as a run. Usually several runs are necessary to record the complete 14C record of one sample (coral, stalagmite, etc.), which is usually reported in F14C representing the blank, background, and fractionation corrected 14C/12C ratio relative to a standard (Reimer et al. Reference Reimer, Brown and Reimer2004).
A LA-AMS run starts with pre-sputtering the gas target for a few cycles with only helium flowing into the ion source to flush the capillary and clean the target surface. Then, the laser and the sample positioner are switched on and the sample starts moving at a predefined, constant velocity vS. At the same time, the gas flow path is connecting the sample box with the ion source and the carbon current rises (Figure 2A). The first two cycles of rising currents are extrapolated (see red line in Figure 2A) to obtain the intercept t0 = t(x = 0) with the measurement time axis, which is correlated to the starting position x0 of the laser. From x0 on with every cycle the distance dx = tC · vS + dL is covered by the laser on the sample.
Figure 2 A—12C current of a typical LA AMS measurement with rise of the current when the laser is turned on and drop in the current when the laser is turned off. B—zoom into 5 cycles to show schematically the movement of the laser-beam spot on the sample. The black rectangles indicate the area of the overlap which is the size of the laser-beam spot. The colors imply that material from this area contributes to two cycles. C—depth profile on the sample; colors show contribution to the respective cycles.
MIXING PROCESSES IN LA AMS
Overlap Due to Laser-beam Width
During a survey (or zigzag) scan in LA-AMS, the AMS records a temporal 14C/12C signal in single cycle steps of 10s while the sample is moved continuously under the laser at a velocity vs . Due to the finite width of the laser spot the 14C/12C signal recorded during two consecutive cycles always contains a spatial overlap (Figure 2B). In this section, a closer look on how to reprocess the AMS data is taken in order to disentangle the overlapping signal.
With every laser pulse, an integral 14C/12C ratio from the area covered by the laser spot is produced. During a scan, the time that each location on the sample is ablated can be expressed with:
${t_L} = {{{d_L}} \over {{v_S}}},$
where dL is the width of the laser-beam spot and vS
the velocity with which the sample is moved under the laser. When starting the laser, the sample simultaneously starts moving, which leads to a linear increase of depth in the cross section at the beginning of the scan (see Figure 2C). At the end of the full scan, this is likewise true but in reversed direction. Additionally, at the end and start of each cycle an area corresponding to the laser-beam spot size (black rectangles in Figure 2B) contributes to two consecutive cycles, indicated by the color gradient in Figure 2B. The cross section illustrates the proportion at each location that contributes to neighboring cycles. The area of the overlap compared to the overall area covered within one cycle depends on the scanning velocity:
${{{d_L}} \over {{v_S}\,\cdot\,{t_C} + {d_L}}}$
. The overlap decreases with higher velocities but so does the spatial resolution. To ensure both, good counting statistics and high spatial resolution it is beneficial to select low scanning velocities down to 5 µm/s (see application). During offline data analysis, the number of cycles that are integrated can be chosen in order to minimize the effect of the overlap and to improve counting statistics while ensuring high spatial resolution by selecting slow scanning velocities.
Cell Washout
The modified ablation volume of the LA setup is V = 900 µL with an optimized He working pressure of 200–500 mbar. The produced COX mixes within this volume before it is transported into the ion source with a He carrier gas flow of typically 1.5 mL/min. Additionally, gas from the ablation volume leaks into the sample box. Welte et al. (Reference Welte, Wacker, Hattendorf, Christl, Koch, Yeman, F. M. Breitenbach, Synal and Günther2017) estimated that while COX is produced at a rate of 6 μgC/min, only 2–3 μgC/min actually reaches the ion source. As a result, the ablation volume is flushed with a flow rate of about 3 mL/min, of which half goes to the ion source and the other half leaks into the sample box (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Yeman, F. M. Breitenbach, Synal and Günther2017). The produced COX is mixed in the ablation volume and transported into the ion source where it is additionally mixed due to the short-term memory effect of the gas target (see section target memory). The washout time constant of these processes was determined experimentally to be τ = 6 s by stopping the laser and therefore the carbon production and measuring the decline in the 12C− current (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Synal and Günther2016b). Thus, the COX produced by each laser pulse (Cn (t)) follows (Bleiner et al. Reference Bleiner, Belloni, Doria, Lorusso and Nassisi2005):
$${C_n}( t ) = {C_{0,n}}{e^{ - {\lambda _w}(t - {t_0})}}$$
At t 0 the laser produces a certain amount of COX (C0) that is washed out of the cell and sputtered off the target with a “decay constant” λw = 1/τ (shown in Figure 3C).
