Soil Dynamics and Earthquake Engineering 42 (2012) 95–104

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Soil Dynamics and Earthquake Engineering

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journal homepage: www.elsevier.com/locate/soildyn

Automatic picking in the refraction microtremor (ReMi) techniqueusing morphology and color processing

J.J. Galiana-Merino a,b,n, F. Ortiz-Zamora a,b, J.L. Rosa-Herranz a,b

a Departamento de Fısica, Ingenierıa de Sistemas y Teorıa de la Senal, Universidad de Alicante, P.O. Box 99, E-03080 Alicante, Spainb University Institute of Physics Applied to Sciences and Technologies, Universidad de Alicante, P.O. Box 99, E-03080 Alicante, Spain

a r t i c l e i n f o

Article history:

Received 16 May 2011

Received in revised form

10 March 2012

Accepted 27 May 2012Available online 2 July 2012

61/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.soildyn.2012.05.024

esponding author at: Departamento de Fısi

e la Senal, Universidad de Alicante, P.O. Box

4 965909636; fax: þ34 965909750.

ail address: juanjo@dfists.ua.es (J.J. Galiana-M

a b s t r a c t

The refraction-microtremor (ReMi) technique is one of the array methods widely used for characteriz-

ing soils by the estimation of the dispersion curve (slowness versus frequency of the Rayleigh waves).

This technique provides a slowness–frequency image where the dispersion curve has to be manually

picked by an expert geophysicist. Therefore, this is always a subjective process based on the visual

perception of the analyst and without any objective measure of the possible deviation or error of the

selected picks. In this paper, a new automatic picking approach based on color processing and

morphology is presented. The mean dispersion curve is obtained, but also some indicators (standard

deviation and weight) of the reliability of the estimated slowness values. The proposed algorithm has

been tested on images with different features and qualities obtained from 18 sites with different

geological characteristics. For all the analyzed images, the estimated dispersion curves are consistent

with the analyst picks in the corresponding frequency range, even in cases of poor quality images.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Soil characterization is a very important issue from the seismo-logical point of view in order to study the possible earthquakeeffects (site effects). In seismically active areas, the knowledge of thecharacteristics of these soils as well as their spatial distribution is ofgreat interest for land use planning and for civil engineering.Therefore, site effect studies (microzonation) have become animportant part of the seismic risk characterization, and a varietyof geotechnical, geophysical and seismological techniques have beendeveloped and applied over the last years to resolve soil character-istics, such as the shear-wave velocity (Vs), density, etc., of a givensite. Among these properties, the shear-wave velocity is consideredto be the single best indicator of stiffness [1,2].

Techniques based on borehole information and related geo-technical analyses are too expensive and time consuming toestimate Vs profiles in urban areas. This is the main reason whynon-destructive methods are increasingly preferred for the esti-mation of the Vs profiles across a soil structure. In recent years,seismic exploration based on ambient noise recordings hasemerged as a promising method, as the data acquisition processcan be relatively cheap and easily applied in urban areas, and theydo not require artificial seismic sources.

ll rights reserved.

ca, Ingenierıa de Sistemas y

99, E-03080 Alicante, Spain.

erino).

These methods are based on the dispersion property of thesurface waves, which is most sensitive to S-wave variations withdepth [3]. As the wavefield generated by surface seismic sources(e.g. weight drop or ambient noise) mainly consists of surfacewaves, the surface wave dispersion curves may be measured andthe corresponding Vs profiles may also be estimated (e.g. [4,5]).

In this context, the common procedures used for recordingambient noise are based on array measurements, where the recordsare obtained from a set of several sensors recording simultaneously.After that, there are several methods for analyzing this recordeddata and obtaining the surface wave dispersion curves. Some of themost popular and standardized techniques used for calculating theexperimental dispersion curves are the refraction microtremor(ReMi) technique [6], the frequency–wavenumber (f–k) transform[7–11], the spatial autocorrelation (SPAC) analysis [12,13] and theextended spatial autocorrelation (ESAC) analysis [12,14,15].

