crosscoherence-based interferometry for the retrieval of first...
TRANSCRIPT
Crosscoherence-based interferometry for the retrieval of first arrivals andsubsequent tomographic imaging of differential weathering
Joachim Place1, Deyan Draganov2, Alireza Malehmir1, Christopher Juhlin1, and Chris Wijns3
ABSTRACT
Exhumation of crust exposes rocks to weathering agents thatweaken the rocks’ mechanical strength. Weakened rocks willhave lower seismic velocity than intact rocks and can thereforebe mapped using seismic methods. However, if the rocks areheavily weathered, they will attenuate controlled-source seis-mic waves to such a degree that the recorded wavefield wouldbecome dominated by ambient noise and/or surface waves.Therefore, we have examined the structure of differentialweathering by first-break traveltime tomography over a seis-mic profile extending approximately 3.5 km and acquired ata mining site in Zambia using explosive sources and a sourcebased on the swept-impact seismic technique (SIST). Seismicinterferometry has been tested for the retrieval of supervirtualfirst arrivals masked by uncorrelated noise. However, use ofcrosscorrelation in the retrieval process makes the method
vulnerable to changes in the source signal (explosives andSIST). Thus, we have developed a crosscoherence-based seis-mic-interferometry method to tackle this shortcoming. Weinvestigate the method’s efficiency in retrieving first arrivalsand, simultaneously, correctly handling variations in thesource signal. Our results illustrate the superiority of the cross-coherence- over crosscorrelation-based method for retrieval ofthe first arrivals, especially in alleviating spurious ringynessand in terms of the signal-to-noise ratio. These benefits areobservable in the greater penetration depth and the improvedresolution of the tomography sections. The tomographic im-ages indicate isolated bodies of higher velocities, whichmay be interpreted as fresh rocks embedded into a heavilyweathered regolith, providing a conspicuous example of differ-ential weathering. Our study advances the potential of seismicmethods for providing better images of the near surface(the critical zone).
INTRODUCTION
Bedrock weathering initiates processes required for life on earthand shapes the near-surface domain called the critical zone (CZ)(Field et al., 2015). One such process is the production of fertilesoils, the most hospitable substrate for organisms, involving thebreakdown of biologically inert fresh rocks into regolith, saprolite,and, ultimately, soil (Graham et al., 2010). Although several factorscontrolling the development of weathering processes have beenidentified, such as the effect of stresses (Molnar et al., 2007; Owenet al., 2007; St Clair et al., 2015; Braun et al., 2016), as well asthe grain size and the density of inherited fractures (Hill, 1996;
Goodfellow et al., 2014), the method by which intricate physicaland chemical processes initiate and develop during rock weatheringis not yet fully understood (Riebe et al., 2016). Unraveling suchprocesses requires identifying the existing couplings between theseverity of the weathering and climactic factors, actively cycledwater, and the role of heterogeneities acquired when the rock masswas at greater depth, to name a few. Therefore, noninvasive geo-physical imaging can play a key role in such approaches by map-ping out the severity of the weathering within the CZ (Parsekianet al., 2015).Because the weathering processes usually alter the mechanical
strength of the rocks (e.g., Goodfellow et al., 2014) and the velocity
Manuscript received by the Editor 3 June 2018; revised manuscript received 5 January 2019; published ahead of production 15 March 2019; published online3 May 2019.
1Uppsala University, Department of Earth Sciences, Villavägen 16, 752 36 Uppsala, Sweden. E-mail: [email protected] (corresponding author);[email protected]; [email protected].
2Delft University of Technology, Department of Geoscience and Engineering, Stevinweg 1, 2628 CN Delft, The Netherlands. E-mail: [email protected].
3First Quantum Minerals Ltd., West Perth, Australia. E-mail: [email protected].© 2019 Society of Exploration Geophysicists. All rights reserved.
