DAS for 2D MASW Imaging A Case Study on the Benefits of Flexible Sub-Array Processing Michael B. S. Yust1 Brady R. Cox2 Joseph P. Vantassel3 and Peter G. Hubbard4

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DAS for 2D MASW Imaging: A Case Study on the Benefits

of Flexible Sub-Array Processing

Michael B. S. Yust1*, Brady R. Cox2, Joseph P. Vantassel3, and Peter G. Hubbard4

(1) The University of Texas at Austin

(2) Utah State University

(3) Virginia Tech

(4) University of California, Berkeley

*corresponding author: yustm@utexas.edu

Abstract

Distributed acoustic sensing (DAS) is a relatively new technology for recording stress wave

propagation, with promising applications in both engineering and geophysics. DAS’s ability to

simultaneously collect high spatial resolution data (e.g., 1-m channel separation) over long arrays (e.g.,

kilometers) suggests that it is especially well suited for near-surface imaging applications such as 2D

MASW (multi-channel analysis of surface waves). 2D MASW aims to produce a pseudo-2D cross-section

of shear-wave velocity (VS) for the purpose of identifying and characterizing subsurface layering and

anomalies. These pseudo-2D VS cross-sections are produced by spatially interpolating numerous 1D VS

profiles extracted from overlapping sub-arrays along the testing alignment. When using traditional seismic

equipment (e.g., geophones and 24-channel seismographs), these sub-arrays are typically collected in a roll-

along configuration, where the equipment is continuously moved along the alignment at some

predetermined sub-array interval. In contrast, DAS does not suffer from the same limitations, as data from

all shot locations are simultaneously recorded along the entire length of the DAS array at a constant channel

separation. This alleviates the requirements to pre-determine sub-array length and sub-array interval during

the data acquisition stage, and allows for multiple sub-array geometries to be investigated during the

processing stage. The present study utilizes DAS data collected at high spatial resolution to evaluate the

effects of sub-array length on 2D MASW results at a single, well-characterized field test site. We organize

the DAS waveforms into multiple sets of overlapping MASW sub-arrays of differing lengths, ranging from

11 m to 47 m, allowing for direct comparison of the derived pseudo-2D VS results at the same site. We

show that the length of the individual MASW sub-arrays has a significant effect on the resulting VS cross-

sections. In particular, there is a tradeoff between long sub-arrays that improve dispersion data quality and

allow deeper characterization and shorter sub-arrays that improve lateral resolution. We also show that sub-

array length has a significant impact on the resolved location of large impedance contrasts at our study site

and evaluate those locations compared to invasive testing. Our results suggest that a priori information

should be used, when possible, to select the optimal sub-array length for 2D MASW analyses to address

project-specific goals. If a priori information is not available, the analysts may need to consider multiple

sub-array geometries, as is made possible by DAS, to properly evaluate the uncertainty of 2D MASW

results. This study demonstrates that DAS is capable of collecting data for 2D MASW in a manner that is

efficient, flexible, and pragmatic.

Introduction

Surface wave methods are powerful tools for non-invasive seismic site characterization. One of the

most popular testing methods is the multichannel analysis of surface waves (MASW), capable of producing

a 1D shear-wave velocity (VS) model of the subsurface (Park et al. 1999, Foti 2000). MASW is traditionally

performed using a linear array of geophones and one or more 24-channel seismographs to record surface

waves generated by an active source (i.e., hammer, weight drop, or vibroseis shaker) located off one or both

ends of the array. As the number of geophones is often fixed by the availability of equipment, the analyst

must balance the finer vertical layer resolution provided by smaller receiver spacings with the greater

characterization depth provided by a longer array (Foti et al. 2018). Soon after the introduction of MASW,

engineers began to explore how this new method could be used to characterize 2D variations of subsurface

VS (Miller et al. 1999). Xia et al. (2000) proposed the use of MASW to construct pseudo-2D VS cross-

sections by combining multiple 1D VS profiles resulting from multiple MASW datasets collected along a

common alignment. This approach came to be known as 2D MASW.

2D MASW surveys typically use the roll-along method (Mayne 1962), with 24 or 48 geophones

mounted on a land streamer system at a fixed receiver spacing. The number of geophones and the choice

of receiver spacing pre-determines the length of the sub-array used during data acquisition and processing.

The land streamer is pulled behind a vehicle, allowing the geophone array to be moved along the survey

alignment and incrementally stopped at a predetermined horizontal distance called the sub-array interval.

