Application of Machine Learning in Deterministic Ground Motion Simulation

Report for SCEC Award #17239

Submitted June 2018

Investigators:

Ricardo Taborda and Naeem Khoshnevis The University of Memphis

I. Project Overview ................................................................................................................................ iA. Abstract ....................................................................................................................................... iB. SCEC Annual Science Highlights ................................................................................................. iC.Exemplary Figure ........................................................................................................................ iiD.SCEC Science Priorities .............................................................................................................. iiE. Intellectual Merit ......................................................................................................................... iiiF. Broader Impacts ......................................................................................................................... iiiG.Project Publications .................................................................................................................... iii

II. Technical Report ............................................................................................................................... 1A. Summary .................................................................................................................................... 1B. Project Objectives and Summary of Accomplishments ................................................................. 1C.Part I: On Prioritizing Ground-Motion Validation Metrics ............................................................... 2

1. Background .......................................................................................................................... 22. Summary of the Methodology ................................................................................................ 23. Summary of Results .............................................................................................................. 2

D.Part II: On Attenuation Parameters .............................................................................................. 41. Background .......................................................................................................................... 42. Summary of the Methodology ................................................................................................ 43. Summary of Results .............................................................................................................. 5

E. References ................................................................................................................................. 6

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I. Project Overview

A. Abstract In the box below, describe the project objectives, methodology, and results obtained and their signifi-cance. If this work is a continuation of a multi-year SCEC-funded project, please include major research findings for all previous years in the abstract. (Maximum 250 words.)

This project focused on investigating and testing the potential use of machine learning methods in three-dimensional (physics-based) ground motion simulation, as a means to optimize data analysis and mod-eling parameters. We concentrated efforts in two particular problems: (i) prioritizing ground motion vali-dation metrics; and (ii) evaluating attenuation models. For the first of these problems, we analyzed a dataset of ground motion validation results with eleven goodness-of-fit metrics using semi-supervised and supervised learning methods. We performed a clustering analysis on the dataset and identified mul-ti-dimensional patterns in order to label the data samples, which allowed us to produce decision trees that with a prioritized and narrowed choice of metrics. In the end, we identified the response spectrum, total energy and peak ground acceleration as the most relevant metrics, followed by the Arias intensity and peak ground velocity. For the second problem, we used machine learning techniques to create sur-rogate simulators that could predict the peak velocity, peak acceleration, area under the envelope of seismograms and response spectrum ordinates, to then feed an optimization method to invert the pa-rameters associated with an attenuation (Q-Vs) relationship. The procedure was tested for both ideal-ized models and realistic models, and it was found to effectively identify the parameters for the assumed Q-Vs relationship when using synthetic data as reference. Initial tests with real data showed promise but require additional optimization steps and user supervision.

B. SCEC Annual Science Highlights Each year, the Science Planning Committee reviews and summarizes SCEC research accomplishments, and presents the results to the SCEC community and funding agencies. Rank (in order of preference) the sections in which you would like your project results to appear. Choose up to 3 working groups from be-low and re-order them according to your preference ranking.

1. Computational Science (CS) 2. Ground Motions 3. Earthquake Engineering Implementation Interface (EEII)

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C. Exemplary Figure (a)

(c)

(b)

Exemplary Figure. (a) Clustering analysis carried out on a large dataset of results from a ground motion simulation validation process comparing the relationships that exist in a multidimensional space of goodness-of-fit metrics. (b) Topology of a decision tree reducing the validation of ground motion simulations to a comparison of only three goodness-of-fit metrics (C4, C5, C8) after having identified the thresholds needed to discretize the validation scores into for different categories (poor, fair, good, and excel-lent). (c) Optimization process to identify Qs-Vs relationships when comparing synthetic results from surrogate simulators with observations.

D. SCEC Science Priorities In the box below, please list (in rank order) the SCEC priorities this project has achieved. See https://www.scec.org/research/priorities for list of SCEC research priorities. For example: 6a, 6b, 6c

P4a, P4c, P2b

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E. Intellectual Merit How does the project contribute to the overall intellectual merit of SCEC? For example: How does the research contribute to advancing knowledge and understanding in the field and, more specifically, SCEC research objectives? To what extent has the activity developed creative and original concepts?

