Accelerating Time-Reversal Imaging with Neural Operators for Real-time Earthquake Locations Hongyu Sun1 Yan Yang1 Kamyar Azizzadenesheli2 Robert W. Clayton1

2025-04-24 0 0 3.28MB 28 页 10玖币

侵权投诉

Accelerating Time-Reversal Imaging with Neural

Operators for Real-time Earthquake Locations

Hongyu Sun ∗1, Yan Yang1, Kamyar Azizzadenesheli2, Robert W. Clayton1,

and Zachary E. Ross1

1Seismological Laboratory, California Institute of Technology, 1200 E. California Blvd.,

Pasadena, CA 91125

2Nvidia Corporation, 2788 San Tomas Expressway, Santa Clara, CA 95051

October 2022

Abstract

Earthquake hypocenters form the basis for a wide array of seismological analyses.

Pick-based earthquake location workﬂows rely on the accuracy of phase pickers and

may be biased when dealing with complex earthquake sequences in heterogeneous me-

dia. Time-reversal imaging of passive seismic sources with the cross-correlation imaging

condition has potential for earthquake location with high accuracy and high resolution,

but carries a large computational cost. Here we present an alternative deep-learning

approach for earthquake location by combining the beneﬁts of neural operators for wave

propagation and time reversal imaging with multi-station waveform recordings. A U-

shaped neural operator is trained to propagate seismic waves with various source time

functions and thus can predict a backpropagated waveﬁeld for each station in negligible

time. These waveﬁelds can either be stacked or correlated to locate earthquakes from

the resulting source images. Compared with other waveform-based deep-learning loca-

tion methods, time reversal imaging accounts for physical laws of wave propagation and

is expected to achieve accurate earthquake location. We demonstrate the method with

the 2D acoustic wave equation on both synthetic and ﬁeld data. The results show that

our method can eﬃciently obtain high resolution and high accuracy correlation-based

time reversal imaging of earthquake sources. Moreover, our approach is adaptable to

the number and geometry of seismic stations, which opens new strategies for real-time

earthquake location and monitoring with dense seismic networks.

keywords: Time reversal imaging, neural operators, earthquake location, wave propagation,

correlation

∗Corresponding author: hongyu-sun@outlook.com

arXiv:2210.06636v1 [physics.geo-ph] 13 Oct 2022

1 Introduction

Source locations are important for earthquake monitoring and early warning (Zhang et al.,

2021), understanding faulting properties and initiation of earthquake sequences (Ross et al.,

2020), and hazard assessment of induced seismicity during industrial injection (Lin et al.,

2020). Routine earthquake location workﬂows usually include phase detection, picking, as-

sociation, and location. With such a sequentially-staged workﬂow, the resulting source

locations heavily depend on the initial picking results. However, picking is usually done on

seismograms from each station separately and may have diﬃculty when the ﬁrst arrivals

overlap with the coda of a larger event. Furthermore, only P and S arrivals are used in

the estimation of earthquake locations, and converted waves that are common in complex

media do not contribute to the workﬂow. Instead, phase pickers may erroneously consider

converted waves as ﬁrst arrivals and introduce errors to the location.

With the availability of dense seismic networks and distributed acoustic sensing, we

can directly locate earthquake sources from full waveforms with time reversal imaging and

beneﬁt from the coherency of phases between stations. With full waveforms of seismograms

instead of picked arrivals, time-reversal imaging has shown its power for revealing earthquake

locations and source mechanisms at local (Zhu et al., 2019), regional (McMechan et al., 1985;

Larmat et al., 2008), and global (Larmat et al., 2006) scales. By backpropagating time-

reversed seismograms at receiver locations, seismic-wave energies will refocus at the origins

of seismic events, provided with reasonably accurate velocity models and assumptions of non

dissipative media (McMechan, 1982; Gajewski and Tessmer, 2005; Artman et al., 2010). We

can distinguish locations and estimate their origin time by detecting the maximum intensity

or reasonable focusing in the resulting source images.