Once the dispersion curve is obtained, the Vs profile can beestimated through different approaches, such as linearized meth-ods [16,17], simulated annealing [18], genetic algorithms [19] orthe neighborhood algorithm developed by Sambridge [20]. Forany of these approaches, the estimation of the Vs profiles dependslargely on the specificity and accuracy of the obtained surfacewave dispersion curves. Therefore, the calculation of the surfacewave dispersion curves becomes a crucial step in all this process,independently of the techniques used.

In the most of the cases (e.g. f–k, SPAC and ESAC analysis), theselection of the dispersion curves follows a clear mathematicalcriterion that can be accomplished through an automatic process.

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–10496

In the case of the ReMi technique, since the arrays are linearand ambient noise comes from all directions, some noise energywill arrive obliquely and appear on the slowness–frequencyimages as peaks at apparent velocities higher than the real in-line phase velocity [6]. Therefore, apparent phase velocitiespicked on the largest spectral ratio peaks in the slowness–frequency (p–f) domain image may provide artificially highvalues. In this case, an automatic selection of the peaks doesnot provide the appropriate dispersion curve. Thus, an expertgeophysicist must try to manually pick points along the lowerboundary of the maximum amplitude region. Louie [6] andStephenson et al. [21] propose some recommendations to carryout the manual picking process. But, in any way, the manualpicking of one or more points at each frequency is highlydependent on the experience of the geophysicist, with thecorresponding lack of accuracy.

In this work, we have developed a new method for estimatingautomatically the dispersion curve in the p–f domain image byusing color analysis and morphology techniques. The proposedmethod follows the guidelines indicated by the ReMi analysis forpicking the points along the lower boundary of the maximumamplitude region, but it is free from the human subjectivity. Theprocess is carried out for an interval of hue values, obtaining apreliminary set of estimated curves. In this way, the algorithmprovides the mean and the standard deviation of the estimateddispersion curve as a result. Moreover, it also assigns a weight toeach frequency, according to the number of the preliminarycurves used for the estimation of the mean value.

In the next sections, the theoretical background, as well as themethodology will be described. After that, the data analysis andthe main obtained results will be presented in detail, showingdifferent estimated Rayleigh wave dispersion curves and compar-ing the results with the manual picking by an expert geophysicist.

2. Theoretical background

2.1. Refraction microtremor (ReMi) technique

The refraction microtremor (ReMi) method [6] provides aneffective and efficient way to estimate the soil characteristicsalong a linear array. The theoretical basis of the analysis is thep-tau transformation [22], which converts a section of multiple

Artifacts

Dispersion curve tr

Fig. 1. Example of slowness–frequency image obtained through the ReMi technique.

the image.

seismograms (x–t plot) to amplitudes relative to the ray para-meter, p, (slowness or inverse velocity) and the intercept time,tau. Subsequently, the power spectrum in the tau direction iscalculated in order to obtain the slowness–frequency (p–f)representation.

The obtained image is rendered with the frequency plottedalong the horizontal (x) axis, the slowness plotted down thevertical (y) axis and the amplitude of the power spectrumrepresented on basis of a pre-defined RGB color scale. Both axesare linear in frequency and slowness and the origin (0,0) of theimage is in the top left-hand corner. We refer to this image asSRGB(x9Frequency, y9Slowness).

If a large component of the recorded wave field consists ofRayleigh waves, then it is possible to identify their phase-velocitydispersion as a function of frequency from the image produced inthe p–f plane. However, the interpretation of the p–f imagesobtained from the ReMi method is not straightforward.