Figure 3 Functions describing A—minimum counting time, B—overlap due to laser-beam width, C—cell washout and short-term target memory, and D—system function. The convolution is implicated by “*” following Eq. (2).
System Function
From ablation spot to the ion source, the initial 14C/12C ratio ablated by every laser pulse is delayed and mixed by the LA AMS system. The three mixing processes (Figure 3A–C) discussed above cause a convolution of the final signal, and hence can be summarized in one system function g (Eq. 2 and Figure 3D): (1) c(tc
) represents the minimum counting time tc
= 10s, (2) l(tL
) describes the overlap with
${t_L} = {{{d_L}} \over {{v_S}}}$
and (3) w(λ
w
) indicates the washout of the ablation volume as well as the short term target memory (λ
w
= 1/6 s−1):
$$g = c({t_C})\,*\, l({t_L})\,*\, w\left( {{\lambda _w}} \right)$$
The constant system function (Figure 3D) describes the response of the LA-AMS setup for this given set of operational parameters. If one of the parameters changes, the system function is updated accordingly. The long term target memory effect would constantly modify the system function and therefore cannot be included here. It will be discussed in the following section.
Target Memory
Model for Target Memory
The gas produced by LA contains COX, which is directed onto the titanium surface of the AMS gas target. The carbon is partially adsorbed by titanium and then sputtered by the Cs beam. At the same time a proportion of the carbon ions is implanted into the titanium (Stout and Gibbons Reference Stout and Gibbons1955; Vlasyuk et al. Reference Vlasyuk, Kurovskij, Lyapunov and Radomysel’skij1986). For our model, we describe the carbon fixed on the target with two reservoirs, where carbon is deposited respectively released at different (long and short) timescales.
The reservoir with the short time constant represents carbon that is deposited on and rapidly removed from the inner, main sputtering region of the gas target. This short-term target memory effect is conceptually indistinguishable from the cell washout, and its time constant is already included in λ w (Eq. 2).
The reservoir with the long time constant is assumed to represent the carbon deposited on and removed from the outer (halo) part of the Cs sputtering region. The time constant λ L of this process is significantly longer compared to the minimum counting time of the AMS, which leads to a memory effect that increases with time. The temporal evolution of this long-term target memory can be described by:
$${{dA(t)} \over {dt}} = - {\lambda _L} \,\cdot \,A(t) + P$$
With P describing the constant carbon deposition rate on the halo sputter region of the target and A(t) representing the released carbon from the outer halo part relative to the total sputtered carbon.
The total C− current from the ion source I is the sum of (1) the ion current from the incoming sample gas (IS) that underwent all previously described mixing processes (i.e. laser width, cell mixing, and the short term target memory) and (2) the current (IT) from the above described long term target memory effect.
$$I = {I_S} + {I_T} = ( {1 - A(t)} )\cdot \, I + A(t) \cdot I$$
Experimental Validation and Determination of Time Constants for the Target Memory Model
Both, the evolution of A(t) and the time constant for the long-term memory effect have to be determined experimentally. Therefore, measurements were performed using the gas interface system (GIS) without LA cell. Hence, mixing effects in the LA setup were avoided and the long-term target memory could be studied exclusively. With the GIS the carbon flow into the ion source can precisely be controlled ensuring equal conditions for all measurements on different targets.