This study contributes to exploring new alternatives that could potentially accelerate the time-to-completion of routine data analysis and computing intensive processes. In particular, the activities car-ried out contribute to the goals of SCEC in areas of the ground motion, scientific computing, and the earthquake engineering implementation interface disciplinary and interdisciplinary groups, and the community modeling environment group. In terms of developing creative and original concepts, the re-search carried out contributed two methodologies not available before. On the one hand, we developed an algorithm for validation of ground motion synthetics that can provide an accurate assessment of the level of accuracy of simulated seismograms when compared to data using only a few metrics (2 or 3), as opposed to the more elaborate methods in use today employing a larger family of goodness-of-fit metrics (11). And on the other hand, we developed a procedure to invert for the parameters defining a Q-Vs relationship in a simulation domain based on an optimization process using training data to predict ground motion metrics.

F. Broader Impacts How does the project contribute to the broader impacts of SCEC as a whole? For example: How well has the activity promoted or supported teaching, training, and learning at your institution or across SCEC? If your project included a SCEC intern, what was his/her contribution? How has your project broadened the participation of underrepresented groups? To what extent has the project enhanced the infrastructure for research and education (e.g., facilities, instrumentation, networks, and partnerships)? What are some possible benefits of the activity to society?

From a broader impacts perspective, the main contribution of this project was to advance the use of machine learning techniques in areas of earth sciences and earthquake engineering. Machine learning is an area of growing interest and in this project we show that there is potential for its use in two types of problems, data analysis and synthesis, and prediction of ground motion characteristics. Furthermore, the project provided a particular learning opportunity for a graduate research assistant. The original pro-posal for this project was prepared by PhD Geophysics student Naeem Khoshnevis in the Center for Earthquake Research and Information at the University of Memphis. Khoshnevis also carried out the research as his own with very little input from the PI of record, Ricardo Taborda.

G. Project Publications All publications and presentations of the work funded must be entered in the SCEC Publications data-base. Log in at http://www.scec.org/user/login and select the Publications button to enter the SCEC Pub-lications System. Please either (a) update a publication record you previously submitted or (b) add new publication record(s) as needed. If you have any problems, please email web@scec.org for assistance.

The results of the project have been shared with the broader scientific and engineering community through poster presentations at annual meetings and workshops, and through two publications (one already accepted to be published at the BSSA, the second one currently in preparation to be submitted to GJI. These publications have been added to the SCEC Publications system. They are:

• Khoshnevis, N. and Taborda, R. (2018). Prioritizing ground motion validation metrics using semi-supervised and supervised learning. Bull. Seismol. Soc. Am. (accepted), doi: 10.1785/0120180056.

• Khoshnevis, N. and Taborda, R. (2018). Evaluation of attenuation models (Q-Vs relationships) used in physics-based ground-motion earthquake simulation combining machine learning and optimization methods (in preparation)

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• Khoshnevis, N. and Taborda, R. (2018a). A look at computational learning as applied to three problems in earthquake ground motion simulation. In Workshop on Machine Learning in Solid Earth Geoscience, Santa Fe, New Mexico, February 20–22.

• Khoshnevis, N. and Taborda, R. (2017a). An application of machine learning techniques to the evaluation of goodness-of-fit scores used in earthquake ground motion validation. In Proc. SCEC Annu. Meet., number EEII-237, Palm Springs, CA, September 10–13.

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II. Technical Report

A. Summary This project focused on investigating and testing the potential use of machine learning methods in three-dimensional (physics-based) ground motion simulation, as a means to optimize data analysis and model-ing parameters. We concentrated efforts in two particular problems: (i) prioritizing ground motion valida-tion metrics; and (ii) evaluating attenuation models. For the first of these problems, we analyzed a dataset of ground motion validation results with eleven goodness-of-fit metrics using semi-supervised and super-vised learning methods. We performed a clustering analysis on the dataset and identified multi-dimensional patterns in order to label the data samples, which allowed us to produce decision trees that with a prioritized and narrowed choice of metrics. In the end, we identified the response spectrum, total energy and peak ground acceleration as the most relevant metrics, followed by the Arias intensity and peak ground velocity. For the second problem, we used machine learning techniques to create surrogate simulators that could predict the peak velocity, peak acceleration, area under the envelope of seismo-grams and response spectrum ordinates, to then feed an optimization method to invert the parameters associated with an attenuation (Q-Vs) relationship. The procedure was tested for both idealized models and realistic models, and it was found to effectively identify the parameters for the assumed Q-Vs rela-tionship when using synthetic data as reference. Initial tests with real data showed promise but require additional optimization steps and user supervision.