The maximum values in the image would correspond to theRayleigh phase-velocity dispersion curve if the microtremor wavefield were traveling in the direction of the linear array ofgeophones. However, the recorded noise includes Rayleigh wavespropagating with similar power in many different directions.Since energy oblique to the array travels faster than energyalong the array, the peaks in the slowness–frequency (p–f) imagewould yield higher velocities than the true Rayleigh wave phasevelocity, if enough noise is not traveling in all directions. There-fore, the Rayleigh wave dispersion curve has to be picked along aminimum velocity envelope of the energy. Louie [6] suggests toalso pick upper and lower-bound values to define a range. Theupper boundary is along the energy peaks, and the lowerboundary is where the spectral ratios approach those of uncorre-lated noise

Typical Rayleigh wave dispersion curves run from small slow-ness values at low frequencies, down to the right toward largerslowness values at higher frequencies. Therefore, the first step inpicking the dispersion curve is to identify the normal-modedispersion trend, down to the right (starting from the upper left)and distinct from the aliasing and artifact trends, which are downto the left (Fig. 1). When the p–f image is rendered using theVspect

TM

color palette, as it is used in this work, the dispersioncurve follows the trend of warm colors that goes from the upper-left section of the image to the lower right. The higher spectralratios are plotted as the warmer colors.

end

The dispersion curve trend, the aliasing effects and the artifacts are identified on

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104 97

Once the dispersion curve trend has been identified, we shouldtry to pick the lowest energy bound of the high-amplitude (highspectral ratios) trend. It means to pick following the zone wherethe warmer colors start to blend with the cooler ones (that isthe transition between the olive green and dark blue colors).This stays closest to the real velocities, and below the higherapparent velocities of waves traveling obliquely to the geophonearray. We should avoid to make picks in areas where the warmercolors are absent (lack of high spectral ratio) or where there aregaps in the trend.

2.2. Color space for processing

The evaluation of color information in the image createsadditional new possibilities for solving problems in computervision. The fundamental difference between color images andgray-level images is that in a color space, a color vector (whichgenerally consists of three components) is assigned to every pixelof a color image. Thus, in color image processing, vector-valuedimage functions are treated instead of the scalar image functionsused in gray-level image processing.

Several coordinate systems are available for representing colorimages [23,24]. The most common one is the RGB color system(red, green and blue components). Nevertheless, for image pro-cessing it is more advisable to use HSI (hue, saturation andintensity), HSV (hue, saturation and value or brightness) or HLS(hue, lightness and saturation) color spaces. These spacesare more closely akin to the human interpretation of colors.The components of these color models are the human perceptualattributes of color: hue, saturation and luminance or intensity.As such, in this work we use the HSI color space for processing.Fig. 2 shows a cylindrical representation of the HSI model, where0rSr1, 0r Ir1, and 0rHr2p. In a discrete lattice, thesevalues are usually normalized to integers in the range [0,255].

The transformation from RGB to the HSI model can be carriedout with the Foley and van Dam formulas [25]. The hue of thecolor, H, characterizes the dominant color contained in a pixel.

Inte

nsity Saturation

Hue

Fig. 2. HSI color space. Cylindrical representation.

Taking the red primary at 01, H can be obtained as

H¼d if BrG

2p�d if B4G

(ð1Þ

with

d¼ cos�1 ðR�GÞþðR�BÞ

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðR�GÞ2þðR�BÞðG�BÞ

q0B@

1CA ð2Þ

The saturation of the color, S, is a measurement of the colorpurity. This parameter is dependent on the number of wave-lengths that contributes to the color perception. S¼1 correspondsto a pure color and S¼0 for an achromatic color. S is given by

S¼ 1�3�minðR,G,BÞ

RþGþBð3Þ

The intensity of the color, I, corresponds to the relativebrightness (in the sense of a gray-level image). The intensity isdefined in accordance with

I¼RþGþB

3ð4Þ

The existence of the singularities in H and S is a disadvantagefor the HSI color space. In addition, hue is undefined for achro-matic colors.

