The Probability Perturbation Method: A New Look at Bayesian Inverse Modeling

Building of models in the Earth Sciences often requires the solution of an inverse problem: some unknown model parameters need to be calibrated with actual measurements. In most cases, the set of measurements cannot completely and uniquely determine the model parameters; hence multiple models can describe the same data set. Bayesian inverse theory provides a framework for solving this problem. Bayesian methods rely on the fact that the conditional probability of the model parameters given the data (the posterior) is proportional to the likelihood of observing the data and a prior belief expressed as a prior distribution of the model parameters. In case the prior distribution is not Gaussian and the relation between data and parameters (forward model) is strongly non-linear, one has to resort to iterative samplers, often Markov chain Monte Carlo methods, for generating samples that fit the data likelihood and reflect the prior model statistics. While theoretically sound, such methods can be slow to converge, and are often impractical when the forward model is CPU demanding. In this paper, we propose a new sampling method that allows to sample from a variety of priors and condition model parameters to a variety of data types. The method does not rely on the traditional Bayesian decomposition of posterior into likelihood and prior, instead it uses so-called pre-posterior distributions, i.e. the probability of the model parameters given some subset of the data. The use of pre-posterior allows to decompose the data into so-called, “easy data” (or linear data) and “difficult data” (or nonlinear data). The method relies on fast non-iterative sequential simulation to generate model realizations. The difficult data is matched by perturbing an initial realization using a perturbation mechanism termed “probability perturbation.” The probability perturbation method moves the initial guess closer to matching the difficult data, while maintaining the prior model statistics and the conditioning to the linear data. Several examples are used to illustrate the properties of this method.     

Geological Observations of Damage Asymmetry in the Structure of the San Jacinto, San Andreas and Punchbowl Faults in Southern California: A Possible Indicator for Preferred Rupture Propagation Direction

We present new in situ observations of systematic asymmetry in the pattern of damage expressed by fault zone rocks along sections of the San Andreas, San Jacinto, and Punchbowl faults in southern California. The observed structural asymmetry has consistent manifestations at a fault core scale of millimeters to meters, a fault zone scale of meters to tens of meters and related geomorphologic features. The observed asymmetric signals are in agreement with other geological and geophysical observations of structural asymmetry in a damage zone scale of tens to hundreds of meters. In all of those scales, more damage is found on the side of the fault with faster seismic velocities at seismogenic depths. The observed correlation between the damage asymmetry and local seismic velocity structure is compatible with theoretical predictions associated with preferred propagation direction of earthquake ruptures along faults that separate different crustal blocks. The data are consistent with a preferred northwestward propagation direction for ruptures on all three faults. If our results are supported by additional observations, asymmetry of structural properties determined in field studies can be utilized to infer preferred propagation direction of large earthquake ruptures along a given fault section. The property of a preferred rupture direction can explain anomalous behavior of historic rupture events, and may have profound implications for many aspects of earthquake physics on large faults.     

Temporal Changes of Shallow Seismic Velocity Around the Karadere-Düzce Branch of the North Anatolian Fault and Strong Ground Motion

We analyze temporal variations of seismic velocity along the Karadere-Düzce branch of the north Anatolian fault using seismograms generated by repeating earthquake clusters in the aftershock zones of the 1999 M_w7.4 İzmit and M_w7.1 Düzce earthquakes. The analysis employs 36 sets of highly repeating earthquakes, each containing 4–18 events. The events in each cluster are relocated by detailed multi-step analysis and are likely to rupture approximately the same fault patch at different times. The decay rates of the repeating events in individual clusters are compatible with the Omori's law for the decay rate of regional aftershocks. A sliding window waveform cross-correlation technique is used to measure travel time differences and evolving decorrelation in waveforms generated by each set of the repeating events. We find clear step-like delays in the direct S and early S-coda waves (sharp seismic velocity reduction) immediately after the Düzce main shock, followed by gradual logarithmic-type recoveries. A gradual increase of seismic velocities is also observed before the Düzce main shock, probably reflecting post-seismic recovery from the earlier İzmit main shock. The temporal behavior is similar at each station for clusters at various source locations, indicating that the temporal changes of material properties occur in the top most portion of the crust. The effects are most prominent at stations situated in the immediate vicinity of the recently ruptured fault zones, and generally decrease with normal distance from the fault. A strong correlation between the co-seismic delays and intensities of the strong ground motion generated by the Düzce main shock implies that the radiated seismic waves produced the velocity reductions in the shallow material.     

