A new mathematical model of asymmetric hydraulic fracture growth

Hydraulic fractures generated by fluid injection in rock formations are often mapped by seismic monitoring. In many cases, the microseismicity is asymmetric relative to the injection well, which has been interpreted by stress gradient along the direction of the hydraulic fracture. We present a mathematical model of asymmetric hydrofracture growth based on relations between the solid‐phase stress and the fracture hydraulics. For single fracture and single injection point, the model has three parameters, hydraulic conductivities of the fracture wings, and normalised stress gradient and predicts the positions of the fracture tips as functions of time. The model is applied to a set of microseismic event locations that occurred during and after an injection process. Two different methods are suggested that make it possible to delineate the fracture tips from the set of microseismic events. This makes it possible to determine the model parameters and to check the agreement between the model prediction and the measured data. The comparison of the measured and modelled growth of fracture wings supports both the assumption of the non‐zero stress gradient and the existence of the post‐injection unilateral growth.     

How well can we simulate complex hydro‐geomorphic process chains? The 2012 multi‐lake outburst flood in the Santa Cruz Valley (Cordillera Blanca,Perú)

Changing high‐mountain environments are characterized by destabilizing ice, rock or debris slopes connected to evolving glacial lakes. Such configurations may lead to potentially devastating sequences of mass movements (process chains or cascades). Computer simulations are supposed to assist in anticipating the possible consequences of such phenomena in order to reduce the losses. The present study explores the potential of the novel computational tool r.avaflow for simulating complex process chains. r.avaflow employs an enhanced version of the Pudasaini ( 2012 ) general two‐phase mass flow model, allowing consideration of the interactions between solid and fluid components of the flow. We back‐calculate an event that occurred in 2012 when a landslide from a moraine slope triggered a multi‐lake outburst flood in the Artizón and Santa Cruz valleys, Cordillera Blanca, Peru, involving four lakes and a substantial amount of entrained debris along the path. The documented and reconstructed flow patterns are reproduced in a largely satisfactory way in the sense of empirical adequacy. However, small variations in the uncertain parameters can fundamentally influence the behaviour of the process chain through threshold effects and positive feedbacks. Forward simulations of possible future cascading events will rely on more comprehensive case and parameter studies, but particularly on the development of appropriate strategies for decision‐making based on uncertain simulation results. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Validation of official erosion modelling based on high‐resolution radar rain data by aerial photo erosion classification

The universal soil loss equation (USLE) is the most frequently applied erosion prediction model and it is also implemented as an official decision‐making instrument for agricultural regulations. The USLE itself has been already validated using different approaches. Additional errors, however, arise from input data and interpolation procedures that become necessary for field‐specific predictions on a national scale for administrative purposes. In this study, predicted event soil loss using the official prediction system in Bavaria (Germany) was validated by comparison with aerial photo erosion classifications of 8100 fields. Values for the USLE factors were mainly taken from the official Bavarian high‐resolution (5 × 5 m²) erosion cadastre. As series of erosion events were examined, the cover and management factor was replaced by the soil loss ratio. The event erosivity factor was calculated from high‐resolution (1 × 1 km², 5 min), rain gauge‐adjusted radar rain data (RADOLAN). Aerial photo erosion interpretation worked sufficiently well and average erosion predictions and visual classifications correlated closely. This was also true for data broken down to individual factors and different crops. There was no reason to assume a general invalidity of the USLE and the official parametrization procedures. Event predictions mainly suffered from errors in the assumed crop stage period and tillage practices, which do not reflect interannual and farm‐specific variation. In addition, the resolution of radar data (1 km²) did not seem to be sufficient to predict short‐term erosion on individual fields given the strong spatial gradients within individual rains. The quality of the input data clearly determined prediction quality. Differences between USLE predictions and observations are most likely caused by parametrization weaknesses but not by a failure of the model itself. Copyright © 2017 John Wiley & Sons, Ltd.     

Application of Large‐Scale Inversion Algorithms to Hydraulic Tomography in an Alluvial Aquifer

Large‐scale inversion methods have been recently developed and permitted now to considerably reduce the computation time and memory needed for inversions of models with a large amount of parameters and data. In this work, we have applied a deterministic geostatistical inversion algorithm to a hydraulic tomography investigation conducted in an experimental field site situated within an alluvial aquifer in Southern France. This application aims to achieve a 2‐D large‐scale modeling of the spatial transmissivity distribution of the site. The inversion algorithm uses a quasi‐Newton iterative process based on a Bayesian approach. We compared the results obtained by using three different methodologies for sensitivity analysis: an adjoint‐state method, a finite‐difference method, and a principal component geostatistical approach (PCGA). The PCGA is a large‐scale adapted method which was developed for inversions with a large number of parameters by using an approximation of the covariance matrix, and by avoiding the calculation of the full Jacobian sensitivity matrix. We reconstructed high‐resolution transmissivity fields (composed of up to 25,600 cells) which generated good correlations between the measured and computed hydraulic heads. In particular, we show that, by combining the PCGA inversion method and the hydraulic tomography method, we are able to substantially reduce the computation time of the inversions, while still producing high‐quality inversion results as those obtained from the other sensitivity analysis methodologies.