In Fig. 3, we show the whole range of possible hue values, from0 to 2p, for some fixed saturation and intensity values. In thisfigure, we have also pointed out the hue interval corresponding tothe transition region indicated by the ReMi technique for thepicks (see Section 2.1). This hue interval is approximatelybetween 1.44p (blue color) and 1.64p (warmer colors).

As we can see in Fig. 3, it does not have any perceptual sense toorder the different colors from the lowest to the highest values(e.g. blue colors higher than red colors). However, we could use adistance function to measure the proximity between two differ-ent colors. In this sense, Peters [26] and Hanbury and Serra [27]use a distance function defined as

dðH,Href Þ ¼9Hðx,yÞ�Href 9 if 9Hðx,yÞ�Href 9rp2p�9Hðx,yÞ�Href 9 if 9Hðx,yÞ�Href 94p

(ð5Þ

0

0.50π

1.00π

1.50π

1.44π 1.64π

Fig. 3. Color wheel representation of hue values from 0 to 2p. The hue interval

[1.44p–1.64p] corresponding to the transition region indicated by the ReMi

technique for the picks is also marked. (For interpretation of the references to

color in this figure legend, the reader is referred to the web version of this article.)

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–10498

where H(x, y) is the hue value estimated at the pixel (x, y) and Href

is a hue value taken as a reference.

2.3. Mathematical morphology and connected operators

Mathematical morphology is a theory and technique for theanalysis and processing of geometrical structures, based on settheory, lattice theory, topology and random functions. Mathema-tical morphology is also the foundation of morphological imageprocessing, which consists of a set of operators that transformimages according to the size of a structuring element. Thus, itbecomes a powerful image-analysis technique with applicationsin filtering, enhancement, feature extraction, etc. [28].

In binary morphology, white objects, (Xi)i A Z�X, contained in abinary image, SBW, are considered as sets. All the morphologicaloperations are based on the interaction between these whiteobjects and another image object of known shape, called thestructuring element, B.

Basic operations in mathematical morphology are erosion anddilation. Erosion and dilation are duals of each other with respectto set complementation and reflection. The erosion of a set X by astructuring element B is denoted by eB(X)

eBðXÞ ¼ ðx,yÞASBW=Bðx,yÞDX� �

ð6Þ

where B(x,y) is the translation of B by the vector (x, y).The dilation of a set X by a structuring element B is denoted by

dB(X)

dBðXÞ ¼ ððx,yÞASBW Þ=Bðx,yÞ \ Xa+� �

ð7Þ

Erosion and dilation can be used in a variety of ways, inparallel and series, to give other transformations including thick-ening, thinning, skeletonization and many other. Two veryimportant transformations based in erosion and dilation areopening and closing. Intuitively, dilation expands an image objectand erosion shrinks it. Opening generally smoothes a contour inan image, breaking narrow isthmuses and eliminating thinprotrusions. Opening is erosion followed by dilation (g¼ed).Closing tends to narrow smooth sections of contours, fusingnarrow breaks and long thin gulfs, eliminating small holes, andfilling gaps in contours. Closing is a dilation followed by erosion(f¼de). Just as with dilation and erosion, opening and closing aredual operations.

An interesting field of mathematical morphology is the con-nected (geodesic) operators [29,30]. In geodesic transformations,the morphological operators applied to an original image involve asecond image, known as the mask, which conditions the finalresults. In our method we use the geodesic operation of areaopening. This operation removes from a binary image all connectedcomponents, X, that have fewer than a minimal defined area, l40.Thus, the area opening of parameter l of X is defined as

glðXÞ ¼ [ XASBW=AreaðXÞZl� �

ð8Þ

3. Proposed method

The proposed picking algorithm operates as follows:

1)

Selection of the slowness–frequency image

Given the recorded image in the original format (e.g. Fig. 4a),as it is provided by the proprietary software package Sei-sOpts ReMiTM [6,31], we remove the gray frame and selectonly the image corresponding to the slowness–frequencyvalues (Fig. 4b). The automatic selection of this image isbased on the RGB color characteristics. Indeed, a gray/black

color has the same value for the three channels in the RGBspace. Therefore, the algorithm runs along all the rows andcolumns and automatically identifies the upper, down, leftand right frontiers of the image where differences appearbetween the RGB values. Once we have this image, therelation between the x and y positions of a pixel (x9Frequency,y9Slowness) and the corresponding frequency and slownessvalues (f, p) are also obtained. For that, we need that the userpreviously introduces the maximum values analyzed ofslowness and frequency.

