The second chapter handles the measurement. These are often collected with a Laser Ablation Inductively Coupled Mass Spectrometer (LA-ICP-MS) and the first problem we encountered was the calibration of this instrument. It is used to measure trace elements with an incredibly high spatial resolution. Of course, it has also some major disadvantages. One of these is that the laser, which is used to ablate the solid substrate, has a variable intensity. In addition several other internal instrumental parameters seem to vary over time in an unpredictable manner. Therefore, people use internal standards for more than twenty years. Such internal standards are elements whose concentration does not vary over the sample. Consequently,all variation detected in these internal standards must be due to artificial variation in the instrument. Because the drift of the instrument is reflected in the measurementofthe internal standard, all other concentrationscan be calibratedaccordingto this internal standard. This simple idea seems to work quite well. Unfortunately, the calibration algorithm does not take into account measurement noise in the signal of the internal standards. This is exactly the improvement that we made: imagine two internal standards, each consisting of the same drift pattern, and disturbed by a different noise pattern. A better approximation of the true drift pattern can be reached by the arithmetic mean of both internal standards.Hereinthe drift remains and the noise cancels out. This idea is further refined, so that the uncertainty on the internal standards can be taken into account as well, and an a priori and an a posteriori verification of the model used is given. Further, the myth of mass dependent internal standards is ruled out and finally a real world example is processed. An additional important property of the proposed calibration is that an internal quality check is performed, which warns the investigator if some artefacts or problems occurred during the measurement. The remaining part of this work is devoted to the reconstruction of time series. One of the major problems with data-processing of proxy records (e.g. stable isotope ratios of oxygen or carbon, or trace elements in shells, sponges, corals, sediment cores, etc ) is the dating of individual observations. All these proxy records are measured as function of a distance, while generally the time series are desired. Due to variations and differences in accretion rate, each record has its unique distance series, which cannot be compared with other records or models. Therefore, distance series are transformed into time series. However, this is only possible if additional information about the accretion rate is available. Unfortunately, this is mostly not the case and thus additional assumptions are necessary. Such assumption can be made about the signal and formally written down in the signal model. In addition,the concept of a time base distortion is introduced.As will be shown,this enables us to estimate variations in accretion rate. For this, we started from a previously estimated time base (if this is unknown, we initialize the time base assuming a constant accretion rate). Next, we allow this base to be distorted due to nonlinear accretion rates or hiatuses and we will show how such a distortion can be estimated. In the third chapter, we have illustrated how the time series can be reconstructed, assuming a periodic proxy-record. Therefore, the concept of time base distortions is introduced. First, we propose a model for variations in accretion rate. Next, we illustrate how this accretion rate can be identified and estimated in the Fourier spectrum of the proxy. This approach is compared with the widely used anchor point method in two manners: the assumptions made are compared and next the sensitivity of both methods w.r.t. stochastic noise is illustrated on a simulation. Three case studies are incorporated to validate the method and to illustrate its usef |