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GEOPHYSICS, VOL. 84, NO. 4 (JULY-AUGUST 2019); P. Q37–Q48, 9 FIGS., 1 TABLE.10.1190/GEO2018-0405.1
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and attenuation of seismic waves depend on the mechanicalproperties of the materials they propagate through (Aki andRichards, 2002), seismic methods are well-suited to image the dis-tribution of weathered rocks. The velocity of the P-waves generallyranges between approximately 5000 and 6000 m/s for fresh graniticrocks and are somewhat higher in more mafic rocks, such as gabbro(Salisbury et al., 2003; Sheriff and Geldart, 2006; Place et al., 2011;Malehmir et al., 2013), whereas values down to a few thousands oreven only a few hundreds of meters per second have been reportedin regoliths and saprolites of granitoidic origin (Vijaya Raghavaet al., 1977; Bandu Rao Naik et al., 1980; Radzevicius and Pavlis,1999; Place et al., 2016). Such differences in velocity have madefirst-break traveltime tomography a popular method to map thenear-surface velocity structure and relate low velocities to weather-ing (Parsekian et al., 2015). However, the mechanical disaggrega-tion of rocks also tends to attenuate the propagation of the seismicwaves. Consequently, there exists a trade-off between the velocitydecrease and attenuation increase that accompanies the weatheringprocesses and affects the efficiency of first-break traveltime tomog-raphy and traditional layer-based generalized ray-based refractionmodels. Specifically, in the crystalline basement, several publishedaccounts have illustrated the significance of near-surface effects inhigh-resolution imaging of deep structures such as mineralizedbodies (e.g., Malehmir et al., 2012). Given the low signal-to-noiseratio (S/N) of reflections in hard-rock environments, determiningaccurate static corrections is often one of the key processing steps,which requires high-quality first breaks along the entire profilelength.The aim of this paper is to investigate the seismic properties of
heavily weathered crystalline rocks using a field example at a min-ing site in Zambia. Although the weathering severely hinders thepropagation of seismic waves and in turn the efficiency of classictraveltime tomography, we use seismic interferometry (SI) to in-crease the S/N of the first arrivals (Schuster [2010], also calledthe retrieval of supervirtual arrivals). SI is a method based onthe calculation of the Green’s function between seismic sourcesand receivers. It aims at retrieving signal hidden in the noise bysummation, and it usually involves crosscorrelating traces. How-ever, because two types of sources were used to acquire the data,for the first time we use SI by crosscoherence in the first step of theSI process of retrieval of supervirtual arrivals to correctly handlechanges in the source signals. Crosscoherence-based SI has beenused earlier (e.g., Wapenaar et al., 2010b); however, its applicationhere to retrieve first arrivals is novel. Our results show that SI bycrosscoherence helps in generating supervirtual arrivals of simplerwaveforms and higher S/N than those obtained using traditional SIby crosscorrelation. This methodological development enables theimaging of severely attenuating rocks by traveltime tomography,therefore expanding the relevance of seismic methods to cases thatare otherwise difficult.
METHOD
Because the quality of the first arrivals is of primary importancefor exploring the subsurface using tomography techniques, in thispaper we make use of SI to combat the high noise level and ulti-mately improve the tomographic imaging. After presenting thestate-of-the-art of SI to retrieve the first arrivals, we introduce SIby crosscoherence as a novel approach to address the limitationsof the traditional SI technique in use for first-arrival retrieval.
State-of-the-art
SI techniques aim to retrieve seismic traces based on the initialformulation of the principle by Claerbout (1968) and several theo-retical developments (e.g., Wapenaar, 2004). Such retrieval is com-monly achieved by crosscorrelating seismic traces recorded atdifferent locations (Wapenaar, 2004; Schuster, 2010; Wapenaaret al., 2010a). When crosscorrelating traces recorded at two differ-ent locations and summing (over controlled sources), the new seis-mic trace retrieved at one of the two locations represents the tracethat would be recorded at this position if a controlled source waslocated at the other position. The retrieval process can also be ap-plied using crossconvolution instead of crosscorrelation (Slob et al.,2007). Combining these two methods of redatuming can advanta-geously be used in controlled-source seismic studies to retrieve firstarrivals originally hidden by a high level of noise (Mallinson et al.,2011; Bharadwaj et al., 2012; Al-Hagan et al., 2014; An et al., 2015;Qiao et al., 2015; Place and Malehmir, 2016). In the following, weillustrate the method by which the signal generated at the sourceposition S and recorded at the receiver location B is retrieved usingthe example of refracted waves (Figure 1); direct and surface wavescan be retrieved by a similar procedure.First, the traces recorded at receivers A and B are crosscorrelated
(Figure 1a). The obtained virtual trace represents the signal thatwould be generated by a virtual source A′ located along the refractor(involving some negative traveltime; see the dashed line inFigure 1a). Repeating the procedure for any source S located ata postcritical distance from receiver A yields virtual traces of equiv-alent kinematics. For this reason, these traces can be stacked tostrengthen the signal occurring at the same correlation lag (the vir-tual signal generated by A′) and attenuate any incoherent noise andother arrivals for which the sources do not fulfill the stationary-phase criteria (e.g., Dong et al., 2006; Mallinson et al., 2011;Mikesell and van Wijk, 2011). The stacked virtual trace is sub-sequently convolved with the trace originally recorded at receiverA when the source was at location S to produce a supervirtual trace,as if generated by the source S and recorded by the receiverB (Bhar-adwaj et al., 2012; see also Figure 1b). Kinematically equivalentsupervirtual traces can be obtained for all receivers A located be-tween S and B whose distance to S is greater than the postcriticaldistance. This second stacking increases the S/N even further. Thestacked supervirtual trace corresponds kinematically to the desiredoutput (the signal generated by S and recorded at station B) but has ahigher S/N. In short, the SI process consists of two successive re-datuming operations achieved by using crosscorrelation and cross-convolution, offering two occasions to improve the S/N by stacking(Mallinson et al., 2011). Such retrieval of first arrivals has provenbeneficial for first-break traveltime tomography and for reflectionimaging through the improvement of surface-consistent static cor-rections (Place and Malehmir, 2016).The advantages of the crosscorrelation- and crossconvolution-
based SI retrieval method are that it is data-driven (no a priori in-formation is required) and that it recovers coherent signals origi-nally hidden within the noise (Schuster, 2010; Wapenaar et al.,2010a). One limitation is the generation of artifacts related to thepresence of other signals in the raw data, such as reflections oroff-plane arrivals violating the assumption of the stationary phase,but insufficiently suppressed by destructive summation outside thestationary-phase regions. Windowing the source gathers around thefirst arrivals (or their supposed occurrence) is an effective practical
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solution to tackle problems related to reflections (Bharadwaj et al.,2012; Al-Hagan et al., 2014; Place and Malehmir, 2016). Anotherlimitation is the introduction of spurious ringyness and broadeningof the waveform of the first arrivals, which affects the resolutionwhen picking first breaks. Applying a spiking-deconvolution filterhas been the most effective solution to address this problem to date(Al-Hagan et al., 2014; An et al., 2015; Place and Malehmir, 2016).