B. Project Objectives and Summary of Accomplishments The main objectives of these project were:

• To gain a better understanding of the participation and relevance of different available goodness-of-fit (GOF) metrics employed in ground motion validation using data analysis techniques.

• To use such dominant GOF metrics to simplify validation processes by developing algorithms that can help predict validation results.

• To explore the use of machine learning techniques to develop surrogate simulators that can help predict basic ground motion intensity measures or characteristics based on suites of simulations used as training data.

• To use such surrogate simulators as a means to produce synthetic results that can serve as prox-ies for replacing inversion methods for complex model parameters (here applied to the case of Q-Vs relationships used in forward ground motion simulations.

At the end of the project we were successful in accomplishing the aforementioned objectives. For the first part of the project related to the GOF analysis, we were able to identify that there are a few GOF metrics that are particularly relevant in the final results of validation of ground motion synthetics when compared to data (response spectrum, total energy, and peak ground acceleration, followed by peak ground veloci-ty). Likewise, we were able to identify that, for the dataset used, the metric of duration—often cited as very significant for engineering applications—was not a particularly effective parameter for validation. We used the reduced number of metrics in the development of various decision trees, which can produce re-sults faster than running a thorough data processing with eleven metrics, and yet indicate the most likely validation category (i.e., poor, fair, good, excellent).

For the second part of the project, we obtained promising results regarding the ability of neural networks to be used to predict ground motion intensity measures such as peak ground velocity, peak ground ac-celeration, ground motion energy (measured as the area under the envelope of a seismogram), and ordi-nates in the acceleration response spectrum at selected periods. We then used an optimization method to use such capability in order to infer attenuation parameters for a predefined Q-Vs relationship. We suc-cessfully tested the methodology for various idealized cases and obtained excellent results in terms of predictability. We also tested a real case but found issues with the ranges that can be covered by the simulation and the surrogate simulators due to imperfection of the underlaying models. Our tests indicat-ed that some of these problems can be overcome through further optimization.

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C. Part I: On Prioritizing Ground-Motion Validation Metrics 1. Background Verification and validation of ground-motion synthetics have received increasing attention in recent years due to advances in deterministic and nondeterministic physics-based earthquake simulations for engi-neering applications. Various methods have been proposed to evaluate, through direct signal-to-signal quantitative comparisons or overall statistical analyses, the similarity between simulation synthetics and recorded data, or with respect to other solutions (e.g., Anderson, 2004; Kristeková et al., 2006, 2009; Ol-sen and Mayhew, 2010; Burks and Baker, 2014; Rezaeian et al., 2015). Some of these methods are bet-ter suited for verification, whereas others are better suited for validation. Amongst them, Anderson (2004) is perhaps the method most widely used today for validation (e.g., Bielak et al., 2010; Chaljub et al., 2010; Guidotti et al., 2011; Maufroy et al., 2015). In essence, this method assesses the similarity of two signals based on the average score of 10 metrics. We have consistently relied on a modified version of Ander-son’s method for the validation of a series of simulations done to reproduce the ground motions of the 2008 Mw 5.4 Chino Hills earthquake (Taborda and Bielak, 2013, 2014), and for the evaluation of velocity models available for southern California (Taborda et al., 2016).

However, it has been pointed out that some of the metrics used in Anderson’s method are redundant, or that other relevant metrics should be considered. Taborda and Bielak (2013), for instance, included the strong-motion duration as an additional metric explicitly, and averaged the scores related to energy and the Arias intensity to avoid double counting their contribution. In the same spirit, Maufroy et al. (2015) re-duced the number of metrics, limiting them to only those with comparable units. Unfortunately, none of these alternatives addresses the underlying questions regarding what are the most important parameters that ought to be taken into account when validating ground motion simulations, and what level of priority should these parameters be given. Lack of consensus about how to answer these questions makes the choice of validation methods and the selection of the comparison metrics a subjective one. This makes it difficult for simulators to identify the sort of changes needed in their models that could lead to better ground-motion predictions. Through the first part of this project we offer data-informed arguments that can help simulators justify focusing on a reduced number of alternative metrics.