Dp¼max p

� �max y9Slowness

� �Df ¼max f

� �max x9Frequency

n o ð9Þ

2)

Selection of the hue interval.

The proposed algorithm repeats the estimation of the disper-sion curve for different hue values, Href. By default, it auto-matically runs from a hue value of 1.44p (blue color) to 1.64p(warmer colors), covering the area where the picking isrecommended (see Fig. 3). We use a wide hue interval inorder to make the algorithm more robust to different imagesand color ranges. However, this hue interval can also beselected by the user, who can choose a narrower range. Withrespect to the number of iterations, Ni, it is set by default to50 although it can be modified. Consequently, the hue stepapplied in the process depends on the selected hue intervaland the number of iterations.

3)

Hue filtering in the HSI space.

The slowness–frequency image is converted from the RGB tothe HSI space, following Eqs. (1)–(4). In this color space, thedistance between the image hue and a reference hue iscalculated according to Eq. (5) (Fig. 4c). After that, using thehue distance result, the image in the RGB space, SRGB(x9Frequency,y9Slowness), is modified according to the following criterion:

SBW ðx9Frequency,y9SlownessÞ ¼0 if dðH,Href ÞrdThreshold

1 if dðH,Href Þ4dThreshold

(ð10Þ

where dThreshold is a margin selected around the Href value. Inour case, dThreshold has been set up by default to 0.20p. Afterthis filtering, the previous image is converted to a black andwhite image, SBW(x9Frequency, y9Slowness), as it is shown in Fig. 4d.

4)

Transformation to the wavenumber–frequency domain.

The new slowness–frequency image, SBW(x9Frequency, y9Slowness),is converted to the wavenumber–frequency domain applyingthese equations:

SBW ðx9Frequency,y9WavenumberÞ ¼ x9Frequency,ð2px9Frequencyy9SlownessÞFn o

ð11Þ

where F is a compression factor which assures that the size ofthe new image, SBW(x9Frequency, y9Wavenumber), remains the samethan SBW(x9Frequency, y9Slowness). This factor is expressed as

F ¼max y9Slowness

� �max y9Wavenumber

� � ð12Þ

with

max y9Wavenumber

� �¼ 2pmax x9Frequency

n omax y9Slowness

� �ð13Þ

Using this transformation, the region of interest, where thepicking process has to be carried out, is transformed from acurvilinear profile into an approximately linear profile. More-over, the use of the factor F implies a horizontal compression.Thus, small irregularities (convexities, gaps, etc.) in the profileof interest are minimized after the transformation, providing

Fig. 4. Graphical description of the results obtained through steps 1 to 5 of the proposed algorithm. (a), (b) Step 1: Removing of the gray frame, (c) Steps 2,3: Hue ltering

with Href¼1.6p, (d) Step 3: Conversion from RGB to B&W, (e) Step 4: Transformation to the f-k domain, (f) Step 5: Morphological operation: Area opening (g) Step 5:

Morphological operation: Dilation. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104 99

an almost continuous shape. In Fig. 4e, one example is shown.Note that after this transformation, all the information of theimage is contained above the diagonal line. Below this line,the pixels are simply white.

5)

Morphological operations.

In this step, two morphological operations are applied inorder to improve the image: area opening and dilation. First,all connected white objects that have fewer than N pixels areremoved from the binary image (Fig. 4f). In the proposedalgorithm, the default connectivity has been set to 50 pixels,which experimentally has demonstrated to work well in theanalyzed images.After that, the image is dilated using a disk shaped structuringelement of 3 pixels radius. Dilation expands the white objects,eliminating small holes and filling gaps in contours (Fig. 4g).