Limitations of SI by crosscorrelation
Retrieving first arrivals using SI requires a certain degree of sim-ilarity of the first-arrival signals for the summation processes towork effectively. In other words, the efficiency of the method de-pends upon the stability of the source signal throughout the acquis-ition of a data set. Strong heterogeneities in the near surface, as wellas acquisition-related factors such as the source coupling, the depthof the sources (if explosives), and the fatigue of the ground whenoperating the source repeatedly at a given location (e.g., vibratingtruck or VIBSIST) may result in a significant variability of thesource signature. While estimating, statistically, and removingthe source signature from each individual shot is possible, it canbe time consuming and impractical. Therefore, in this paper, weimplement crosscoherence in the SI retrieval of first arrivals andexamine its consequences in the example of first-break tomography.In seismic applications other than the retrieval of first arrivals,
crosscoherence has proven to more appropriately handle changesin the source signals than crosscorrelation and be more stable inthe presence of noise when constructing source gathers from am-bient noise data (Wapenaar et al., 2010b; Nakata et al., 2011; Nish-itsuji et al., 2016). Laboratory measurements at ultrasonicfrequencies have also illustrated the superiority of crosscoherencein retrieving reflections with a higher time resolution than crosscor-relation (Draganov et al., 2018). Therefore, in the present study, weinvestigate the potential benefits of using crosscoherence instead ofcrosscorrelation in retrieving the first arrivals in an active-sourcedata set, with the aim of integrating sub-data sets acquiredfrom sources with significantly different signatures (SIST andexplosives).
SI by crosscoherence
In this subsection, we present an analytical comparison betweencrosscorrelation and crosscoherence to predict their effect in retriev-ing first arrivals. The crosscorrelation of two traces recorded at twodistinct points A and B is defined in the Fourier domain as
CrArB ¼ uðrA; sÞu�ðrB; sÞ; (1)
where uðrA; sÞ denotes the seismic wavefield recorded by a receiverr located at A when using an active source at location s and * in-dicates the complex conjugation. Note that no symbol is used in thispaper to indicate multiplication. The crosscoherence is defined asthe frequency-normalized crosscorrelation, expressed as
HrArB ¼ CrArB
juðrA; sÞjjuðrB; sÞj¼ uðrA; sÞu�ðrB; sÞ
juðrA; sÞjjuðrB; sÞj; (2)
where jj indicates that the amplitude spectrum is used. Ignoring thepresence of noise, the seismic wavefield as recorded at r from asource at s can be written as a product in the Fourier domain:
uðr; sÞ ¼ WðsÞGðr; sÞ; (3)
whereWðsÞ is the signal generated by the source (source signature)at s and Gðr; sÞ is the Green’s function between r and s. Substitut-ing equation 3 into equations 1 and 2 yields
CrArB ¼ jWðsÞj2GðrA; sÞG�ðrB; sÞ (4)
and
HrArB ¼ GðrA; sÞG�ðrB; sÞjGðrA; sÞjjG�ðrB; sÞj
; (5)
respectively. Comparing equations 4 and 5 shows that, unlike inthe case of crosscorrelation, the source term WðsÞ is absent fromexpression 5 with crosscoherence. In other words, the result of
Figure 1. Two-step workflow to retrieve first arrivals by SI. The wave velocity is assumed to be lower in the shallow layer to give rise torefracted waves. (a) Traces obtained at receivers A and B from postcritical sources are crosscorrelated (⊗) and stacked over sources S toproduce a virtual trace with a high S/N. The use of crosscoherence (⊖) is also investigated in this paper. (b) The virtual trace is convolved(*) with a real trace recorded at A and summed over the receivers A between S′ and B to produce a supervirtual trace in B, equivalent to the realtrace but with a higher S/N. The dashed lines indicate a negative traveltime. Modified after Place and Malehmir (2016).
