Aftershock point cloud data provide direct evidence for the characteristics of underground faults. However, there has been a dearth of studies using state-of-the-art visual analytics methods to explore the data. In this paper, we present a novel interactive visual analysis approach for visualizing the aftershock point cloud. Our method employs a variety of interactive operations, rapid visual computing functions, flexible display modes, and various filtering approaches to present and explore the desired information for the fault geometry and aftershock dynamics. The case study conducted for the 2016 Central Italy earthquake sequence shows that the proposed approach can facilitate the discovery of the geometry of the four main fault segments and three secondary fault segments. It can also clearly reveal the spatiotemporal evolution of the aftershocks, helping to find the fluid-driven mechanism of this sequence. An open-source prototype system based on the approach is also developed and is freely available.

Fault complexity of earthquakes is universal in all types of faults (strike-slip, normal, and reverse). Usually, the faults are divided into a number of subparallel segments along the strike by geometrical discontinuities (Manighetti et al., 2015). In some cases, the depth segmentation of a fault is also observed (Elliott et al., 2011) where the cascading earthquake occurs successively along the dip. The geometrical discontinuities in the complex fault structure can sometimes impede and stop the rupture propagation and limit the earthquake magnitude. In some cases these act as a high-permeability conduit to allow fluid migration and control the spatiotemporal sequence of the subsequent earthquakes (Walters et al., 2018). The elastic-rebound theory based on the earthquake cycle concept is commonly applied for long-term earthquake prediction. However, the complex fault structure complicates the seismic hazard assessment because theoretical models based on simplistic assumptions (e.g., single dynamic rupture) were found to be inapplicable to natural faults (Barbot et al., 2012). The time intervals for cascading fault rupture due to fault segmentation range from seconds to years on a case-by-case basis, while the control factors of the faults are still not clearly understood. Therefore, it is highly important to understand the complex fault geometry, and such understanding may provide useful insight into fault mechanics and help to constrain the existing theoretical models.

Due to the past lack of ability to conduct high-resolution observations, it
is always difficult to define the geometry of the active fault system.
Recent developments of both geodetic and seismic observation techniques make
it possible to reveal the fault geometry at the surface and depth. Advanced synthetic aperture radar (SAR) geodesy provides near-field deformation and can be used to directly map
the fault surface and constrain the deep fault through deformation
inversion. The construction of an increasing number of seismic stations
allows for the identification of the locations of a large number of aftershocks
following the main shocks. The point cloud of the located aftershocks
contains the information regarding both the three-dimensional coordinates
and precise time of occurrence that can directly reveal the fault geometry
and temporal evolution of the earthquake sequence. Current interpretation
methods for the aftershock cloud are mostly case-specific rather than general,
and to date, no standard processing procedure for the visualization of these
data has been available. While many studies plot the cross-section profile
of the aftershock point cloud to reveal the dip of the fault plane (Irmak
et al., 2012; Hengesh and Whitney, 2016; Li et al., 2010; Elliott et al.,
2013), these simple visualization methods usually have the following
limitations:

Lack of interactive operations: the visualization methods provide a static display without an interactive interface to assist the users in effectively performing analyses through various human–computer interactions.

Lack of visual analysis: the current methods simply present these data without computing the feature (e.g., plane fitting or local outlier factor value calculation) to enhance the structure.

Lack of noise filtering: while the aftershock locations normally contain many uncertainties, most studies do not consider either the identification or removal of these noisy points.

Visual analytics is a research direction of the field of data visualization (Wong and Thomas, 2004), which integrates new computational and theory-based tools with innovative interactive techniques and visual representations to enable human–information discourse. How to efficiently transform large earth observation data into knowledge is a tremendous challenge in the era of big data (Xia et al., 2018). Visual analytics is highly advantageous and has good potential in complex data analytics for intuitive information representation and dynamic data exploration (Ward et al., 2015). The importance of scientific visualization has been recognized for a long time (McCormick, 1988). Specifically, in geophysics, the visualization of seismic refraction data has already been widely applied to explore the distribution of petroleum and gas (Liu et al., 2018; Raposo et al., 2016). However, to date, studies using state-of-the-art visual analytics methods to explore other kinds of seismic data (e.g., aftershock point cloud) to gain information about earthquakes have been lacking.