6)

Dispersion curve detection in the wavenumber–frequency

image.

In the processed image, the region of interest is alwayslocated in the upper left corner of the image and thetransition between white and black colors in the objectslocated in this region of the image corresponds to thedispersion curve. Therefore, an specific routine has beendesigned for detecting the upper border of the objects locatedat the upper left corner of the image.In the first step the algorithm, starting at the point (0, 0), runsup–down, left–right on the image looking for a black pixel,which would be the first pixel (x1, y1) of the region of interest(Fig. 5a).Once the first pixel has been identified, the algorithm takesthis pixel as new starting point for the next iteration.Now, the proposed algorithm analyzes the next column,x1þ1, running from y1�10 to y1þ10 looking for a transitionfrom white to black colors (Fig. 5b), which corresponds tothe next point of interest, (x2, y2). The margin of 10 has been

Fig. 5. Dispersion curve detection in the wavenumber–frequency image. Detection of the first point of the curve (a); detection of the dispersion curve at different points of

the image (b and c); and end of the detection process (d).

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104100

chosen experimentally for considering small changes inthe slope of the object of interest. However, as it was commen-ted in step 4, the transformation to the wavenumber–frequencydomain provides a nearly linear profile for the region of interestand thus, abrupt changes of slope are not expected.For the next iteration, the point (x2, y2) is taken as starting pointand therefore, the analysis for the next column, x2þ1, goes fromy2�10 to y2þ10. The process is repeated column by column aslong as a white to black transition is detected in each iteration(Fig. 5c).The process ends when white to black transitions are notdetected for six consecutive columns (Fig. 5d). We have chosenexperimentally the value of 6, which is small enough to preventfrom aborting the process by a sudden change or gap in theobject of interest, or from continuing with other black objectdifferent to the object of interest.

7)

Dispersion curve estimation in the slowness–frequency domain.

Once the dispersion curve has been estimated in thewavenumber–frequency image, the inverse transformationis applied in order to estimate the corresponding dispersioncurve in the frequency–slowness image.

y9Slowness ¼y9Wavenumber

2px9FrequencyFð14Þ

The morphological operation (area opening and dilation ofwhite objects) tends to overestimate the estimated slownessvalues. This means that the dispersion curve is correctlyestimated on the object of interest, but it may be located onthe pink region of the object (see Fig. 4c). This irregular biascan be corrected by analyzing the estimated dispersion curvein Fig. 4c and modifying the slowness values at eachfrequency position in such a way that the dispersion curvegoes along the edge of black and pink colors.

Once the dispersion curve has been estimated on the image as afunction of the pixel positions (x9Frequency, y9Slowness), the associateddispersion curve (slowness versus frequency) can be obtained as

p¼ y9SlownessDp

f ¼ x9FrequencyDf ð15Þ

As the dispersion curve has been estimated through the analysisof the pixels of the image, the estimated result is not acontinuous line, as can be seen in Fig. 5. To eliminate thisquantification effect, a median filter of order 20 is applied onthe previously estimated curve.

8)

Estimation of the mean dispersion curve.

As it was commented previously (step 2), the proposedalgorithm repeats the estimation of the dispersion curve fordifferent hue values, Href. Therefore, steps 2–7 are repeatedsince all the selected hue values, Href, are analyzed and all theNi (number of iterations) dispersion curves are estimated.

After that, the mean dispersion curve and the correspondingstandard deviation are calculated with some restrictions thatassure the feasibility of the dispersion curves used.

First of all, if the frequency bandwidth of one dispersion curveis narrower than the mean frequency bandwidth estimated for allthe estimated dispersion curves then, this curve is rejected. Notethat we are comparing the number of frequency points (band-width) analyzed in each curve, but not the frequency values.