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crosscoherence is independent of the source signal and still containsthe Green’s functions, the retrieval of which is the aim of SI tech-niques (Claerbout, 1968). Therefore, crosscoherence can be usedadvantageously in the first step of first-arrival retrieval to handlepossible changes in phase, frequency, or energy of the sources whenstacking over a series of source gathers (Figure 1a). The source sig-nature is reintroduced in the second step (Figure 1b) when forming asupervirtual trace by convolving with a real trace:
uSVðrB;s 0Þ¼XAmax
A¼Amin
Wðs 0ÞGðrA;s 0ÞXSmax
S¼Smin
GðrA;sÞG�ðrB;sÞjGðrA;sÞjjG�ðrB;sÞj
;
(6)
where the subscript SV indicates the supervirtual character of thewavefield and the second summation term represents the stackedvirtual trace (as illustrated in Figure 1a). Because stacking of thedifferent uSVðrB; sÞ over receivers A (Figure 1b) is achieved usingtraces belonging to a given source gather, a unique source termWðsÞ is present and gives the supervirtual first arrivals their originalcharacter. Writing equation 6 in the case of crosscorrelation wouldcontain the product of three source terms, generating the ringynessobserved in previous studies and addressed in them by spiking de-convolution (Al-Hagan et al., 2014; An et al., 2015; Place and Mal-ehmir, 2016). Therefore, crosscoherence has a strong potential tocorrectly handle changes in the source signature and intrinsicallyavoid spurious ringyness of the supervirtual first arrivals. Moreover,by adding a term in equation 3 that would represent uncorrelatednoise and comparing the standard derivations of equations 4 and5, Nakata et al. (2011) show that the use of crosscoherence producesmore stable results than those obtained by crosscorrelation or sim-ple trace deconvolution. Finally, we investigated the optimal valueof a regularization parameter in the denominators of the equationsabove and found, when processing data, that none was required. Apossible explanation is that the numerator and the denominator aresmall when the spectral amplitude is low, which is in agreementwith a previous study (Nakata et al., 2011). To sum up, SI by cross-coherence presents the potential advantages of (1) being data-driven(no spiking deconvolution is required, and no regularization param-eter required, at least in the case of the data presented below),(2) correctly handle changes in the source signature, and (3) produc-ing more stable results that other SI techniques in the presence of
noise. These potential advantages motivated the application of thetechnique to field data.
CASE STUDY
Geologic setting
The seismic data used in this study were acquired in the imme-diate vicinity (approximately 2–3 km) of the Kansanshi main open-pit mine, located in the North-Western province, Zambia (Figure 2).The deposit occurs in the center of the Lufilian arc, a Pan-Africanfold-and-thrust belt that was active from the Late Proterozoic to theLate Cambrian (Broughton et al., 2002). The Lufilian arc containsmetasedimentary rocks of the Late Proterozoic Katangan Super-group lying unconformably on an Early and Middle Proterozoiccrystalline basement. The metasedimentary assemblage comprisesa massive diamictite of glacial origin (and belonging to the Mwa-shia and basal Lower Kundelungu equivalents), which is a regionalmarker known as the Grand Conglomerate (Barron, 2003). The di-amictite is stratigraphically found above sequences of carbonate-evaporites-siliciclastic composition (Roan Group equivalent), andit is overlain by a series of carbonatic and siliciclastic rocks (LowerKundelungu Group) (Broughton et al., 2002; Barron, 2003).Gabbroic intrusions are found in the metasediments and predatethe regional metamorphism and deformation (upper greenschistto amphibolite facies during the Lufilian Orogeny) (Tembo,1994; Broughton et al., 2002).Kansanshi is one of the largest Zambian copper ore bodies
outside the Copperbelt. The mineralization consists of late-metamorphic quartz-carbonate-sulfide veins and includes Cu, Au,U, Th, Mo, and V (Torrealday et al., 2000; Broughton et al.,2002). Hydrothermal alteration haloes have been identified in theimmediate vicinity of the mineralized veins and also account forthe mineral resources (Broughton et al., 2002). Humid subtropicalconditions have led to penetrative weathering and, to some extent,remobilization of the ore. Weathering is penetrative in the sense thatit affects all rock types including the gabbros (Broughton et al.,2002; Lobo-Guerrero Sanz, 2005).
Seismic-data acquisition
Seismic data were recorded in 2013 with the motivation to inves-tigate the structural domes localizing the mineralization, as well aspossible postdeposition faulting. For the present study, we selected
one line from this data set because this line wasacquired using explosives and a VIBSIST source(Park et al., 1996; Cosma and Enescu, 2001;Yordkayhun et al., 2009). In the present paper,the latter will be referred to as the swept-impactseismic technique (SIST). In addition, only onemain facies (diamictite) is present along thecentral part of the line, which facilitates the in-terpretation (Figure 2). Key acquisition parame-ters are presented in Table 1 and are partlydetailed below.Vertical-type geophones with a natural fre-
quency of 28 Hz were planted every 10 m. A totalof 345 geophones were cable connected to adata-acquisition system. The SIST source wasactivated three times at each receiver location.
Figure 2. Location of the seismic profile superimposed onto the geologic map of theKansanshi area, Zambia. Geologic map courtesy of First Quantum Minerals Ltd.