The demanding computational cost and sometimes low spatial imaging resolution hinder

the universal application of time reversal imaging from earthquake location. Conventional

time reversal imaging methods simultaneously backpropagate entire seismograms and thus

result in source images by implicitly stacking waveﬁelds at all stations. However, such result-

ing source imaging generally suﬀers from low imaging resolution, which makes it challenging

to search for source locations from records with low signal-to-noise ratio (SNR). Most re-

cently, Sun et al. (2015); Nakata and Beroza (2016) propose a cross-correlation imaging

method to enhance the spatial resolution of time-reversal source imaging by individually ex-

trapolating waveﬁelds at each station and then cross-correlating these waveﬁelds. However,

the computational cost increased by this method is proportional to the number of stations,

which imposes challenges for real-time earthquake location with a dense seismic network. To

reduce the computational cost of waveﬁeld extrapolation, researchers have grouped several

receivers and performed backward wave propagation for each group before cross-correlation

(Zhu et al., 2019; Lin et al., 2020; Wu et al., 2022); however, this comes at a cost of reduced

image resolution, and the choice of grouping strategy only depends on experience and is not

straightforward (Bai et al., 2022). In addition, Baker et al. (2005) directly image earthquake

source locations with Kirchhoﬀ reconstruction of ground motions. Li et al. (2020a) approx-

imate wave-equation solutions with simpliﬁed Gaussian beam for eﬃcient source location

with time reversal methods.

Deep learning has become state of the art for most earthquake monitoring tasks, leading

to advances in our knowledge about the Earth (Ross et al., 2020; Li et al., 2021; Yang et al.,

2022a). On one hand, inspired by traditional pick-based earthquake location workﬂows, deep

learning has been used in each step of the sequential workﬂow (Zhang et al., 2022), including

earthquake detection (Ross et al., 2018a), phase picking (Ross et al., 2018b; Zhu and Beroza,

2019), phase association (Ross et al., 2019; Zhu et al., 2022), and location (Smith et al., 2022).

On the other hand, various deep learning methods are developed to infer earthquake locations

directly from continuous waveforms (van den Ende and Ampuero, 2020; Zhang et al., 2021;

M¨unchmeyer et al., 2021; Shen and Shen, 2021). By introducing time reversal imaging to

deep learning, we propose to combine physical laws of wave propagation with deep neural

operators and to determine source locations directly from waveforms recorded at all stations

in a seismic network with relatively high accuracy.

In this work, we propose to achieve time-reversal imaging with neural operators for real-

time earthquake location. Neural operators (Kovachki et al., 2021) are a generalization of

neural networks to learn operators that map between inﬁnite dimensional function spaces.

It has been used to solve various partial diﬀerential equations (PDEs) with state-of-the-

art eﬃciency (Li et al., 2020b). In seismology, Yang et al. (2021, 2022b) used Fourier

neural operators (Li et al., 2020b) to solve the acoustic and elastic wave equations in 2D

and demonstrate their ability to accelerate forward modeling for full-waveform inversion.

Here, we train a U-shaped neural operator (Rahman et al., 2022) with random source time

functions. This allows for the neural operator to learn backward wave propagation and

predict time reversed waveﬁelds with negligible compute time. The predicted waveﬁelds

can be either stacked or correlated; they result in a source image that can be searched for

the earthquake location. We test the neural operators on both a synthetic dataset and a

real dataset taken from the 2016 IRIS community waveﬁeld experiment in Oklahoma (Sweet

et al., 2018). We ﬁnd that time reversal modeling with the trained neural operator enables

us to locate earthquake locations from correlation-based source images with high resolution

and eﬃciency. We use the 2D acoustic wave equations to illustrate our method but it is

straightforward to extend the method to elastic and 3D cases.

2 Method

We ﬁrst brieﬂy review time-reversal imaging of seismic sources. Then, we introduce the basics

of neural operators and propose to achieve time reversal modeling by training a U-shaped

neural operator for wave propagation with various source time functions. Our approach to

synthesizing a training dataset for waveﬁeld backpropagation is also detailed.

2.1 Time reversal imaging

The principle of time reversal states that time reversed waveﬁelds will refocus to original

source locations during backpropagation regardless of the complexity of the propagation

medium since the acoustic wave equation in a nondissipative and heterogeneous medium is

invariant for time reversal (Fink, 2006). Time reversal imaging with seismic data d(xs,xr, t)

emitted from passive sources xsand observed at stations xrconsists of the following steps:

•Reversing seismograms in time with d(xs,xr, T −t) = d(xs,xr, t) where Tdenotes the

time window;

•With a predetermined velocity model, solving the wave equation with the reversed

records d(xr, T −t) taken as new “source time functions” excited at the receiver loca-

tions;

•Applying imaging conditions to the backpropagated waveﬁelds Ri,(i= 1, ..., N) where

Nis the number of receivers;

•Searching for the spatial and temporal locations of sources xsin the imaging result

I(x, t).