The sub-array interval is typically set equal to some portion of the total sub-array length (e.g., 1/4 or 1/3),

such that there is significant spatial overlap between adjacent sub-arrays. The sub-array interval also

determines the horizontal distance between the 1D VS profiles that will ultimately be interpolated to obtain

the pseudo-2D VS image. Typically, a source such as a weight drop is attached to the towing vehicle to

generate the active shots. In the interest of rapid data acquisition, generally only one shot location with a

fixed offset is used for each MASW sub-survey Even when data is collected using larger, mobile or

stationary geophone arrays, the traces are often reorganized to mimic the roll-along method with a single

shot location (Park & Miller 2005a, 2005b, Thitimakorn et al. 2005).

The 2D MASW process has been used successfully on a variety of near-surface imaging tasks. In

their initial paper, Xia et al. (2000) were able to successfully identify multiple subsurface features, including

a bedrock channel in Olathe, Kansas, which was later confirmed with drilling, and a known steam tunnel at

the University of Kansas. Thitimakorn et al. (2005) utilized 2D MASW to survey a 1950 m segment of

Interstate 70 in St. Louis, Missouri. They used 12 4.5 Hz vertical geophones at a 3-m spacing with 12-

channel sub-arrays (33 m) to construct a pseudo-2D VS cross-section with a sub-array interval of 12 m

between 1D VS profiles. Based on this 1950-m-long cross-section, Thitimakorn et al. (2005) were able to

identify depths to bedrock ranging from 6 m to 13.4 m, which agreed well with 19 boreholes drilled along

the testing alignment. Park & Miller (2005a, 2005b) performed 2D MASW at 84 sites near Lawton,

Oklahoma and 10 sites in Kansas to check for voids or other weak areas. They performed multiple 2D

MASW surveys at each location with three parallel alignments and used a fourth alignment perpendicular

to and bisecting the other three to ensure the site was characterized as thoroughly as possible. They used 48

stationary geophones at a 1.22-m spacing which were recompiled to simulate 24-channel roll-along

acquisition with a 1.22-m sub-array interval. Mohamed et al. (2013) performed 24 collocated P-wave

refraction and 2D MASW surveys at a site outside of Cairo, Egypt. They used 13 sub-arrays consisting of

24 geophones with 1-m spacings and a sub-array interval of 4 m to collect data at 24 sites. Mohamed et al.

(2013) found that the 2D MASW surveys were more effective than P-wave refraction at detecting near-

surface anomalies and low-velocity layers. The 2D MASW cross-sections identified low-velocity regions

that, when boreholes were drilled at the site, were confirmed to correspond to claystone layers experiencing

swelling due to nearby water sources, including irrigation and a swimming pool. Ismail et al. (2014)

performed both 2D MASW and shear-wave reflection profiling along two alignments in southern Illinois

totaling 3.7 km. They used sub-arrays consisting of 48 geophones with 1.5-m spacings and a sub-array

interval of 7.5 m. They were able to map the depth to bedrock, including identification of near-surface

faults, with the results from both methods agreeing well. Ismail et al. (2014) noted that, while the reflection

survey was better able to resolve thin near-surface layering in the unconsolidated sediments above bedrock,

the 2D MASW surveys provided better estimates of VS and were easier to perform. While not exhaustive

by any means, the above-cited studies are indicative of successful applications of 2D MASW using

traditional equipment and the standard roll-along method with a single, predetermined survey geometry

(i.e., number and spacing of geophones, sub-array length, sub-array offset interval, shot location, etc.).

However, despite its successful use in many projects, the potential of 2D MASW is still limited by practical

constraints which require the analyst to determine that geometry prior to the data acquisition stage. This

significantly reduces the options available during the processing stage and can have a significant impact on

the survey results.

Multiple studies of synthetic data (Park 2005, Mi et al. 2017, Crocker et al. 2021, Arslan et al.

2021) have found that array geometry, especially array length, has a significant impact on the vertical and

horizontal resolution of 2D MASW and its ability to accurately resolve layer boundaries and VS anomalies

in the subsurface. Additionally, Yust (2018) demonstrated that using only a single shot location can result

in misinterpretation of dispersion data if significant higher-mode energy is present. While using multiple

shot locations helps minimize the risk of mode misidentification, it is not easy to implement using the roll-

along method with traditional equipment. Thus, 2D MASW could be improved if a single, predetermined

survey geometry did not have to be specified at the data acquisition stage, which would allow for greater

flexibility at the data processing stage. This study aims to demonstrate how distributed acoustic sensing

(DAS) can be used to collect field data for 2D MASW without the restrictions of traditional geophone

arrays, allowing for greater flexibility in data acquisition and processing. Specifically, we examine how

changing the length of each MASW sub-array, which is trivial for 2D MASW data collected using DAS,

affects the resulting VS cross-sections at a well-characterized site. However, before the testing performed

in this study can be fully discussed, it is important to first cover additional background information about

how traditional 2D MASW testing is performed, such that modifications to the traditional approach

discussed later in the paper can be better understood.

