Malcolm Sambridge

Sea level and global ice volumes from the Last Glacial Maximum to the Holocene

Significance Several areas of earth science require knowledge of the fluctuations in sea level and ice volume through glacial cycles. These include understanding past ice sheets and providing boundary conditions for paleoclimate models, calibrating marine-sediment isotopic records, and providing the background signal for evaluating anthropogenic contributions to sea level. From ∼1,000 observations of sea level, allowing for isostatic and tectonic contributions, we have quantified the rise and fall in global ocean and ice volumes for the past 35,000 years. Of particular note is that during the ∼6,000 y up to the start of the recent rise ∼100−150 y ago, there is no evidence for global oscillations in sea level on time scales exceeding ∼200 y duration or 15−20 cm amplitude. The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet’s dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are: (i) a rapid final fall in global sea level of ∼40 m in <2,000 y at the onset of the glacial maximum ∼30,000 y before present (30 ka BP); (ii) a slow fall to −134 m from 29 to 21 ka BP with a maximum grounded ice volume of ∼52 × 106 km3 greater than today; (iii) after an initial short duration rapid rise and a short interval of near-constant sea level, the main phase of deglaciation occurred from ∼16.5 ka BP to ∼8.2 ka BP at an average rate of rise of 12 m⋅ka−1 punctuated by periods of greater, particularly at 14.5–14.0 ka BP at ≥40 mm⋅y−1 (MWP-1A), and lesser, from 12.5 to 11.5 ka BP (Younger Dryas), rates; (iv) no evidence for a global MWP-1B event at ∼11.3 ka BP; and (v) a progressive decrease in the rate of rise from 8.2 ka to ∼2.5 ka BP, after which ocean volumes remained nearly constant until the renewed sea-level rise at 100–150 y ago, with no evidence of oscillations exceeding ∼15–20 cm in time intervals ≥200 y from 6 to 0.15 ka BP.

A regionalized upper mantle (RUM) seismic model

Seismic velocity heterogeneity in the Earths mantle is strongly concentrated near its top. The shallow heterogeneity of the mantle correlates strongly with surface tectonics. We use these observations as constraints of a tomographic experiment aimed at building a regionalized upper mantle (RUM) reference model. We use a select set of teleseismic travel times to minimize the mapping of mislocation into structure. The data selection emphasizes the robustness of individual picks. The form of the RUM model is a set of velocity profiles as functions of depth through the upper mantle for each of the different tectonic provinces of Earth. Together the profiles constitute a three-dimensional model which incorporates considerable structural detail but is described by only 90 parameters and has only about 22 degrees of freedom. This is achieved by irregularly sampling a detailed regionalization of the globe, by detailed mapping of subducted lithosphere in the mantle as defined by seismicity, and by combining these structures in an irregular grid in which bookkeeping is efficiently handled. The resulting RUM model includes subducting slabs as sharp fast features in the upper mantle. Old continents are fast; young oceans are slow. Models have been derived for both compressional and shear velocity. The RUM model is designed to represent as much of upper mantle heterogeneity as seen by body wave travel times as possible with a simple model. It can be useful as a reference model for individual tectonic regions. Travel times are efficiently generated for the RUM model. Mislocations of explosions of known location are significantly reduced when corrections for the RUM model are applied to travel time residuals for a spherically symmetrical Earth model.

Mixture modeling of multi-component data sets with application to ion-probe zircon ages

A method is presented for detecting multiple components in a population of analytical observations for zircon and other ages. The procedure uses an approach known as mixture modeling, in order to estimate the most likely ages, proportions and number of distinct components in a given data set. Particular attention is paid to estimating errors in the estimated ages and proportions. At each stage of the procedure several alternative numerical approaches are suggested, each having their own advantages in terms of efficiency and accuracy. The methodology is tested on synthetic data sets simulating two or more mixed populations of zircon ages. In this case true ages and proportions of each population are known and compare well with the results of the new procedure. Two examples are presented of its use with sets of SHRIMP 238U206Pb zircon ages from Palaeozoic rocks. A published data set for altered zircons from bentonite at Meishucun, South China, previously treated as a single-component population after screening for gross alteration effects, can be resolved into two components by the new procedure and their ages, proportions and standard errors estimated. The older component, at 530 ± 5 Ma (2σ), is our best current estimate for the age of the bentonite. Mixture modeling of a data set for unaltered zircons from a tonalite elsewhere defines the magmatic 238U206Pb age at high precision (2σ ± 1.5 Ma), but one-quarter of the 41 analyses detect hidden and significantly older cores.