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The three records were subsequently decoded using the shift-stackmethod (Park et al., 1996) to improve the S/N (see an example of asource gather in Figure 3a). A fixed-spread geometry was used forthe data acquisition. However, due to the unexpected loss of the lineconnection, an apparent truncation of the SIST gathers occurred atlow-number source locations. The acquisition was then continuedusing explosives in holes of approximately 12–15 m depth drilled atevery fifth receiver location, this time with all 345 geophones con-nected. These shot gathers are characterized by a higher S/N thanthose from the SIST gathers (see an example of a shot gather inFigure 3b), suggesting that the consolidation of the data set (byreplacing the SIST gathers by explosive-source shot gathers whereavailable) could be beneficial for the refraction and the reflectionimaging provided that the variations in the source signaturesthroughout the data set are properly handled.The generally low S/N of the first arrivals and potential later re-
flections (Figure 3) may be due to a combination of (1) the varioussources of noise present during the acquisition (e.g., the mining ac-tivities as well as core drilling taking place next to the profile) and(2) the pronounced weathering causing a strong attenuation of theseismic waves. The poor quality of the first breaks hindered unam-biguous reflection imaging with the data set. It is worth noting thatthe surface waves are clearly recorded at short offsets (Figure 3) andmay even obscure the body waves. First arrivals are recorded atlarger offsets before being hidden below the noise level (Figure 3).
RESULTS FROM SI
The data set was split into three batches to retrieve the first arriv-als using the two-step SI techniques as illustrated in Figure 1. Thedata collected using SIST and explosives were considered sepa-rately to produce supervirtual first arrivals such as those representedin Figures 4b, 4c, 5b, and 5c, respectively. The waveforms obtainedby crosscorrelation exhibit some pronounced ringyness as ex-plained earlier, especially in the case of the data generated by ex-plosives (Figures 5b and 6k–6o), whereas the waveforms obtainedby crosscoherence appear closer to those in theraw data although still different (compare thepanels in Figure 5a and 5c, and the exampletraces in Figure 6). This illustrates that crossco-herence can provide data with clearer first arriv-als and does not require an extra step such asspiking deconvolution to achieve that.The third batch of retrieved data was obtained
using all the source gathers recorded with explo-sives and complemented with SIST source gath-ers where available. Such a combination of thedata sets enables potential benefits from the highfold offered by the numerous SIST gathers(although of a relatively low S/N) and the fewer,but more energetic, gathers recorded from the ex-plosives. Moreover, the intercalation of differentsources offers a good case to investigate the ef-fect of different source signatures in retrievingthe first arrivals. Similar to the cases with the sep-arate data sets, crosscoherence again helps re-trieve waveforms of a higher conformity to theoriginal ones (compare Figure 4a with 4e andFigure 5a with 5e), as opposed to the spuriousringyness resulting from crosscorrelation as a
first-step retrieval operation (compare Figure 4d with 4e and espe-cially the explosives data in Figure 5d and 5e, as well as Figure 6a–6e and 6k–6o). The results also show some significant improvementof the S/N in the SIST data (Figure 4b–4e) with no or very littleincrease of the noise level in the explosive gathers (Figure 5cand 5e). To conclude, in addition to offering less ambiguous datafor picking, retrieval of supervirtual refractions using crosscoher-ence as a first-step tool offers a higher overall quality of the com-bined data set mainly through the increase of the S/N of the SISTgathers.The amplitude spectra (Figure 6f–6j and 6p–6t) of the example
traces exhibit isolated peaks in the case of the data obtained by SI bycrosscorrelation, consistent with the ringyness observed in the timedomain. The spectra obtained after SI by crosscoherence are morecomplex, showing energy in a broader frequency range. However,the spectra of the SI data still show some prominent differences tothose of the raw data. On a general note, the fact that the average
Figure 3. (a) Source gather recorded with a SIST source at location number 33.(b) Source gather recorded with explosives at location number 10. Direct arrivals areindicated by the blue arrows, and surface waves (as well as possible sound waves)are indicated by the red arrows. Note the low S/N of the direct arrivals.
Table 1. Summary of the main acquisition parameters(September 2013).
Survey parameters
Source Explosives (12–15 m depth) and SIST
Nominal source interval 10 m
Number of source points 345
Geophones Vertical. Natural frequency: 28 Hz
Receiver spacing 10 m
Instrument Sercel Lite system and Sercel 428 XML
Number of channels 345 (maximum active channels)
Record length Variable
Sampling interval 1 ms
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noise level is significantly decreased by the SI techniques suggeststhat the noise present in the original data is predominantly uncorre-lated. Our results exhibit only a slight improvement of the S/N whencomparing supervirtual data obtained by crosscorrelation (Figure 4dand 4e) and crosscoherence (Figure 5d and 5e), which is not as dra-matic as that observed in reflection interferometry by Nakataet al. (2011).