In this study, we propose a novel interactive visualization method for
exploring the 3-D aftershock point cloud data. This method can help
researchers to better understand the complex fault geometry in three ways:

A set of interactive operations is provided to stimulate creative analysts and exploit the researchers' background knowledge.

On-the-fly computation of the local outlier factor (LOF), 2-D projection, and plane fitting are supported in the visual analysis so that the hidden features of the fault structure can be discovered dynamically.

Noisy or irrelevant aftershock points can be filtered to reduce the distractions from invalid information.

Flowchart of the proposed approach.

Figure 1 shows the flowchart of the proposed approach. Initially, we imported the aftershock point data from an earthquake catalog or the literature into our system. At the same time, the LOF values for all of the points are computed automatically. Then, the points are presented in a 3-D view window, allowing free rotation, panning, and zooming to observe the point structure. The earthquake fault, with data either from an existing source or from inferred information, can be imported into the 3-D view as well. After defining the parameters for the projection (i.e., strike and dip of the plane and azimuth of the projection direction), the 2-D points are rapidly computed and presented. Then, some interactions, i.e., coloring and filtering, can be performed on the 3-D point clouds and 2-D plane projection to enhance the structure. From the 2-D plane projection, two interactions are further provided for exploring the fault geometry and aftershock dynamics. The first is the selection and plane fitting of a point cluster on a potential plane. After interactively selecting the clustered points, a plane will be automatically fitted by a robust estimator to reveal the potential fault structure. The second is the observation of aftershock migration. Animation of the aftershocks is provided so that a preliminary recognition of the migration direction can be obtained. Then, the user can define a propagation direction to further explore the aftershock evolution. After assigning the direction, the distance traveled by the aftershocks along the specified direction as a function of time will be plotted, which is helpful in discovering the driving factor of aftershock migration. We note that when the preliminary exploration of the fault geometry or earthquake dynamics is finished, the users can return to the previous interactions to refine their interpretation of the data.

As shown in Fig. 2, the user interface includes four main components. The first component is the operation tools panel with all the buttons, sliders, text boxes, and labels. It includes most interactions in the visual analytics. The second component is the 3-D view panel for presenting cloud points and fault planes. The third component is the 2-D view panel for presenting the points in the 2-D projection plane. The fourth component is a temporal panel that switches between 3-D fault plane fitting plotting and propagation distance–time plotting, corresponding to the explorations of the fault geometry and aftershock dynamics, respectively.

Visual interface of our approach consisting of four interrelated
components:

The easy-to-use interactions represent a significant difference between the proposed method and conventional aftershock interpretation methods. The traditional static displays prevent the analyst from directly and rapidly exploring the aftershock data. However, the easy-to-use interactive displays can lead to deeper insights into 3-D aftershock cloud point data and the discovery of new fault structures or spatiotemporal evolution patterns. These interactive operations are described as follows.

Because of the limitations due to the resolution of seismic data inversion,
there is some uncertainty in the location of the aftershocks, so that some
earthquake points show large deviations from the fault plane. Usually, the
original aftershock data do not contain any information about this
uncertainty, and we cannot eliminate these outliers. In this study, we
proposed to use the LOF, which is commonly used in the identification of the
outliers in the lidar point cloud (Wang et al., 2019) to detect the
anomalous points that deviate distinctly from the fault plane. The LOF
(Breunig et al., 2000) is based on the concept of local density, which
is estimated by the reachability distance of the object to its

Let

The local reachability density of an object p is then defined by

The LOF for point p is then obtained by

An example of LOF scores for 2-D points. Each point is colored by its LOF score. The radius of red circles on five selected points is in direct proportion to their LOF score (plotted in the center). It is observed that the central points with high density have low LOF scores, while the surrounding points have high ones.

Projecting the 3-D aftershock point cloud to a 2-D plane can significantly
enhance the fault geometry features. As mentioned above, we offer an
interactive way to rapidly compute the projection when a plane and
projection direction are assigned. To make the interactive operation
user-friendly for geologists, we use geological terms, i.e., strike and dip
(to define the orientation of the projection plane), and azimuth angle (to
define the projection angle). We firstly calculate 3-D geographic coordinates
of the projected points on the projection plane for aftershocks according to
the line–plane intersection equation. The 3-D geographic coordinates are
then transformed to a 2-D local coordinate system by two element rotations: a

The rotation matrices (

When the analyst identifies a potential linear feature from the
cross-section plot, the plane fitting can rapidly evaluate the possible
feature and provides the precise geometric parameters. In this study, we
used an algorithm based on the singular value decomposition (SVD) to fit a plane
to the given 3-D aftershock points. The calculation of the parameters of the
plane (

Given a set of points

Fit a plane using the available points.