Monte Carlo analysis of inverse problems

Monte Carlo methods have become important in analysis of nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. In such cases a direct mathematical treatment is impossible, but the forward relation materializes itself as an algorithm allowing data to be calculated for any given model. Monte Carlo methods can be divided into two categories: the sampling methods and the optimization methods. Monte Carlo sampling is useful when the space of feasible solutions is to be explored, and measures of resolution and uncertainty of solution are needed. The Metropolis algorithm and the Gibbs sampler are the most widely used Monte Carlo samplers for this purpose, but these methods can be refined and supplemented in various ways of which the neighbourhood algorithm is a notable example. Monte Carlo optimization methods are powerful tools when searching for globally optimal solutions amongst numerous local optima. Simulated annealing and genetic algorithms have shown their strength in this respect, but they suffer from the same fundamental problem as the Monte Carlo sampling methods: no provably optimal strategy for tuning these methods to a given problem has been found, only a number of approximate methods.

Transdimensional inversion of receiver functions and surface wave dispersion

[1] We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade-offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South-East Australia) are jointly inverted to provide a probabilistic 1D model of shear-wave velocity beneath a given station.

Genetic algorithm inversion for receiver functions with application to crust and uppermost mantle structure beneath eastern Australia

Genetic algorithm (GA) inversion, a nonlin- ear global optimization technique, has been applied to determine crustal and uppermost mantle velocity struc- ture from teleseismic receiver functions. With a new vicinity of the receiver. The influence of the source can be largely eliminated by source equalization in which the radial component of motion is deconvolved with the vertical component to generate a receiver function (Langston,1979) which isolates conversions from P to

Quantitative absorbance spectroscopy with unpolarized light: Part II. Experimental evaluation and development of a protocol for quantitative analysis of mineral IR spectra

generated at boundaries beneath the recording site. The receiver function waveform can be inverted in the

Genetic algorithms: a powerful tool for large-scale nonlinear optimization problems

Abstract The predictions of the theory of light propagation in weakly absorbing anisotropic minerals are tested against systematic measurements of the infrared absorbance spectra of calcite, olivine, and topaz oriented in both principal and random sections, using both polarized and unpolarized light. We show that if the linear polarized maximum absorbance is smaller than ~0.3, or if the ratio of maximum and minimum absorbance is close to unity, then (1) the polarized maximum and minimum absorbances as well as the unpolarized absorbance are, to a good approximation, linearly proportional to thickness, regardless of the direction of the incident light; (2) the angular variation of polarized light absorption is indistinguishable from the theoretical predictions within the uncertainty of the measurements; (3) for any section the unpolarized absorbance is the mean of the polarized maximum and minimum absorbance; and (4) the average unpolarized absorbance of randomly oriented grains is one third of the Total Absorbance (defined as the sum of the three principal absorbances). Therefore, calibrations relating Total Absorbance to absorber concentration in minerals that have been developed from measurements with polarized light parallel to the principal axes may be applied to measurements with unpolarized light on a population of randomly oriented sections. We show that 10 such measurements are sufficient to achieve a petrologically useful accuracy. The method enables water concentrations in nominally anhydrous minerals to be determined from samples where the preparation of oriented specimens is not feasible, such as high-pressure experimental runs and fine-grained mantle xenoliths. The method may also be used for obtaining quantitative measurements on low-symmetry minerals.

Multiple reflection and transmission phases in complex layered media using a multistage fast marching method

Genetic algorithms represent an efficient global method for nonlinear optimization problems, that are encountered in the earth sciences. They share the favorable characteristics of random Monte Carlo over local optimization methods in that they do not require linearizing assumptions nor the calculation of partial derivatives, are independent of the misfit criterion, and avoid numerical instabilities associated with matrix inversion. The additional advantages over conventional methods such as iterative least squares is that the sampling is global, rather than local, thereby reducing the tendency to become entrapped in local minima and avoiding a dependency on an assumed starting model. In contrast to random Monte Carlo, however, they also share a desirable characteristic of the local methods in that they assimilate and take advantage of information collected during the sampling of the model space, resulting in an extremely efficient and robust optimization technique. This paper describes the basic genetic algorithm, briefly highlights some recent applications in the earth sciences and concludes that, in this field, the methodology should have many applications.

Finding acceptable models in nonlinear inverse problems using a neighbourhood algorithm

Traditional grid-based eikonal schemes for computing traveltimes are usually confined to obtaining first arrivals only. However, later arrivals can be numerous and of greater amplitude, making them a potentially valuable resource for practical applications such as seismic imaging. The aim of this paper is to introduce a grid-based method for tracking multivalued wavefronts composed of any number of reflection and refraction branches in layered media. A finite-difference eikonal solver known as the fast marching method (FMM) is used to propagate wavefronts from one interface to the next. By treating each layer that the wavefront enters as a separate computational domain, one obtains a refracted branch by reinitializing FMM in the adjacent layer and a reflected branch by reinitializing FMM in the incident layer. To improve accuracy, a local grid refinement scheme is used in the vicinity of the source where wavefront curvature is high. Several examples are presented which demonstrate the viability of the new method in highly complex layered media. Even in the presence of velocity variations as large as 8:1 and interfaces of high curvature, wavefronts composed of many reflection and transmission events are tracked rapidly and accurately. This is because the scheme retains the two desirable properties of a single-stage FMM: computational speed and stability. Local grid refinement about the source also can increase accuracy by an order of magnitude with little increase in computational cost.