In Figure 4A the temporal evolution of the ion currents measured on four gas targets over 20, 40, 60, and 80 cycles is shown. First, the target is pre-sputtered, then the gas is introduced at a carbon flow of 2.2 µg/min and after the respective amount of cycles (at time t = toff) the capillary to the ion source is shut stopping the gas flow into the ion source. This leads to an immediate drop in the ion current caused by the emptying of the capillary, which then continues to decrease slowly indicating the contribution of the long-term target memory. The dashed lines in Figure 4A mark the ion current level determined 25 cycles after each toff clearly showing that the long-term target memory increases with measurement time. Without the gas in the ion source the ionization and negative ion extraction efficiency increases by roughly 100% (supplementary information). To compare the remaining current with its contribution under gas condition the ion current is halved.
Figure 4 A—12C ion current on the high energy side from four different targets at same carbon flow from GIS into the ion source. Carbon flow was stopped after counting times of 20, 40, 60, 80 cycles; B—zoom into the drop of 12C current of the black curve in A. The decline follows two exponential function with long and short time constant.
Using the above described model for the target memory, the temporal evolution of the ion current from the gas target after toff is described by two exponential functions with short (λ S ) and long (λ L )-time constants, respectively.
$${I_{meas}}( {t \gt {t_{off}}} ) = {I_{meas}}({t_{off}})\,\cdot\,((1 - A( {{t_{off}}} ))\,\cdot\,{e^{ - {\lambda _S}t}} + A( {{t_{off}}} )\,\cdot\,{e^{ - {\lambda _L}t}})$$
Consequently, two exponential decay functions are fitted to the data (red and blue curves in Figure 4B). The observed behavior of the measured data matches well with the sum of the two curves (“total memory” in Figure 4B) indicating that the two-compartment model is sufficient to describe the target memory adequately. The fitted time constant from the four targets (Figure 4A) for the long-term memory is λ L = (1.7 ± 0.2) · 10−3 s −1 corresponding to a time constant τL~600 s. With measurement durations up to 100 cycles (1000s), the long-term target memory continuously increases without reaching equilibrium (compare Figure 4A). Hence, the parameters λL, and P to describe and correct for the long-term target memory have to be considered. However, in the LA-AMS setup the short-term target memory is already included in the washout function as discussed before.
CORRECTION PROCEDURE AND APPLICATION
Based on the above results, a dedicated correction procedure for LA AMS measurements was developed. The initial aim was to first correct the data for the long-term target memory and subsequently deconvolve it using the system function described previously. In reality, the measured data contains a finite level of noise, e.g. due to counting statistics of the AMS, which is amplified during deconvolution compromising this data correction approach. Even though in theory noise can be included in the system function if it is constant and a characteristic noise sample is available (Xiaodan et al. Reference Xiaodan, Kaixue and Mei2016), in the case of LA-AMS, the noise level depends on the 14C/12C ratio of the sample preventing a general description of noise to be included in the system function. In cases of rapid and large (i.e. step like) 14C/12C signal changes in a sample, e.g. due to the presence of the bomb peak, the system function still can be used to determine the timing and duration of the signal change. A two-step process is chosen for such cases: first, the parameters of both, the system function and long-term target memory are experimentally determined by analyzing a sequence of samples with known and alternating 14C/12C ratios (Figure 5A). Then, the position and duration of a step like 14C/12C change in an unknown sample can be determined (1) by correcting for the long-term target memory and (2) by fitting a step function to the data that has been convolved with the experimentally determined system function. At the start of every measurement day, this rectangular function has to be determined in order to assess the actual parameters for correction.
Figure 5 A—rectangular function (blue) measured with LA AMS (black). Parameters are fitted so after target memory correction the measured data yield the sample value (red). B—build-up of target memory, C—evolution of F14C on target.