2. Summary of the Methodology We proposed an algorithm to reduce and prioritize the number of validation metrics based on a previously acquired collection of validation data samples (i.e., our dataset). To do this, we identified rules with dis-junctive characteristics, in the form of decision trees, that lead to outcomes representative of the overall validation analysis. In our case, we defined such outcome in terms of four validation categories or classes representative of the quality of the validation, namely, poor (P), fair (F), good (G), and excellent (E). The development of such decision trees requires a proper classification of the data. The classification process was done through a clustering analysis where the data is considered to be part of a multi-dimensional space defined by the GOF metrics in consideration. The data is analyzed in sub-spaces of 2, 3 and 4 metrics and clustered to minimize the distance to a user-constrained set of samples fixed at the scores associated with the given validation categories. In the end, the clustering process results in a labeled da-taset that can be analyzed with an algorithm designed to maximize the effectiveness of a large number of combinations of decision trees. We then identified the trees with the greatest effectiveness and the least possible number of metrics (i.e., the simpler trees). This, in turn, allows us to identify the metrics and their participation in the selected trees, which is indicative of the relevance of the individual metrics in the col-lective results.

3. Summary of Results Figure 1 shows a sample of the results obtained during the clustering process and one of the final deci-sion trees. The clustering analysis allows us to see the relevance of the metrics and their relationships—not only in terms of correlation, but also in how well the different validation categories can be distinguish from each other based on those metrics in a multi-dimensional space. In turn, the construction of multiple decision trees (here we only show one for brevity) facilitates identifying the participation of the different metrics in reaching a successful classification of the validation scores, and these participations are indica-tive of the priority of such metrics. In short, we found that the most relevant metrics for validation are the response spectrum in combination with the total energy, followed by the peak ground response in

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(a)

(b)

Figure 1. (a) Clustering analysis carried out on a large dataset of results from a ground motion simulation validation process comparing the relationships that exist in a multidimensional space of goodness-of-fit metrics. (b) Topology of a decision tree reducing the validation of ground motion simulations to a comparison of only three goodness-of-fit metrics (C4, C5, C8) after having identified the thresholds needed to discretize the validation scores into for different categories (poor, fair, good, and excellent).

Figure 2. Comparison of GOF validation scores obtained using (a) an 11-metric Anderson (2004)-type GOF scoring, and (b) the T1 combination GOF validation classification. In both cases, the top plots show maps with a distribution of the scores or classes outcome at each station, where the contours are drawn for illustration purposes only; while the bottom plots show histograms with the count of stations for each GOF score interval or validation class. On the right side, the results of both methods are compared by superimposing the results of the counts from using Anderson’s method (dashed-line empty bars) next to those obtained using the T1 algorithm (filled bars). The color version of this figure is available only in the electronic edition.

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acceleration and velocity, and the Arias intensity. In their absence, other relevant metrics are the peak ground displacement and the Fourier spectrum. The least relevant metrics are the shape of the integrals for the energy and the arias intensity (i.e., normalized as indirect measurements of the evolution of the ground motion in time) and the strong phase duration (measured between 5 and 95% of the integral of squared time series of velocity).

D. Part II: On Attenuation Parameters 1. Background The accurate solution of wave propagation problems requires the appropriate representation of energy losses due to internal friction in geomaterials. These losses are important for the adequate estimation of the amplification and duration of seismic waves in regions with high dissipative properties. The amplitude of seismic waves decreases as the distance from source increases. In the absence of large deformations (i.e., nonlinearities), this is due to geometric spreading, intrinsic attenuation, and scattering. In 3D ground motion simulations, the geometric spreading and scattering (as a result of large scale heterogeneities rep-resented in velocity models) are inherently considered. Intrinsic attenuation, on the other hand, is handled via the numerical representation of mechanisms designed to mimic the losses due to internal friction. The parameters of these mechanisms are defined based on the quality factor Q, which is, in turn, commonly defined as a function of the shear wave velocity, Vs (e.g., Brocher 2008, 2005; Olsen et al 2003; Graves 2008; Taborda and Bielak 2013).

