A physical model of the high-frequency seismic signal generated by debris flows

We propose a physical model for the high‐frequency (>1 Hz) spectral distribution of seismic power generated by debris flows. The modeled debris flow is assumed to have four regions where the impact rate and impulses are controlled by different mechanisms: the flow body, a coarser‐grained snout, a snout lip where particles fall from the snout on the bed, and a dilute front composed of saltating particles. We calculate the seismic power produced by this impact model in two end‐member scenarios, a thin‐flow and thick‐flow limit, which assume that the ratio of grain sizes to flow thicknesses are either near unity or much less than unity. The thin‐flow limit is more appropriate for boulder‐rich flows that are most likely to generate large seismic signals. As a flow passes a seismic station, the rise phase of the seismic amplitude is generated primarily by the snout while the decay phase is generated first by the snout and then the main flow body. The lip and saltating front generate a negligible seismic signal. When ground properties are known, seismic power depends most strongly on both particle diameter and average flow speed cubed, and also depends on length and width of the flow. The effective particle diameter for producing seismic power is substantially higher than the median grain size and close to the 73rd percentile for a realistic grain size distribution. We discuss how the model can be used to estimate effective particle diameter and average flow speed from an integrated measure of seismic power

A physical model of the high-frequency seismic signal generated by debris flows

We propose a physical model for the high‐frequency (>1 Hz) spectral distribution of seismic power generated by debris flows. The modeled debris flow is assumed to have four regions where the impact rate and impulses are controlled by different mechanisms: the flow body, a coarser‐grained snout, a snout lip where particles fall from the snout on the bed, and a dilute front composed of saltating particles. We calculate the seismic power produced by this impact model in two end‐member scenarios, a thin‐flow and thick‐flow limit, which assume that the ratio of grain sizes to flow thicknesses are either near unity or much less than unity. The thin‐flow limit is more appropriate for boulder‐rich flows that are most likely to generate large seismic signals. As a flow passes a seismic station, the rise phase of the seismic amplitude is generated primarily by the snout while the decay phase is generated first by the snout and then the main flow body. The lip and saltating front generate a negligible seismic signal. When ground properties are known, seismic power depends most strongly on both particle diameter and average flow speed cubed, and also depends on length and width of the flow. The effective particle diameter for producing seismic power is substantially higher than the median grain size and close to the 73rd percentile for a realistic grain size distribution. We discuss how the model can be used to estimate effective particle diameter and average flow speed from an integrated measure of seismic power

Measuring Basal Force Fluctuations of Debris Flows Using Seismic Recordings and Empirical Green's Functions

We present a novel method for measuring the fluctuating basal normal and shear stresses of debris flows by using along‐channel seismic recordings. Our method couples a simple parameterization of a debris flow as a seismic source with direct measurements of seismic path effects using empirical Green's functions generated with a force hammer. We test this method using two large‐scale (8 and 10 m³) experimental flows at the U.S. Geological Survey debris‐flow flume that were recorded by dozens of three‐component seismic sensors. The seismically derived basal stress fluctuations compare well in amplitude and timing to independent force plate measurements within the valid frequency range (15–50 Hz). We show that although the high‐frequency seismic signals provide band‐limited forcing information, there are systematic relations between the fluctuating stresses and independently measured flow properties, especially mean basal shear stress and flow thickness. However, none of the relationships are simple, and since the flow properties also correlate with one another, we cannot isolate a single factor that relates in a simple way to the fluctuating forces. Nevertheless, our observations, most notably the gradually declining ratio of fluctuating to mean basal stresses during flow passage and the distinctive behavior of the coarse, unsaturated flow front, imply that flow style may be a primary control on the conversion of translational to vibrational kinetic energy. This conversion ultimately controls the radiation of high‐frequency seismic waves. Thus, flow style may provide the key to revealing the nature of the relationship between fluctuating forces and other flow properties

Measuring Basal Force Fluctuations of Debris Flows Using Seismic Recordings and Empirical Green's Functions

We present a novel method for measuring the fluctuating basal normal and shear stresses of debris flows by using along‐channel seismic recordings. Our method couples a simple parameterization of a debris flow as a seismic source with direct measurements of seismic path effects using empirical Green's functions generated with a force hammer. We test this method using two large‐scale (8 and 10 m³) experimental flows at the U.S. Geological Survey debris‐flow flume that were recorded by dozens of three‐component seismic sensors. The seismically derived basal stress fluctuations compare well in amplitude and timing to independent force plate measurements within the valid frequency range (15–50 Hz). We show that although the high‐frequency seismic signals provide band‐limited forcing information, there are systematic relations between the fluctuating stresses and independently measured flow properties, especially mean basal shear stress and flow thickness. However, none of the relationships are simple, and since the flow properties also correlate with one another, we cannot isolate a single factor that relates in a simple way to the fluctuating forces. Nevertheless, our observations, most notably the gradually declining ratio of fluctuating to mean basal stresses during flow passage and the distinctive behavior of the coarse, unsaturated flow front, imply that flow style may be a primary control on the conversion of translational to vibrational kinetic energy. This conversion ultimately controls the radiation of high‐frequency seismic waves. Thus, flow style may provide the key to revealing the nature of the relationship between fluctuating forces and other flow properties