Traditional 2D MASW

Traditional MASW testing consists of three main steps: acquisition of surface-wave data in the

field, processing the collected records to extract experimental dispersion data, and inverting the

experimental dispersion data to produce a 1D subsurface VS model (Foti et al. 2015). The inverted 1D VS

model is typically assumed to best represent the 1D layering and material properties beneath the center of

the MASW array. However, due to the nature of the dispersion processing and inversion stages, which are

inherently 1D, the VS profile represents a lateral average of all the materials beneath the array. 2D MASW

follows these same three steps and adds a fourth one: combining multiple 1D VS profiles to create a pseudo-

2D velocity cross-section along the testing alignment. Therefore, 2D MASW requires many adjacent

MASW surveys to produce the 1D VS profiles that allow for pseudo-2D interpolation. Due to the large

amount of data that needs to be collected (e.g., hundreds of shot records), the focus when performing data

acquisition in the field for 2D MASW analysis is generally on efficiency. Hence, the roll-along method

described above is typically utilized.

As the processing and inversion of 2D MASW data for each sub-array follows that of MASW, the

following discussion will focus on only those aspects that are of particular importance. The interested reader

is referred to the following references for more information (Park et al. 1998, Park et al. 2007, Foti et al.

2015, Foti et al. 2018, Vantassel & Cox 2022). Dispersion processing of surface wave data can be performed

on the raw recorded wavefield or, if using a sweeping source, the wavefield cross-correlated with the source

(Xia et al., 2000). The recordings can then be transformed to the frequency-wavenumber domain using

various wavefield transformations (e.g., Nolet & Panza 1976, McMechan & Yedlin 1981, Park et al. 1998,

Zywicki 1999, Xia et al. 2007, Luo et al. 2009a). For many datasets, the referenced transformations produce

similar, although typically not identical, estimates of surface wave dispersion (Foti et al. 2015, Rahimi et

al. 2021, Vantassel & Cox 2022). As such the MASW transform can be considered a source of dispersion

uncertainty (Vantassel & Cox 2022). If multiple shot locations are used for each sub-array, differences in

surface wave dispersion may also energy, these differences can also be quantified as part of the site-specific

dispersion uncertainty (Cox & Wood 2011, Vantassel & Cox 2022). However, due to the additional time

and effort required to use multiple transformations and multiple shot offsets, 2D MASW acquisitions

typically use a single transformation and a single shot location and do not quantify dispersion uncertainty.

Once the experimental dispersion data has been obtained through wavefield processing a model of

the subsurface is inferred through inversion (i.e., solving an inverse problem). Briefly, the inversion seeks

to find the 1D ground model whose theoretical dispersion data best fits the experimental dispersion data

measured in the field (Park et al. 1998). The 1D ground model in the inversion is defined by a set number

of layers each defined by their thickness, mass density, compression-wave velocity, and VS. The inverse

problem is challenging as it is ill-posed, non-linear, and mixed-determined, with no guarantee of a unique

solution (Foti et al. 2015). To find the ground models whose theoretical dispersion best fits the experimental

data there are two main search approaches: gradient-based and gradient-free. Gradient-based methods, also

referred to as local-search methods, rely on an initial starting model and the gradients of the misfit function

(typically an L2 norm) with respect to each of model’s parameter to converge to a local minimum through

an iterative process (Socco et al. 2010). Gradient-free methods, also referred to as global-search methods,

instead rely on sampling the model solution space to find the model(s) that best fit the data. These searches

can be purely random (earlier samplings do not affect later samplings) or adaptive (later samplings learn

from previous samplings). As local-search methods are faster than global-search methods (i.e., they

typically require the solution of fewer forward problems) they have been used in the vast majority of

previous 2D MASW studies (Foti et al. 2018). However, local-searches are known to be less rigorous then

global-search and as a result are susceptible to becoming stuck in sub-optimal solutions (i.e., local minima

and saddle points in the space of the inversion objective function) and should be used cautiously in

environments where an accurate starting model cannot be selected a priori (Socco et al. 2010).

In addition to the optimization algorithm, the inversion is also strongly influenced by the

inversion’s parameterization (i.e., the number of assumed layers and the upper and lower limits of each

parameter). Most 2D MASW studies consider only a single layering parameterization consisting of many

layers with fixed thickness. These layers are often of uniform thickness, but may increase in thickness with

depth (Xia et al. 2000). While the use of many layers may increase the ability of the inversion algorithm to

fit the target dispersion data, it can also result in unrealistic VS profiles with large changes in velocity over

short depth intervals, especially when velocity reversals are allowed at all layer boundaries (Song et al.

2020; Crocker et al. 2021). To address these issues, parameterization methods such as the layering ratio

(Cox & Teague 2016) and layering by number (Vantassel & Cox 2021) approaches can be used to

systematically investigate the sensitivity of the inversion to the choice of layering parameterization.