Design of the Experiment
Two carbonate materials with well-known but significantly different 14C/12C ratios (marble F14C = 0 and a modern sample F14C = 0.9) were positioned closely side by side. In order to create an ideal rectangular signal function, first one sample is ablated with a comparably slow lateral velocity of vS = 10 μm/s followed by a quick movement (2000 μm/s) to the next sample while material is continuously being ablated. This sequence is repeated several times as shown in Figure 5A, where the effect of the long-term target memory causing the modern sample to appear increasingly older and vice versa can clearly be observed. We note that the precision decreases with time, which is caused by declining ion currents during the measurement. This effect is quite common in gas-AMS because of the accumulation of carbon on the gas target (Fahrni et al. Reference Fahrni, Wacker, Synal and Szidat2013). However, during this experiment the measurement time was twice as long as for a normal gas AMS measurement and therefore the effect of decreasing precision is exaggerated (Figures 5A and 6). From the comparison of the recorded signal (black dots in Figure 5A) with the ideal rectangular function (blue line in Figure 5A) all necessary correction parameters can be determined.
Figure 6 In pink the convolution of rectangular function (blue) with the system function and fitted to the long-term target memory corrected data (black).
Determination of Long-Term Target Memory
To correct the long-term target memory, the time evolution of the proportion of the long-term target memory (A(t)) and the corresponding 14C/12C variation (F14CT(t)) are determined. Using Eq. (3) an iterative approach is chosen to determine the parameters P and λ L .
Starting with A(t = 0) = 0, A(t + 1) is calculated as (see Figure 5B):
$$A( {t + 1}) = A( t) + dA = A(t) - {\lambda _L}\,\cdot\, A(t)\,\cdot\,dt + P\,\cdot\,dt$$
With dt representing the 10 s minimum integration time of the AMS. Then, the evolution of F 14 CT (t) (Figure 5c) of the target memory is calculated:
$$F_{}^{14}{C_T}( {t + 1}) = ( {( {A( t ) - {\lambda _L}\,\cdot \,A( t )} )\,\cdot \,{F^{14}}{C_T}( t ) + P\,\cdot \,{F^{14}}{C_{meas}}(t + 1)} )/A(t + 1)$$
Finally, the corrected 14C/12C data (F14CS,T(t)) is calculated (red triangles in Figure 5a):
$$F_{}^{14}{C_{S,T}}\left( {t + 1} \right) = ({F^{14}}{C_{meas}}(t + 1) - {F^{14}}{C_T}(t)\,\cdot \,A(t))/(1 - A(t))$$
By comparing the corrected 14C/12C ratios with the measured data using a minimized χ2 approach, the parameters P and λ L are obtained. In the above example the fitted parameters are P = 3·10−4 s −1 (σ < 10 %) and λ L = 0. These values are used to correct the measured 14C/12C ratios for the long-term target memory (red triangles in Figure 5A). The fact that λ L approaches zero in this case indicates that the relative contribution of the long-term target memory linearly increases at least over the time range of about 20 min. Every measurement day the parameters P and λ L have to be determined anew due to varying measurement conditions.
Determination of Washout and Short-Term Target Memory
The time constant for the cell washout and the short-term target memory (1/λ
W
) are determined by comparing the measured and long-term target memory corrected data (
$F_{}^{14}{C_{S,T}}(t)$
) with the rectangular function (blue line in Figures 5a and 6).
$F_{}^{14}{C_{S,T}}(t)$
is a result of a convolution of the system function (g) with the idealized rectangular function (s). Because the direct deconvolution of
$F_{}^{14}{C_{S,T}}(t)$
is impeded by the presence of noise, the original data is reconstructed by fitting the system function (g), using λ
W
as fitting parameter, so that the convolution of the system function (g) with the true sample signal (s) agrees with the long-term memory corrected data (Figure 6).
The best fit is shown in pink in Figure 6a, with λ W = 0.13 s −1. Hence the washout time constant of our system is τ W ∼ 8s. This is similar to previous estimates of the washout time of the original setup (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Yeman, F. M. Breitenbach, Synal and Günther2017).
Application to a Stalagmite Record
The potential of a known system function is demonstrated by the measurement of a speleothem with intermediate growth stop. There is multiple evidence for a hiatus in the stalagmite record (Welte et al. Reference Welte, Wacker, Hattendorf, Christl, Koch, Yeman, F. M. Breitenbach, Synal and Günther2017). It is, however, not clear whether this was an abrupt growth stop or a gradual ceasing of carbonate accretion. To solve this question, the 14C record of the stalagmite is determined with LA AMS and the above correction procedure is applied to calculate the spatial extent of the growth stop.
The LA AMS measurement with vS = 5 μm/s reveals a quick rise from F14C = 0.05 to F14C = 0.29 (Figure 7A). Looking at the raw data, the rise covers approximately 10 data points (10 s each), which translates in a spatial extent of the growth stop of about 575 μm (10 cycles + laser-beam width). This certainly is an overestimation of the length of the growth stop because of the described mixing processes. To correct for these processes, first, the long-term target memory is corrected using the parameters discussed herein, and subsequently the complete system function (Eq. 2) is used (with the known parameters tC , tL , and λ w ) to determine a more realistic estimate of the length of the growth stop. Starting with an ideal step function (width = 0 μm) the convolved signal is calculated. Based on a χ2 fit the start of the rise and the width of the step function are optimized (blue line in Figure 7). The best fit of the convolved signal (pink curve in Figure 7) to the data in this first case is obtained with a width of the step function of 365 μm. This procedure was also applied to the same stalagmite record using a laser scanning velocity of 25 μm/s. The width derived from the measurement at 5 µm/s is 365 µm (Figure 7A), which is shorter than the initially estimated width of 575 µm. This shows that the correction procedure enables a more precise and robust determination of the start and the duration of the growth stop. In case of the fast scanning velocity of 25 μm/s, the laser crosses the step like signal in less than two cycles, which is too fast to resolve the step width. As a result, the growth stop appears as an ideal step with zero width (see Figure 7B and D) implying that the minimal achievable resolution is defined by the distance covered by the laser during two measurement cycles (20 sec). Using this practical estimate of the spatial resolution, structures with about 175 µm (two cycles + laser-beam width) can be resolved with the slow scanning velocity, while only 575 µm are reached with the fast scanning velocity.
Figure 7 Growth stop in a stalagmite measured with different velocities and scanning directions in black, in blue the idealized F14C of the sample, and in pink its convolution with the system function. The grey area in B is the equivalent distance covered in A.
CONCLUSION
For the spatially highly resolved 14C analysis of carbonates by Laser Ablation AMS a new approach for data handling was developed. The main processes causing mixing and delay of the signal were described. The minimum counting time of the AMS, the finite laser-beam width, the washout of the ablation cell and the short-term memory of the target are constant processes within one measurement and therefore summarized to one system function. The long-term target memory is a slow process building up due to adsorption of carbon on the target. To determine the parameters for long-term target memory correction and the system function an artificial rectangular function put together by two samples of high and low 14C/12C ratios is analyzed. As a result, we estimated the washout time constant to be ~ 8 s. Lastly, with a complete system function, rapid changes are located on the sample more precisely, as demonstrated by measuring a growth stop in a stalagmite. Only the slow scanning velocity can provide the necessary resolution to determine the width of the growth stop of 365 μm. This method is also applicable for determining the position and duration of rapid, high magnitude changes of the 14C signal such as the 14C bomb pulse. It will be implemented in routine data analysis of such records produced with LA-AMS.
ACKNOWLEDGMENTS
Financial support was given by SNF (project 160064) and is gratefully acknowledged. We thank Anton Vaks for providing the stalagmite sample material from Okhotnichya Cave. Many thanks to the anonymous reviewers for their insightful comments that helped to improve this manuscript.
SUPPLEMENTARY MATERIAL
To view supplementary material for this article, please visit https://doi.org/10.1017/RDC.2019.139