Frequency-area distribution of earthquake-induced landslides : abstract

Discovering the physical explanations behind the power-law distribution of landslides can provide valuable information to quantify triggered landslide events and as a consequence to understand the relation between landslide causes and impacts in terms of environmental settings of landslide affected area. In previous studies, the probability of landslide size was utilized for this quantification and the developed parameter was called a landslide magnitude (mL). The frequency-area distributions (FADs) of several landslide inventories were modelled and theoretical curves were established to identify the mL for any landslide inventory. In the observed landslide inventories, a divergence from the power-law distribution was recognized for the small landslides, referred to as the rollover, and this feature was taken into account in the established model. However, these analyses are based on a relatively limited number of inventories, each with a different triggering mechanism. Existing definition of the mL include some subjectivity, since it is based on a visual comparison between the theoretical curves and the FAD of the medium and large landslides. Additionally, the existed definition of mL introduces uncertainty due to the ambiguity in both the physical explanation of the rollover and its functional form. Here we focus on earthquake-induced landslides (EQIL) and aim to provide a rigorous method to estimate the mL and total landslide area of EQIL. We have gathered 36 EQIL inventories from around the globe. Using these inventories, we have evaluated existing explanations of the rollover and proposed an alternative explanation given the new data. Next, we propose a method to define the EQIL FAD curves, mL and to estimate the total landslide area. We utilize the total landslide areas obtained from inventories to compare them with our estimations and to validate our methodology. The results show that we calculate landslide magnitudes more accurately than previous methods

An updated method for estimating landslide‐event magnitude

Summary statistics derived from the frequency–area distribution (FAD) of inventories of triggered landslides allows for direct comparison of landslides triggered by one event (e.g. earthquake, rainstorm) with another. Such comparisons are vital to understand links between the landslide‐event and the environmental characteristics of the area affected. This could lead to methods for rapid estimation of landslide‐event magnitude, which in turn could lead to estimates of the total triggered landslide area. Previous studies proposed that the FAD of landslides follows an inverse power‐law, which provides the basis to model the size distribution of landslides and to estimate landslide‐event magnitude (mLS), which quantifies the severity of the event. In this study, we use a much larger collection of earthquake‐induced landslide (EQIL) inventories (n=45) than previous studies to show that size distributions are much more variable than previously assumed. We present an updated model and propose a method for estimating mLS and its uncertainty that better fits the observations and is more reproducible, robust, and consistent than existing methods. We validate our model by computing mLS for all of the inventories in our dataset and comparing that with the total landslide areas of the inventories. We show that our method is able to estimate the total landslide area of the events in this larger inventory dataset more successfully than the existing methods. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd

Factors controlling landslide frequency‐area distributions

A power‐law relation for the frequency‐area distribution (FAD) of medium and large landslides (e.g., tens to millions of square meters) has been observed by numerous authors. But the FAD of small landslides diverges from the power‐law distribution, with a rollover point below which frequencies decrease for smaller landslides. Some studies conclude that this divergence is an artifact of unmapped small landslides due to lack of spatial or temporal resolution; others posit that it is caused by the change in the underlying failure process. An explanation for this dilemma is essential both to evaluate the factors controlling FADs of landslides and power‐law scaling, which is a crucial factor regarding both landscape evolution and landslide hazard assessment. This study examines the FADs of 45 earthquake‐induced landslide inventories from around the world in the context of the proposed explanations. We show that each inventory probably involves some combination of the proposed explanations, though not all explanations contribute to each case. We propose an alternative explanation to understand the reason for the divergence from a power‐law. We suggest that the geometry of a landslide at the time of mapping reflects not just one single movement but many, including the propagation of numerous smaller landslides before and after the main failure. Because only the resulting combination of these landslides can be observed due to a lack of temporal resolution, many smaller landslides are not taken into account in the inventory. This reveals that the divergence from the power law is not necessarily attributed to the incompleteness of an inventory. This conceptual model will need to be validated by ongoing observation and analysis. Also, we show that because of the subjectivity of mapping procedures, the total number of landslides and total landslide areas in inventories differ significantly, and therefore the shapes of FADs also differ considerably

Integrating landslide and liquefaction hazard and loss estimates with existing USGS real-time earthquake information products

The U.S. Geological Survey (USGS) has made significant progress toward the rapid estimation of shaking and shaking-related losses through their Did You Feel It? (DYFI), ShakeMap, ShakeCast, and PAGER products. However, quantitative estimates of the extent and severity of secondary hazards (e.g., landsliding, liquefaction) are not currently included in scenarios and real-time post-earthquake products despite their significant contributions to hazard and losses for many events worldwide. We are currently running parallel global statistical models for landslides and liquefaction developed with our collaborators in testing mode, but much work remains in order to operationalize these systems. We are expanding our efforts in this area by not only improving the existing statistical models, but also by (1) exploring more sophisticated, physics-based models where feasible; (2) incorporating uncertainties; and (3) identifying and undertaking research and product development to provide useful landslide and liquefaction estimates and their uncertainties. Although our existing models use standard predictor variables that are accessible globally or regionally, including peak ground motions, topographic slope, and distance to water bodies, we continue to explore readily available proxies for rock and soil strength as well as other susceptibility terms. This work is based on the foundation of an expanding, openly available, case-history database we are compiling along with historical ShakeMaps for each event. The expected outcome of our efforts is a robust set of real-time secondary hazards products that meet the needs of a wide variety of earthquake information users. We describe the available datasets and models, developments currently underway, and anticipated products