TOMOGRAPHY IMAGING
First-break picking
The onset of the first arrivals, seen as a trough, was picked forimaging the subsurface using traveltime tomography. Semiauto-
matic picking was used where the quality of the signal enabledit, but most of the picking was performed manually. For comparisonpurposes and because of the increased S/N between (1) raw data,(2) supervirtual data by crosscorrelation, and (3) supervirtual databy crosscoherence, the number of picks increases when picking thefirst arrivals in that order. The picking on the supervirtual data ob-tained using SI by crosscorrelation was strongly limited by the am-biguity related to the ringyness of the waveform. The use ofcrosscoherence alleviated this ambiguity. Another advantage ofthe crosscoherence is that it did not produce as much smearingas the crosscorrelation does; distinct along-profile variations inthe arrival time and the waveforms were better preserved and re-solved by crosscoherence (e.g., between receiver locations 90and 125 in Figure 5). These observations regarding ringyness
and smearing are in agreement with the fact thatretrieval of first breaks using crosscorrelation in-volves the product of three source terms (see,e.g., Al-Hagan et al., 2014), whereas retrievalof first arrivals using crosscoherence involvesonly one.The first-break picks from the supervirtual
data were later plotted on raw data for a consis-tency check (where the first arrivals could beidentified). This was particularly useful at shortoffsets due to the limitations of the first-arrivalretrieval methods as noted in previous studies(Qiao et al., 2015; Place and Malehmir, 2016).A reciprocity check was then carried out to dis-card all picks having a reciprocal whose time dif-ference was more than 5 ms. Picks with noreciprocal (i.e., no pick related to a propagationthe other way around) were kept. A total of 9334picks collected from the raw data remained afterthe reciprocity test, representing approximately8.7% of the 107,384 available traces. Similarly,15,469 and 18,265 picks (representing 14.4%and 17.0% of the available traces) were obtainedfrom the supervirtual data by crosscorrelationand crosscoherence, respectively.The traveltime matrices in Figure 7a–7c show
that the first-arrival retrieval techniques are mosteffective for gathers with sources from locations1 to 275. In this domain, denser clusters of picksare obtained and larger distances from the sourcecan be reached. The source gathers from 275 to345 have not been significantly improved usingSI, likely due to the extremely low S/N of theoriginal data. In this domain, no first breakcan reliably be picked from the data acquiredwith the SIST source, even after the SI process.Plotting the three populations of picks as a func-tion of the offset illustrates that more picks can becollected in the offset range of 200–2300 m usingSI techniques, especially by crosscoherence(Figure 6d). This figure also denotes a relativelylow number of picks at short offsets (0–200 m)because of the difficulty to separate distinctly,and with confidence, the body waves from thesurface waves (Figure 3).
Figure 4. Source gather recorded with the SIST source at location number 33. (a) Rawdata shown after automatic gain control (AGC) (0.25 s) and exhibiting a low S/N. Win-dowed supervirtual first arrivals retrieved by (b) crosscorrelation and (c) crosscoherence asa first step in the retrieval process using data acquired by SISTonly. (d and e) The same as(b and c), respectively, but using source gathers recorded with explosives instead of SISTwhere available. The vertical arrows point at an example trace magnified in Figure 6.
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First-break traveltime tomography
Inversions of first-arrival times were performed in 2D with thePStomo_eq tomography code (Benz et al., 1996; Tryggvason et al.,2002; Tryggvason and Bergman, 2006) with a cell size of 5 m in thehorizontal and vertical directions. All picked traveltimes were givenequal weight. The starting velocity model included low velocity(350 m∕s) just below the topographic surface with a linear increaseto 5000 m∕s at a 300 m depth. The velocity above the surface wasset to 330 m∕s (sound-wave velocity in air). Eight iterations werecarried out. Picks obtained from the raw and supervirtual data wereused separately for producing three sections (Figure 8).
RESULTS
The first-break traveltime tomography sec-tions presented in Figure 8a–8c have rms valuesof 4.7, 5.1, and 5.0 ms, respectively. The rms val-ues are relatively high and are thought to be re-lated to the limited quality of the first arrivals,even after SI. One benefit of the SI first-arrivalretrieval method is a general increase in the im-aged depth, in agreement with the increasingaverage length of the rays from the raw to thesupervirtual data (Figure 7d). Ray-density pro-files (Figure 8d–8f) highlight the increasingray density at depth together with the numberand length of rays (Figure 7d). Moreover, thedelineation of velocity anomalies is clearer whencomparing Figure 8c with 8a. For example, fea-tures between 0 and 700 m along the profile andapproximately 1300 m in elevation are much bet-ter resolved in Figure 8c. Similarly, wide undu-lations of the high-velocity materials fromapproximately 1500 to 2500 m using the rawdata (Figure 8a) are most likely a smoothing ef-fect of smaller scale bodies with contrastingvelocity as depicted in the inversion using thesupervirtual data (especially in Figure 8c). Ona general note, the increase in resolution of thevelocity structure from Figure 8a to 8c can prob-ably be attributed to the additional picks pro-vided by the two different SI techniques(Figure 7).The obtained velocity values range from a few
hundred meters per second to several thousandmeters per second, in agreement with the pres-ence of extremely weathered rocks, as seen atthe surface, and fresh metamorphic rocks, re-spectively (Figure 9). Zones of high-velocity val-ues are found in the form of isolated blobssurrounded by lower velocity materials ratherthan a continuous body found at depth as de-picted in other studies (see, e.g., the layeredmodel of Radzevicius and Pavlis, 1999). Inother words, finding relatively fast material ata certain depth does not mean that the materialbelow is even faster. This is in agreement withsome downhole logging data (made availableby the mining company but not presented here)
showing nonmonotonic variations of the P-wave velocity withdepth. Comparisons with geologic information (Figures 2 and 9,top) also show that major lithologic contacts are not highlightedby any specific signature in the velocity field. Only the presenceof gabbro at approximately 900 m may be linked to a high-velocityanomaly (Figure 9). Although lithologic changes have been re-ported at both ends of the profile, the geophysical character in suchlithologies seems quite similar to that of the diamictite occurring inthe central part of the profile. Similarly, features in the velocity fielddo not seem to be associated with the occurrence of structures asdepicted in the geology (top Figure 9). Dipping low-velocity zonescan be found to be associated with the surface expression of faults,but many other similar low-velocity anomalies are imaged in areaswhere no fault has been reported at the surface.