There is, however, no consensus about the most appropriate Q-Vs relationship. Moreover, some of the aforementioned studies were limited to lower frequencies (f ≤ 0.5 Hz). Olsen et al (2003), for example, constructed several simple distributions of Qs and Qs and identified those that provide the best fit be-tween simulated and recorded seismograms in the frequency range 0–0.5 Hz based on the evaluation of the peak ground velocities for the 1994 Northridge earthquake. Ideally, one would invert for Q values us-ing standard tomography procedures to help improve Q models. Unfortunately, these problems are non-unique and the computational requirements are very high, even for very low frequencies (~0.3 Hz). There is therefore the need to find alternative methods that can help improve Q models at a lower computational cost.

2. Summary of the Methodology Here, we assume that all materials in a given spatial domain follow a Qs-Vs relationship of the form

Qs = c + aVsb

where a, b and c are arbitrary parameters controlling the relationship. These parameters are, in general, unknown. They may also be dependent on depth and frequency but for this project we consider them to be constants. Then, given a set of surface observations for a known velocity structure and seismic source, with unknown dissipative properties, the goal is to determine the parameters a, b and c that would lead to the best estimation of a series of intensity measures when comparing synthetics with ob-servations.

To that end, we developed surrogate simulators of ground motion intensity measures using artificial neu-ral networks (ANNs). In particular, we developed two alternative simulators, one that will predict peak ground acceleration only, and another that would predict peak ground acceleration, peak ground velocity, spectral acceleration, and a measure of energy (in the form of the area under the envelope of the seis-mogram computed using the amplitude of the Hilbert transform). These ANNs were trained using actual 3D simulations for a fraction of the total number of forward simulations needed to find the parameters a, b and c.

The surrogate simulators are then used to produce a large suit of results for the intensity measures which are compared to those of the observations and subjected through a genetic algorithm (GA) used to identi-fy which combination of the parameters a, b and c is the optimal combination to minimize a cost function in an optimization process. This optimization process does not necessarily find the parameters them-selves but identify the nominal velocity at which the Qs-Vs relationship has the least possible standard deviation at any given observation point, therefore, in effect, allowing us to identify the associated param-

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eters associated with the Qs-Vs relationship satisfying those conditions, then narrowing the choices to an acceptable set of parameters.

3. Summary of Results We tested the proposed method on four different problems: a homogenous half-space, two different lay-ered models over half-spaces, and a heterogenous domain. For the former three cases we used synthetic solutions as the observations and then found the parameters using the proposed procedure having trained the ANN with other solutions for random parameters not including those for the synthetic observa-tions. For the heterogeneous domain we considered two cases, one with synthetic observations and an-other with real observations from the Mw 5.4 2008 ChinoHills earthquake. In all cases we were able to identify the parameters, though for the most realistic of cases an additional optimization process was needed to narrow the standard deviation. (a)

(c)

(b)

Figure 3. (a) Training data is generated based on 1000 random combination of a, b and c. (b) Feedforward multi-layer perceptron neural networks used in the study. Hidden layers use tangent sigmoid and output layer uses linear activation functions. Dots used to simplify the structure for presenting purposes. (c) Some of stations in a heteroge-neous domain that pass the criteria, where the cyan line in synthetic represent the closest available data in training dataset that leads to optimizing the process towards finding the best possible Qs-Vs parameters.

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E. References Anderson, J. G. (2004). Quantitative measure of the goodness-of-fit of synthetic seismograms, Proc. 13th

World Conf. on Earthquake Eng., Vancouver, British Columbia, Int. Assoc. Earthquake Eng. Paper 243.

Bielak, J., R. W. Graves, K. B. Olsen, R. Taborda, L. Ramírez-Guzmán, S. M. Day, G. P. Ely, D. Roten, T. H. Jordan, et al. (2010). The ShakeOut earthquake scenario: Verification of three simulation sets, Geophys. J. Int. 180, no. 1, 375–404, doi: 10.1111/j.1365-246X.2009.04417.x.