After this first selection, the mean and the standard deviationare calculated for each frequency point. If the standard deviationis twice the mean standard deviation obtained for all thefrequency points then, this frequency point is rejected. If thenumber of slowness values used for estimating the mean value atone frequency point is lower than the 10% of the number ofcurves then, this frequency point is also rejected.

Slo

wne

ss (

s/m

)

Frequency (Hz)0

0.005

0.000

0.010

0.015

0.020ReMi Espectral Ratio

0.0 2.5

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16 18 20

Vel

ocity

(m

/s)

Frequency (Hz)

Estimated dispersion curveManual picks

2015105

Fig. 6. Estimated dispersion curve obtained for the example explained through Figs. 4 and 5(a). Comparison between the estimated dispersion curve and the geophysicist

picks (b).

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104 101

In this case we have applied these restrictive criteria for theselection of the curves and the slowness values, but any othercriteria might be also valid if they guarantee the feasibility of thesamples used for estimating the mean dispersion curves. Anyway,the absence of these criteria would not seriously affect theestimated mean values, but it would increase the standarddeviation and then, the error associated to the estimation of themean curve.

Thus, the proposed algorithm returns as a result a 4-columnfile with the following parameters: frequency, mean slowness,standard deviation and weight (number of curves used for theestimation of the mean value). The file is saved as a four-columnASCII file, in the same format that the Geopsy package software[11,32] uses for characterizing the dispersion curve data.

In Fig. 6a, we show the mean dispersion curve obtained for theexample explained through Figs. 4 and 5. In Fig. 6b, we comparethe estimated dispersion curve with the one picked by a geophy-sicist. We can see that there are not significant differencesbetween both curves. The only difference is with respect to thefirst pick (2.2 Hz, 300 m/s) indicated by the geophysicist and notreached by the proposed method, which starts at 2.7 Hz.

Nevertheless the inclusion (or not) of this manual pick might bea matter of discussion attending to the recommendations of theReMi method, which suggests to avoid picking near the area ofartifacts (see Fig. 1).

4. Results and discussion

The proposed method has been applied on images obtainedfrom the ReMi technique at 18 sites around the province ofAlicante (southeastern Spain). We have selected sites with differ-ent geological characteristics and images of different quality inorder to test the performance of the proposed automaticalgorithm.

The seismic noise measurements were taken using a 24-channelseismic refraction equipment (RAS-24 Exploration Seismograph‘‘Seistronix’’) with 10-Hz vertical-component geophones spaced atregular intervals (4–10 m) along a linear profile. From Louie [6], wecould consider that the equipment and configuration used wereenough to estimate in some cases the Rayleigh dispersion curves atfrequencies as low as 2 Hz and shear-wave velocity profiles up to

Slo

wne

ss (

s/m

)

0.005

0.000

0.010

Frequency (Hz)

ReMi Espectral Ratio

0.0 2.5

Slo

wne

ss (

s/m

)

0.005

0.000

0.010

Frequency (Hz)

Slo

wne

ss (

s/m

)

0.005

0.000

0.010

Frequency (Hz)

Slo

wne

ss (

s/m

)

0.005

0.000

0.010

Frequency (Hz)

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Fig. 7. Estimated dispersion curves obtained automatically at 4 sites with different geological characteristics and different images features.

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104102

100 m depths. The data acquisition was prepared to capture four32-s records at a sample rate of 500 Hz. Each one of the foursegments was taken with different gain (12, 24, 36 and 48 dB) tohave the option to improve the signal to noise ratio through astacking of the four.

The array data were processed according to the ReMi analysis(Louie, 2001) using the SeisOpts ReMiTM software [6,31]. Thus,the recorded data were transformed from the time–distance

domain to the slowness–frequency image. After that, theseimages were analyzed by the proposed method in order toestimate the corresponding empirical dispersion curves.