Figure 5. Source gather recorded with explosives located at location number 10.(a) Raw data shown after AGC (0.25 s) and exhibiting a low S/N. Windowed super-virtual first arrivals retrieved by (b) crosscorrelation and (c) crosscoherence as a firststep in the retrieval process using data acquired by explosives only. (d and e) The sameas (b and c), respectively, but using additional source gathers recorded with SISTwhereavailable. The vertical arrows point at an example trace magnified in Figure 6.
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Figure 6. (a-j) Example of trace 81 obtained at location number 33 and at the same stages as in Figure 4. (a) Raw data, (b) trace retrieved bycrosscorrelation, and (c) crosscoherence as a first step in the retrieval process using data acquired by SISTonly. (d and e) The same as (b and c),respectively, but using source gathers recorded with explosives instead of SIST where available. (f-j) Normalized amplitude spectra of thetraces (a-e), respectively. (k-o) Example of trace 150 obtained at location number 10 and at the same stages as in Figure 5. (k) Raw data, (l) traceretrieved by crosscorrelation, and (m) crosscoherence as a first step in the retrieval process using data acquired by explosives only. (n and o)The same as (l and m), respectively, but using source gathers recorded with explosives instead of SIST where available. (p-t) Normalizedamplitude spectra of the traces (k-o), respectively.
Figure 7. Traveltime matrices representing thepicks collected from the consolidated data set afterthe reciprocity test. (a) Raw data, (b) supervirtualdata by crosscorrelation, and (c) supervirtual databy crosscoherence. The light-gray areas in (a-c)represent nonactive channels during the acquisi-tion. (d) The number of picks as a function ofthe source-receiver offset for all source gathers.
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DISCUSSION
Seismic-interferometry method
First-arrival times are needed for first-break tomography andstatic corrections. Our study illustrates the capability of crosscoher-ence SI in generating waveforms closer in appearance to thosepresent in the raw data than those obtained using crosscorrelationSI. Therefore, involving crosscoherence does not seem to require anextra processing step such as spiking deconvolution, as crosscorre-lation usually does. Beyond requiring extra effort, deconvolution issubjective as its parameters are chosen by the user. The fully data-driven nature of SI by crosscoherence may be more preferable. This
is even more the case when considering an iterative approach suchas that of Al-Hagan et al. (2014) because spurious ringyness wouldbuild up for every iteration. As seen in our results (Figures 4 and 5),the limited smearing in the supervirtual source gathers is anotheradvantage of the method. Finally, we tested the use of one-bit nor-malization (Cupillard et al., 2011) with the aim of improving thequality of the stack in the first step of the SI process (Figure 3a);however, we did not observe a significant improvement of the finalsupervirtual signals.The reconstruction of first arrivals at short distances from the
source is still challenging (Figures 4 and 5), as observed in previousstudies (Qiao et al., 2015; Place and Malehmir, 2016). The presence
Figure 8. First-break tomographic inversions using traveltimes picked on (a) raw first arrivals, (b) supervirtual first arrivals (using crosscor-relation), and (c) supervirtual first arrivals (using crosscoherence). Associated ray density sections are given in (d-f), respectively.
Figure 9. The same as Figure 8c with contours instead of color scale and arrows for enhancing the velocity gradients. Colored bands on the toprefer to the geologic units mapped in Figure 2, using the same color code. The figure is shown with a slight vertical magnification.
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of direct and refracted waves in short-offset traces may create ar-tifacts through the processing. Moreover, at short offsets, the bodywaves are strongly contaminated by surface waves. The presence ofsurface waves, direct body waves, and (virtual) refracted waves, allpotentially retrieved by SI, could therefore explain the limited effi-ciency of the retrieval techniques at short offsets. Fortunately, theraw data generally offer a fair depiction of the first arrivals at shortoffsets, whereas the supervirtual data are more reliable at larger off-sets, which makes the integration of the picks a satisfactory solution(see another example in Place and Malehmir, 2016). In the future,muting all traces within the crossover distance of the refracted arriv-als could be a solution to this problem, although this may requiresome manual sorting.The approach described in this paper is generalizable to 3D data
sets (An et al., 2015), provided that the azimuthal information of thesource and receiver pairs is considered. In such contexts, theoreticalstudies indicate that direct, refracted, and surface waves can be re-trieved with great efficiency because sources are located at the sur-face and surround the receiver pairs (Wapenaar et al., 2010a).However, deeper sources are still missing to enable the goodretrieval of the reflections. Using ambient body-wave noise fromsources at depth (e.g., blasting and drilling) may be a solution tothis problem. In our study area, this type of noise is generatedtoo far away to be usable for this purpose. A 3D receiver grid,allowing for better studying azimuthal changes, is better suitedshould ambient noise be used for reflection-imaging purposes.