Once the inversion process has produced a 1D VS profile (or several 1D VS profiles if different

inversion layering parameterizations are considered and uncertainty is acknowledged) for each MASW sub-

array, those profiles can then be combined into a pseudo-2D VS cross-section. This is done by placing each

1D profile at the lateral position corresponding to the middle of the respective MASW sub-array. The VS

values between those positions can then be interpolated (Xia et al. 2000). Luo et al. (2009b) examined the

assumption that the 1D VS profiles were located at the midpoint of the MASW sub-array and found it to be

reasonable. They also found that the dispersion data extracted from MASW testing is primarily affected by

the subsurface conditions under the receiver spread itself and not under the space between the receivers and

the shot location. As the primary goal of most 2D MASW surveys is to identify subsurface features such as

low stiffness zones and layers with high impedance contrast, the lateral resolution of the pseudo-2D cross-

section is a critical part of the analysis. Park (2005) examined the impact of sub-array length and sub-array

interval using synthetically generated waveforms. Park found that the array length should be balanced

between maximizing length, to improve dispersion data quality and maximize characterization depth, and

minimizing length to reduce the amount of spatial averaging that occurs within each sub-array. This spatial

averaging caused smearing of the subsurface details, resulting in reduced lateral resolution for longer arrays.

Park (2005) also found that the sub-array interval should be kept below the sub-array length and that there

should be some overlap between successive sub-arrays. Mi et al. (2017), Arslan et al. (2021), and Crocker

et al. (2021) evaluated the ability of 2D MASW to detect anomalous structures within the subsurface. Mi

et al. (2017) analyzed a combination of synthetic and field data sets and concluded that anomalous velocities

could not be accurately resolved for features shorter than the sub-array length. Arslan et al. (2021) and

Crocker et al. (2021) utilized over 3,000 synthetic data sets to examine the detection and resolution abilities

of MASW depending on anomaly size and depth. They found that anomalies less than half the length of the

sub-array were unlikely to be detected. They also cautioned against blind application of 2D MASW to

detect anomalies due to the inherently 1D nature of all surface wave methods. Despite the important

influence of sub-array length on characterization depth, dispersion data quality, and lateral resolution, its

effects on 2D MASW results have not been extensively studied. Due to the impracticality of adjusting

geophone sub-array lengths in the field using traditional MASW equipment, these studies have largely been

limited to synthetic data sets. In response, this study aims to examine the effects (i.e., data quality, vertical

and lateral resolution of layer boundaries, etc.) of sub-array length by comparing pseudo-2D VS cross-

sections of a single, well-characterized field site using DAS with ground truth obtained from invasive

methods.

Distributed Acoustic Sensing for 1D and 2D MASW

DAS is a relatively new technology for recording stress wave propagation, with promising

applications in both engineering and geophysics (Daley et al. 2013, Lindsey et al. 2017, Spikes et al. 2019,

Hubbard et al. 2021a). DAS uses light propagated through fiber-optic cables to collect data over very large

scales (e.g., kilometers) while still maintaining very high spatial resolution (e.g., meters), a feat that is not

possible with traditional sensing methods such as geophone arrays (Soga & Luo 2018). This is

accomplished by measuring the change in length of sections of fiber-optic cable using backscatter

interferometry (Hartog 2018). The DAS array itself has two major components; the interrogator unit (IU)

which produces the source light and measures backscatter, and the fiber-optic cable which carries the light

as a waveguide and acts as a distributed interferometer. As light pulses are sent down the cable by the IU,

some of the light reflects back toward the IU in the form of Rayleigh backscatter (Nakazawa 1983). In

quantitative DAS, backscattered light originating from two locations along a sensing cable are compared to

determine the change in length of the cable between them. The distance between these reflection points is

set by the IU and is known as the gauge length. The change in optical phase between two backscatter sources

locations is used to calculate the change in length between those points and, by extension, the strain in the

cable (Hubbard et al. 2022). The fiber-optic cable acts as a linear array of sensors where each gauge length

is a sensor, referred to as a channel. The cable can be either laid across the ground surface (Spikes et al.

2019) or buried to improve coupling with the soil (Galan-Comas 2015, Vantassel et al. 2022). Importantly,

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DASfor2DMASWImaging:ACaseStudyontheBenefitsofFlexibleSub-ArrayProcessingMichaelB.S.Yust1*,BradyR.Cox2,JosephP.Vantassel3,andPeterG.Hubbard4(1)TheUniversityofTexasatAustin(2)UtahStateUniversity(3)VirginiaTech(4)UniversityofCalifornia,Berkeley*correspondingauthor:yustm@utexas.eduAbstractDistributedaco...

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DAS for 2D MASW Imaging A Case Study on the Benefits of Flexible Sub-Array Processing Michael B. S. Yust1 Brady R. Cox2 Joseph P. Vantassel3 and Peter G. Hubbard4

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