In Fig. 7, we show the results obtained automatically for foursites with different geological characteristics and different imagefeatures. Only the upper half of the obtained images, where iscontained the information of interest, is shown. In all the analyzedcases we obtain reliable dispersion curves in the frequency range of

Slo

wne

ss (

s/m

)0.005

0.000

0.010

Frequency (Hz)0

ReMi Espectral Ratio

0.0 2.5

Slo

wne

ss (

s/m

)

0.005

0.000

0.010

Frequency (Hz)0

5 10 15

5 10 15

Fig. 8. Dispersion curves estimated on two different poor-quality images.

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interest, according to the ReMi recommendations and the geophy-sicist experience.

Note that typical dispersion curves run from small slownessvalues at low frequencies, down to the right toward largerslowness values at higher frequencies. Therefore, a change of thistendency at low frequencies (increase of the slowness values)indicates the lower frequency limit of the dispersion curve.In Fig. 7a–c, the change of this tendency at low frequencies canbe identified as a local minimum of slowness, which is located inthese figures at 2.6, 3.4 and 3.6 Hz, respectively. At high frequen-cies, a change of the normal tendency (decrease of the slownessvalues) indicates the higher frequency limit of the dispersioncurves.

These assumptions are always considered independently ofthe method used for estimating the dispersion curve: for examplein the application of the frequency–wavenumber (f–k) or theextended spatial autocorrelation (ESAC) methods.

With these considerations, the valid dispersion curves asso-ciated with the four examples shown in Fig. 7 are included in thefollowing frequency ranges: 2.6–12.0 Hz, 3.4–18.4 Hz, 3.6–23.2 Hzand 2.6–14.6 Hz.

Finally, in Fig. 8 we also show two cases where the analyzedimages present a very poor quality. In both images, the transitionbetween blue and warmer colors is not well defined, especially athigh frequencies. Moreover, the aliasing limit is not identified inone of the images (Fig. 8a). Despite these inconveniences, theproposed algorithm also provides satisfactory dispersion curves inan automatic way. With respect to the valid dispersion curves,they are included in the range of 2.7–6.0 Hz and 2.1–11.7 Hz forFig. 8(a) and (b), respectively.

5. Conclusions

The ReMi technique is one of the widely used methods forestimating the dispersion curve associated with a site. This technique

provides a slowness–frequency image where the dispersion curve hasto be manually picked by an expert geophysicist. Therefore, this isalways a subjective process based on the visual perception of theanalyst and without any objective measure of the possible error ordeviation of the selected picks.

In this paper, we present a new automatic method forestimating the dispersion curve from the slowness–frequencyimages provided by the ReMi technique. The proposed methodis based on color processing and morphology, and estimatesproperly the dispersion curves for all the analyzed images, evenin cases of poor quality.

Our algorithm has been tested on images with differentfeatures and qualities obtained from 18 sites with differentgeological characteristics. For all the analyzed images, the esti-mated valid dispersion curves are according to the guidelinesestablished by Louie [6] and the manual picking that an expertgeophysicist might select in the corresponding frequency range.

The proposed algorithm runs automatically and provides afour-column ASCII file with the following parameters: frequency,mean slowness, standard deviation and weight. In this way, weobtain the mean dispersion curve, but also some indicators(standard deviation and weight) of the reliability of the estimatedslowness values. Furthermore, this file can be directly used byother softwares for estimating the shear-wave velocity profilefrom the obtained dispersion curve.

Acknowledgments

This work has been carried out thanks to the financial supportof the Spanish Government (MARSH-CGL2007–62454) and theGeneralitat Valenciana (Projects GV05/247, REN2001-1674/RIESand REN2003-01975). We are also very grateful to the LocalSeismic Network, University of Alicante (supported by Diputacionde Alicante) for providing us instruments and software for the

J.J. Galiana-Merino et al. / Soil Dynamics and Earthquake Engineering 42 (2012) 95–104104

experiments. Finally, we would like to thank P. Jauregui for hishelp in analyzing the data.

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