Brocher TM (2005) Compressional and shear wave velocity versus depth in the San Francisco bay area, California: Rules for USGS Bay Area Velocity Model 05.0.0. Tech. Rep. OFR-2005-1317, U.S. Geo-logical Survey, URL http://pubs.usgs.gov/of/2005/1317/.

Brocher TM (2008) Compressional and shear-wave velocity versus depth relations for common rock types in northern California. Bull Seismol Soc Am 98(2):950{968, DOI 10.1785/0120060403.

Burks, L. S., and J. W. Baker (2014). Validation of ground-motion simulations through simple proxies for the response of engineered systems, Bull. Seismol. Soc. Am. 104, no. 4, 1930–1946, doi: 10.1785/0120130276.

Chaljub, E., P. Moczo, S. Tsuno, P.-Y. Bard, J. Kristek, M. Kaser, M. Stupazzini, and M. Kristekova (2010). Quantitative comparison of four numerical predictions of 3D ground motion in the Grenoble Valley, France, Bull. Seismol. Soc. Am. 100, no. 4, 1427–1455, doi: 10.1785/0120090052.

Graves RW (2008) The seismic response of the San Bernardino basin region during the 2001 Big Bear lake earthquake. Bull Seismol Soc Am 98(1):241–252, DOI 10.1785/0120070013.

Guidotti, R., M. Stupazzini, C. Smerzini, R. Paolucci, and P. Ramieri (2011). Numerical study on the role of basin geometry and kinematic seismic source in 3D ground motion simulation of the 22 February 2011 Mw 6.2 Christchurch earthquake, Seismol. Res. Lett. 82, no. 6, 767–782, doi: 10.1785/gssrl.82.6.767.

Kristeková, M., J. Kristek, and P. Moczo (2009). Time-frequency misfit and goodness-of-fit criteria for quantitative comparison of time signals, Geophys. J. Int. 178, no. 2, 813–825, doi: 10.1111/j.1365-246X.2009.04177.x.

Kristeková, M., J. Kristek, P. Moczo, and S. M. Day (2006). Misfit criteria for quantitative comparison of seismograms, Bull. Seismol. Soc. Am. 96, no. 5, 1836–1850, doi: 10.1785/0120060012.

Maufroy, E., E. Chaljub, F. Hollender, J. Kristek, P. Moczo, P. Klin, E. Priolo, A. Iwaki, T. Iwata, V. Etienne, et al. (2015). Earthquake ground motion in the Mygdonian basin, Greece: The E2VP verifi-cation and validation of 3D numerical simulation up to 4 Hz, Bull. Seismol. Soc. Am. 105, no. 3, 1398–1418, doi: 10.1785/0120140228.

Olsen KB, Day SM, Bradley CR (2003) Estimation of Q for long-period (> 2 sec) waves in the Los Ange-les basins. Bull. Seismol. Soc. Am. 93(2):627–638, DOI 10.1785/0120020135.

Olsen, K. B., and J. E. Mayhew (2010). Goodness-of-fit criteria for broadband synthetic seismograms, with application to the 2008 Mw 5.4 Chino Hills, California, earthquake, Seismol. Res. Lett. 81, no. 5, 715–723, doi: 10.1785/gssrl.81.5.715.

Taborda, R., and J. Bielak (2013). Ground-motion simulation and validation of the 2008 Chino Hills, Cali-fornia, earthquake, Bull. Seismol. Soc. Am. 103, no. 1, 131–156, doi: 10.1785/0120110325.

Taborda, R., and J. Bielak (2014). Ground-motion simulation and validation of the 2008 Chino Hills, Cali-fornia, earthquake using different velocity models, Bull. Seismol. Soc. Am. 104, no. 4, 1876–1898, doi: 10.1785/0120130266.

Taborda, R., S. Azizzadeh-Roodpish, N. Khoshnevis, and K. Cheng (2016). Evaluation of the southern California seismic velocity models through simulation of recorded events, Geophys. J. Int. 205, no. 3, 1342–1364, doi: 10.1093/gji/ggw085.