Calculate the distance (

Calculate the root mean square error (RMSE) of all of the
distances (

Find points with distances 3 times larger than RMSE and define them as outliers.

Remove these points, and then return to step 1.

Stop when there is no outlier found, and return the plane parameter.

The proposed visualization approach has been implemented in a software
package (Aftershock Visualization, AFV1.0;

On 24 August 2016 (01:36 UTC, local time 03:36), a destructive earthquake
(

Seismotectonic setting of the Central Italy earthquake sequence. The three major earthquakes in the sequence are denoted by the red stars and beach ball symbols, and the two recent large historical events are colored in black. The dashed black rectangles represent the surface projection of the fault planes adopted in this study. The bold black lines are the two seismogenic normal fault systems, namely, the Mt. Vettore–Mt. Bove Fault system (VBFS) and the Mt. Gorzano Fault system (GFS). The pink line shows the simplified trace of the preexisting compressional front named the Olevano–Antrodoco–Sibillini (OAS) Thrust. Aftershocks are marked by the small dots with different colors. The blue, purple, and yellow points represent the events taking place on 24 August–24 October 2016, 24–30 October 2016, and 30 October 2016–8 October 2017, respectively.

Many recent studies reported in the literature have revealed a very complex fault geometry for this earthquake sequence. In addition to the main range-front normal faulting structures that were adopted in many early studies (Liu et al., 2017; Tinti et al., 2016), recent studies find increasing evidence for some additional minor antithetic and synthetic faults (Chiaraluce et al., 2017; Scognamiglio et al., 2018; Walters et al., 2018; Cheloni et al., 2017). The activation of this secondary fault structure has important implications for evaluating the seismic hazard in this section of the Central Apennines. The complex fault geometry also plays an important role in channeling fluid diffusion and affects the spatial order of the cascading earthquakes. The aftershock distribution provides direct evidence for the fault geometry and underground dynamics. By interactively visualizing these data, we can obtain useful information regarding both the fault geometry and earthquake dynamics. Additionally, a relocated aftershock dataset has been provided in the work of Chiaraluce et al. (2017), making this earthquake sequence an ideal case for applying our proposed interactive visualization method. Below, we demonstrate the benefits of our method in identifying fault geometry and aftershock migration.

According to previous studies, several fault segments are involved in this earthquake sequence. Some of these are the main fault segments located in the GFS–VBFS, while others are secondary fault segments including a NE-dipping normal fault antithetic to the GFS–VBFS and a preexisting compressional structure that is likely related to a segment of the Olevano–Antrodoco–Sibillini Thrust. We will show how our interactive visualization method can facilitate the recognition of these structures.

Following the flowchart shown in Fig. 1, we first import the relocated aftershock data from the results obtained by Chiaraluce et al. (2017) to the 3-D view. Some of the basic interactions provided by this package, i.e., zooming, panning, rotating, data tips, and data brushing, can be used to explore the data. LOF values were then calculated for all points to identify the aftershock outliers. We can interactively select to show some of the points according to their location, depth, magnitude, LOF, and time, and we can project them to a desired plane. After we find a linear feature in the projection plane, we select the points comprising the linear feature and automatically fit a plane to the feature (Fig. 6).

Fault geometry identification and plane fitting.

First, we identify the four main fault planes by projecting the cloud point
to a plane with a 70

Geometry parameters of the inferred fault from the aftershock point cloud. Strike and dip are given in degrees; all other parameters are measured in kilometers.

Second, we explore the point cloud to find other secondary faults. Since
there is no hint of the existence of these faults, we use the basic
interaction tools in the 3-D view and the filtering function in our package to
find the possible fault geometry. An obvious cluster of aftershock points is
found on an antithetic NE-dipping plane in the Norcia area. We therefore
also project the cloud point to a plane with a 70

Besides the static analysis of aftershocks to find the fault geometry, the timing information of aftershocks has the potential to reveal earthquake dynamics related to fluid diffusion, afterslip, and/or pressure transients. Fluid diffusion is a main factor in triggering seismicity as observed in many tectonic regimes (Vidale and Shearer, 2006). It was also proposed to have been present in the nearby 2009 L'Aquila earthquake (Malagnini et al., 2012). The migration of the aftershocks could provide some evidence for such diffusive processes. Walters et al. (2018) found a significant fluid-driven aftershock migration between the Amatrice earthquake and Visso earthquake controlled by the fault intersection in this earthquake sequence.

Observation of aftershock migration.

To observe the spatiotemporal process, we project the aftershocks of the
seismogenic fault to be along a horizontal vector with an azimuth 15

Next, we can define a starting point and an assumed direction in the projection plane. After drawing the starting point and the propagation line, the distances of the aftershocks to the starting point along this direction can be calculated automatically. They are then plotted as a function of time to further reveal the time evolution of the aftershocks. Following the work of Walters et al. (2018), we defined a starting point in the peak slip of the Amatrice earthquake and a direction perpendicular to the Pian Piccolo fault. A clear temporal trend of the aftershocks was then observed in the plot (Fig. 7b). Therefore, the observed spatiotemporal pattern of aftershock migration can be interpreted by the seismologist to understand the earthquake mechanism and infer the possible controlling factor for the fault rupture. In this case, the diffusive-like aftershock temporal trend can be further interpreted using a pore fluid source model. Through the interactive visualization operations, we can observe that aftershock propagation is consistent with a diffusive process and can also observe the spatial concentration of the aftershocks along the fault intersection. This information can be used to derive the conclusion, as described in the work of Walters et al. (2018), that the intersecting structures act to channel the fluids and control the timing and order of the subsequent earthquakes.

We present a novel interactive approach and develop a prototype system to illustrate 3-D aftershock point clouds that can help the geophysicist and seismologist to better understand the geometry of a complex fault system and the spatiotemporal pattern of the aftershocks. Moreover, it can be applied in an educational scenario to facilitate student learning. In this approach, we design a set of interactive operations to facilitate the exploration of the data. Fast computation of LOF, 2-D projection, and plane fitting are implemented in addition to the visualization to reveal additional, hidden information, which is not obvious in the original data. Additionally, the point cloud can be visualized in many ways (e.g., 3-D view, 2-D plane projection, and animation), aiding viewers in interpreting the aftershock point cloud. A wide range of data filtering options (e.g., by magnitude, depth, location, time, and LOF) enable the users to avoid interference from invalid data in order to focus on the useful information.

It is widely accepted that visual analytics with interactive visual
interfaces can amplify human cognitive capabilities, and it is suitable for
solving some complex problems relying on closely coupled human and machine
analysis. When applied to the aftershock catalog, visual analytics can
therefore help to discover some new fault planes or weak signals of
aftershock migrations, which might be hard to observe directly from the
data. Specifically, the designed visual analytics procedure can assist the
knowledge discovery from the aftershock catalog in several ways:

by accelerating the fault segment discovery processing through 3-D view manipulation (e.g., zooming, panning, and rotating);

by enhancing the recognition of fault segment patterns through rapid visual computing functions (e.g., interactive projection, plane fitting, and fault data fusing);

by reducing the influence from low-quality or irrelevant aftershock points through various filtering methods (e.g., depth, LOF, time, and magnitude filtering);

by enabling the aftershock migration exploration by providing more cognitive resources (e.g., animation and propagation distance–time plotting).

The research data are included in the Supplement.

The supplement related to this article is available online at:

This work was conducted by CW and JJ under the supervision of QL. The paper was prepared by CW and JJ with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This research has been supported by the Shenzhen Scientific Research and Development Funding Program (grant nos. KQJSCX20180328093453763, JCYJ20180305125101282, JCYJ20170817104236221, and JCYJ20170412142144518), the Open Fund of the State Key Laboratory of Earthquake Dynamics (grant no. LED2016B03), the NSFC (grant nos. 61802265 and 41974006), Guangdong Provincial Natural Science Foundation (grant no. 2018A030310426), and the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Land and Resource (grant no. KF-2018-03-004).

This paper was edited by Caroline Beghein and reviewed by two anonymous referees.