Simple Topographic Parameter Reveals the Along-Trench Distribution of Frictional Properties on a Shallow Plate Boundary Fault

The critical taper model of a sedimentary wedge best describes the first-order mechanics of a subduction zone wedge. The tapered wedge geometry, which is conventionally defined by two parameters, the slope angle and the basal dip angle, is responsible for the strength of a megathrust. By applying this theoretical model to subduction zones, fault frictional properties and earthquake occurrences can be compared among subduction zones, and within a single subduction zone, the spatial distribution or temporal change of fault strength can be investigated. The slope angle can be accurately estimated from bathymetry data, but the basal dip angle must be inferred from the subsurface structure, and it requires highly accurate depth-converted seismic reflection profiles. Thus, application of the critical taper model is often limited by a lack of a sufficient number of highly accurate profiles, and the spatial distribution of frictional coefficients must be inferred from relatively few data, generally less than a dozen points. To improve this situation, we revisited the theoretical formula of the critical taper model. We found that the effect of the décollement dip angle β on the critical taper model of a sedimentary wedge is negligible when the pore fluid pressure ratio is high or internal friction is small, conditions which are met in many subduction zones. Therefore, this finding allows frictional variation to be approximated by using only the slope angle variation obtained from the bathymetry. We applied this approximation to the Japan Trench as an example of this approximation, and were able to estimate the friction coefficient distribution on the shallow plate boundary fault from 71 data points. We found that the area where the friction coefficient was smaller than the mean corresponded to the segment where a large coseismic shallow rupture occurred during the 2011 Tohoku-oki earthquake (Mw 9.0). This result shows that by approximating tapered wedge geometry using a simple topographic parameter that can be obtained from existing global bathymetry, we can quickly estimate the distribution of frictional properties on a plate boundary fault along a trench and related seismic activity.

Differences in stem taper of black alder (Alnus glutinosa subsp. barbata) by origin

Black alder (Alnus glutinosa subsp. barbata (C.A. Mey.) Yalt.) is an important tree species in Turkey both economically and ecologically. Accurate taper and volume equations are required by most inventory systems to estimate upper stem diameter, form, and tree volume. Stem analysis data were used to examine the differences in taper and volume of black alder trees grown in naturally regenerated, plantation, and coppice stands. Statistically significant differences were observed in taper and volume of black alder trees grown in stands from these three origins. Error in total stem volume inside bark was the greatest when the taper model was fitted to plantation data and applied to seed data compared with the model fitted to coppice data and applied to seed data. Therefore, to accurately predict upper stem diameter and total or merchantable stem volume, in addition to selecting species-specific taper models, forest managers should consider the origin of the model-fitting data when choosing an appropriate taper model for their stands.

Taper models for black locust in west Poland

The diameter at any point on a stem and tree volume are some of the most important types of information used in forest management planning. One of the methods to predict the diameter at any point on a stem is to develop taper models. Black locust ( L.) occurs in almost all forests in Poland, with the largest concentration in the western part of the country. Using empirical data obtained from 13 black locust stands (48 felled trees), seven taper models with different numbers of estimated parameters were analysed for section diameters both over and under bark using fixed and mixed-effects modelling approaches. Assuming a lack of additional measurements, the best fitted taper models were used for the prediction of over bark volume using both methods. The predicted volume was compared with the results from different volume equations available for black locust. The variable-form taper model with eight estimated parameters fitted the data the best. The lowest root mean square error for volume prediction was achieved for the elaborated fixed-effects taper model (0.0476), followed by the mixed-effects taper model (0.0489). At the same time, the difference between the volume relative errors achieved based on the taper models does not differ significantly from the results obtained using the volume equations already available for black locust (two of the three analysed).Robinia pseudoacacia

Comparison of Fixed- and Mixed-effects Approaches to Taper Modeling for Scots Pine in West Poland

Diameter measurements along the stem, which are the basis for taper models, usually have a hierarchical structure. Mixed-effects models, where fixed and random effects are distinguished, are a possible solution for this type of data. However, in order to fully absorb the potential of this method, random effects prediction, which requires additional measurements (diameter along stem), is recommended. This article presents a comparison of various fitting methods (mixed- and fixed-effects model approaches) of the variable-exponent taper model created by Kozak for determining the outside bark diameter along the stem and predicting the tree volume of Scots pine trees in west Poland. During the analysis, it was assumed that no additional measured data were available for practical use; therefore, for the mixed-effects model approach, fixed effects prediction without random effects was applied. Both fitting strategies were compared based on modeling and an independent validation data set. The comparison of mixed- and fixed-effects fitting strategies for the diameter along the stem indicated that the taper model fitted using the mixed-effects model approach better fit the data. Moreover, the error rate for the total tree volume prediction for the independent data set was lower for the mixed-effects model solution than for the fixed-effects one.