Geologic findings
Tying geophysical data (in this paper P-wave velocity) with geo-logic information (the severity of the weathering) has been no easytask for earth scientists. It is particularly difficult when character-izing weathering because no scale system has yet captured the in-tensity of weathering, therefore preventing any straightforward linkwith the P-wave velocity estimates. Nevertheless, because velocityvariations in our data extend over one order of magnitude(Figure 8) and mechanical weakening accompanies weathering(Goodfellow et al., 2016), we suggest that the tomographic imagesof our study represent a reasonable first-order estimate ofweathering.Compartmentalization of weathering has been reported previ-
ously as controlled by faults of various scales (Place et al.,2016). This could also be the case for our data and, thus, partlyaccount for the observed differential velocity patterns (Figure 8a).However, the presence of velocity gradients in all directions point-ing toward isolated blobs of relatively fast velocity materials (Fig-ure 8b) suggests the preservation of kernels as weathering develops.This is consistent with our previous statement that the anomalies inthe seismic images cannot reasonably be interpreted as a result offaulting alone. Kernels have been reported as “corestones” at themeter to decameter scale (e.g., Røyne et al., 2008), and they areknown as tors when reaching the surface and expressing themselvesas prominent morphological features (e.g., Goodfellow et al., 2014).Such tors are not observed here.Figure 9 shows that the P-wave velocity field does not exhibit any
particular relation to the topographic surface as observed in othercase studies (St Clair et al., 2015). We interpret this as being due totopographic variations that are not sufficiently pronounced in thispart of the world to influence the stress field. Consequently, thestress field is dominated by lithostatic pressure (Bird et al., 2006).
The smooth velocity increase observed in the first tens of meterssuggests that our tomographic image is in a near-vertical plane.Nevertheless, due to the horizontal variations in the velocity fieldat greater depth, closely spaced 2D profiles, or 3D acquisitionwould be useful in this geologic environment for taking into ac-count off-profile ray propagation and accurately locating the veloc-ity anomalies. Regardless, recording of active seismics with largeoffsets at the scale of several kilometers in such heavily weatheredmaterials is not common (Parsekian et al., 2015), but our resultsshow that our methodological developments improve the scopeof seismic methods in this case. Although this study illustratesthe efficiency of SI to increase the penetration and resolution, de-fining the bottom of the CZ in such environments (Riebe et al.,2016) is still a technical issue (efficiency of the geophysical meth-ods), as well as a conceptual problem (fresh rocks can be preservedwithin a regolith). We anticipate that further applications of SImethods may provide useful insights about the CZ structure andits dynamics, as well as resources such as, to name but a few, drink-ing water, geothermal energy, and mining.
CONCLUSIONS
Weathered rocks impede the propagation of seismic waves,which makes them a challenging target for seismic imaging. Weinvestigated the use of SI to improve the S/N of the first arrivalsand, in this manner, combat the strong attenuation present alonga 3.5 km long profile acquired in heavily weathered materials inZambia. Because two sources with different signatures and energywere used in this acquisition, we have introduced the use of cross-coherence, instead of crosscorrelation as is usually done, to the in-terferometric retrieval of first arrivals while forming one integrateddata set. About twice as many first breaks could be picked on thedata after this process, which enabled greater penetration and res-olution in the subsequent tomographic imaging. Instead of a smoothand large-scale weathering front, our data revealed the preservationof high-velocity material, interpreted as fresh rock, in the form ofkernels embedded in the regolith, therefore exemplifying prominentdifferential weathering laterally and vertically. By illustrating theefficiency of the seismic imaging over an unusually long profilein such heavily weathered materials, this study exemplifies new ap-proaches to unlock the potential of seismic imaging in, and below,the CZ. Even though crosscoherence seems superior to cross-correlation to retrieve first arrivals in the conditions of the seismicexperiment presented here, much effort is still required to interfero-metrically retrieve denoised first arrivals of higher fidelity comparedwith those of the raw data.
ACKNOWLEDGMENTS
We would like to thank First Quantum Minerals for funding thedata acquisition and Uppsala University (UU) and the TechnicalUniversity of Delft for supporting part of this research throughthe Smart Exploration project. Smart Exploration has received fund-ing from the European Union’s Horizon 2020 research and inno-vation programme under grant agreement no. 775971. We thankthe three anonymous reviewers whose comments helped to improvethis manuscript. We are also grateful to our colleagues at the Depart-ment of Earth Sciences of UU for acquiring the seismic data used inthis study. We would also like to thank B. Goodfellow (the Geo-logical Survey of Sweden), K. Lidmar-Bergström (Stockholm
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University), J. Lehmann (University of Johannesburg), S. Le Cam(University of Lorraine), and H. Sadeghisorkhani (UU) for con-structive discussions as well as A. Tryggvason (UU) for providingus with PStomo_eq. GLOBE Claritas under license from the Insti-tute of Geological and Nuclear Sciences Limited, Lower Hutt, NewZealand was used to carry out part of the seismic data preparationand processing.
DATA AND MATERIALS AVAILABILITY
Data associated with this research are available and can be ob-tained by contacting the corresponding author.
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