A synthesis of sociological and biological perspectives on sustainable land use in Namaqualand

A transdisciplinary synthesis, grouped into four main themes, of the key papers in this Special Issue on Namaqualand is provided. Perspectives on current environmental, economic and social issues in the region are interpreted in the context of the past and are used to inform future trajectories of change and development needs within the region. Firstly, in terms of the climatic and biophysical environment, Namaqualand's rich biodiversity is not uniformly distributed and is explained in terms of the spatially heterogeneous geological, pedological and topographical gradients that characterize the region. Spatial and temporal variation in rainfall over long time frames would also have promoted speciation within isolated, poorly-dispersed, leaf succulent populations. Future climate models propose a decrease in rainfall across the region with an associated reduction in livestock production. The second theme provides an historical perspective on changing land use practices in Namaqualand over the last 2000 years. It suggests that they have frequently been influenced by events originating far from the region such as colonial expansion, apartheid legislation and globalization. Local people, particularly marginalised communal farmers have had to adapt to these outside influences within an increasingly confined landscape that has progressively eroded their mobility and restricted their ability to utilise the spatial and temporal variability inherent in semi-arid environments. The third theme shows how livelihood diversification has been one of the key ways in which local people from communal areas have adapted to change. While farming makes up a relatively small part of the income of most households it enhances the resilience of livelihoods in the region. The fourth theme is concerned with land reform, conservation and restoration in Namaqualand. While a significant amount of land has been transferred to previously-marginalised groups, equitable access to these resources is lacking. An exclusively commercial orientation within the extension and development programmes of the Department of Agriculture further hampers the effectiveness of land reform as a tool for reducing levels of poverty in the majority of households in the region. Conservation initiatives could enhance livelihood options in Namaqualand but are viewed by some as being in competition with the state's land reform programme and are too recent to reflect significant regional benefits at this stage. While restoration is possible in severely degraded lands, the costs and operational difficulties in these event-driven, semi-arid systems are emphasised. Finally, this synthesis suggests that the important exogenous drivers of change in the 21st century are likely to be climate, biodiversity conservation initiatives, land redistribution and continued processes of de-agrarianisation as a result of macro-economic change. A focus on building institutions, encouraging livestock mobility within a significantly expanded commons and supporting livelihood diversification are some of the approaches necessary to address the development needs of Namaqualand.     

Contribution of allochthonous carbon to American shad production in the Mattaponi River,Virginia, using stable isotopes

Our objective was to quantify the contribution of autochthonous, locally-produced phytoplankton, and allochthonous, terrestrial-derived organic matter (OM) to the production of young-of-year (YOY) American shad(Alosa sapidissima) using stable isotopes. We measured the carbon and nitrogen stable isotope composition of YOY American shad in the tidal fresh water of the Mattaponi River, a tributary in the York River estuary, during three consecutive years. The isotopic ratios of larval American shad varied among years, indicating a switch from reliance on a primarily autochthonous food web pathway during low and moderate discharge years (50–90%; 2002, 2004) to a primarily allochthonous pathway during a high discharge year (< 35% phytoplankton; 2003). Reliance on phytoplankton by larval fish declined exponentially with increasing Mattaponi River discharge. In 2003, juvenile production was also supported by allochthonous OM, though autochthonous phytoplankton accounted for an increasingly large fraction during June through August, up to 40–55%. We also found a long-term, positive relationship between the duration of above average flow during April through June in the Mattaponi River and a corresponding index of juvenile American shad abundance. The largest American shad cohort recorded since 1967 was observed in 2003, a high discharge year. The production of this cohort was largely supported by allochthonous OM. The results suggest an important link between river discharge, energy flow, and recruitment, wherein high discharge favors reliance on terrestrial carbon by YOY American shad, owing to changes in zooplankton diet, macroinvertebrate abundance, or both, and also favors high American shad abundance.     

Pan evaporation and wind run decline in the Cape Floristic Region of South Africa (1974�C2005): implications for vegetation responses to climate change

In many regions of the world, increasing temperatures in recent decades are paradoxically associated with declining pan evaporation, but evidence is sparse for this trend from the southern hemisphere in general and sub-Saharan Africa in particular. In this study, we examined changes in pan evaporation and four other meteorological variables (rainfall, wind run, temperature and vapour pressure deficit) at 20 climate stations in the predominantly winter-rainfall Cape Floristic Region (CFR) of South Africa over the period 1974?C2005. Our results show that pan evaporation has declined significantly at 16 climate stations at an average rate of 9.1 mm a^???2 while wind run has declined significantly at all climate stations by more than 25% over the study period. Annual rainfall has not changed significantly at any of the climate stations while maximum temperature has increased significantly at all but one climate station at an average rate of 0.03°C a.^???1 over the study period. The trends in vapour pressure deficit are mixed and no clear regional pattern is evident. Our results raise important questions about the predicted catastrophic impact that the projected changes in twenty-first century climates will have on the rich flora of the region. If evaporative demand has declined over the last 30 years in the Cape Floristic Region then it is possible that more water has become available for plant growth, infiltration and runoff despite the widespread increase in temperature. However, decreased pan evaporation and wind run combined with increased temperatures could potentially reduce transpiration and exacerbate heat stress of plants on increasingly frequent hot and windless days during the summer drought. Contrary to other predictions for the area, it is also likely that the changing conditions will decrease the frequency and/or intensity of fires which are an important component of the ecology of the fire-adapted CFR. Consideration of other factors besides changes in temperature and rainfall are essential in debates on the impact of climate change on the vegetation of this region.     

Lipid correction for carbon stable isotope analysis of deep-sea fishes

Stable isotope analysis of fish tissue can aid studies of deep-sea food webs because sampling difficulties severely limit sample sizes of fish for traditional diet studies. The carbon stable isotope ratio (δ¹³C) is widely used in food web studies, but it must be corrected to remove variability associated with varying lipid content in the tissue. A lipid correction has not been determined for any deep-sea fish. These fishes are ideal for studying lipid correction because lipid content varies widely among species. Our objective was to evaluate an application of a mass balance δ¹³C correction to a taxonomically diverse group of deep-sea fishes by determining the effect of lipid extraction on the stable isotope ratios, examining the quality of the model parameters derived for the mass balance correction, and comparing the correction to published results. We measured the lipid extraction effect on the nitrogen stable isotope ratio (δ¹⁵N) and δ¹³C of muscle tissue from 30 North Atlantic species. Lipid extraction significantly increased tissue δ¹⁵N (+0.66‰) and δ¹³C values, but the treatment effect on δ¹³C was dependent on C:N, a proxy for lipid content. We compared the lipid-extracted δ¹³C to the δ¹³C predicted by the mass balance correction using model variables estimated from either all individuals (pooled) or species-by-species or using published values from other species. The correction using the species-by-species approach performed best; however, all three approaches produced corrected values that were generally within 0.5‰ of the measured lipid-free δ¹³C and that had a small over-all bias (<0.5‰). We conclude that a generalized mass balance correction works well for correcting δ¹³C in deep-sea fishes, is similar to that developed for other fishes, and recommend caution when applying a generalized correction to fish with high lipid content (C:N >8).