Conventional time reversal imaging employs the summation operator as an imaging con-

dition:

I(x, t) =

n=1

Ri(x, t).(1)

By searching for maximum intensities or best focusing of sources, we can obtain source images

I(x, t0) where t0denotes the origin time of the seismic event. The summation is in practice

implicit since it is equivalent to backpropagating time-reversed records d(xr, T −t) at all

receivers at once. Thus, only one simulation is required with the entire dataset. However,

it surfers from low imaging resolution. Physical artifacts due to incoming waveﬁelds from

other sources and outgoing waveﬁelds from focused sources make it challenging to search for

source locations from low SNR dataset (Nakata and Beroza, 2016). By contrast, correlation-

based time reversal imaging considers one record at each receiver as an independent source

for backpropagation, and replaces the summation operator by multiplication:

I(x, t) =

n=1

Ri(x, t).(2)

The correlation imaging condition greatly improves the imaging quality by suppressing ar-

tifacts in conventional time reversal imaging, as they are supposed to be zero-valued in the

resulting image. Ideally, hypocenters would only appear in I(x, t) when all the backpropa-

gated waveﬁelds coincide in both space and time. It turns out that this imaging condition

is less sensitive to the frequency components of seismic data. However, treating each station

individually is computationally demanding and thus challenging for real-time monitoring of

seismicity.

2.2 Neural operators and U-shaped architecture

Operator learning is an emerging machine learning paradigm that aims to learn mappings

between function spaces. Recently, Li et al. (2020c); Kovachki et al. (2021) proposed neural

operators as data-driven grid-independent PDE solvers. The structure of a one-layer neural

operator shares the formula of the general solution for linear PDEs parameterized by m:

u(x) = ZGm(x,y)f(y)dy.(3)

Figure 1: U-shaped neural operator for time reversal modeling. The architecture contains L

Fourier neural layers: Gi, i = 1, ..., L.Pand Qare up- and down-projections parameterized

by neural networks, respectively. The input is a source time function f(x, t) sampled from a

Gaussian random ﬁeld. The output is the waveﬁeld simulated with its input as source time

function on a predetermined velocity model. The velocity model is not an implicit input but

required for simulating a training dataset with a conventional PDE solver. For the 2D wave

equation, both input and output are 3D volumes with equivalent number of grid points (2D

space and 1D time).

In seismology, Gdenotes the Green’s function of the wave equation, depending on m(i.e.

velocities discretized at x), and fis the source time function. Likewise, neural operators use

the following integral kernel operator as a basic form:

u(x)=(KV )(x) = ZK(x,y)V(y)dy,(4)

where Kdenotes kernel convolution. By sequentially stacking Llinear kernel operators

and introducing Lnon-linear activation functions σ, we can build a neural operator Nθ

parameterized by θto estimate the solution of PDEs:

Nθ:= Q◦σL(WL+KL)◦... ◦σ1(W1+K1)◦P, (5)

where Wdenotes a linear transform. Pis an encoder lifting the input to a high dimensional

channel space. Qis a decoder projecting the representation back to the original space.

Figure 1 shows the architecture of a U-shaped neural operator (UNO; Rahman et al.,

2022) that we use in this study. By replacing the convolutional layers in the U-net (Ron-

neberger et al., 2015) with Fourier neural operator layers (Li et al., 2020b), UNO improves

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

AcceleratingTime-ReversalImagingwithNeuralOperatorsforReal-timeEarthquakeLocationsHongyuSun*1,YanYang1,KamyarAzizzadenesheli2,RobertW.Clayton1,andZacharyE.Ross11SeismologicalLaboratory,CaliforniaInstituteofTechnology,1200E.CaliforniaBlvd.,Pasadena,CA911252NvidiaCorporation,2788SanTomasExpressway,San...

展开>> 收起<<

Accelerating Time-Reversal Imaging with Neural Operators for Real-time Earthquake Locations Hongyu Sun1 Yan Yang1 Kamyar Azizzadenesheli2 Robert W. Clayton1.pdf

共28页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Accelerating Time-Reversal Imaging with Neural Operators for Real-time Earthquake Locations Hongyu Sun1 Yan Yang1 Kamyar Azizzadenesheli2 Robert W. Clayton1

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: