Shallow oceanic crust: Full waveform tomographic images of the seismic layer 2A/2B boundary

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jb008972, 2012 Shallow oceanic crust: Full waveform tomographic images of the seismic layer 2A/2B boundary Gail L. Christeson, 1 Joanna V. Morgan, 2 and Michael R. Warner 2 Received 25 October 2011; revised 20 March 2012; accepted 21 March 2012; published 3 May [1] We present results of full-waveform tomographic inversions of four profiles acquired over young intermediate- and fast spreading rate oceanic crust. The mean velocity-depth functions from our study include a km-thick low-velocity, low-gradient region beneath the seafloor overlying a km-thick high-gradient region; together these regions compose seismic layer 2A. Mean layer 2A interval velocities are km/s. The mean depth to the layer 2A/2B boundary is km, and mean velocities within the upper 0.25 km of layer 2B are km/s. Previous velocity analyses of the study areas using 1-D ray tracing underestimate the thickness of the high-gradient region at the base of layer 2A. We observe differences in the waveform inversion velocity models that correspond to imaging of the layer 2A event; regions with a layer 2A event have higher velocity gradients at the base of layer 2A. Intermittent high velocities, which we interpret as massive flows, are observed in the waveform inversion velocity models at km below the seafloor (bsf) over 10 25% of the intermediate-spreading profiles and 20 45% of the fast spreading profiles. The high-gradient region located km bsf at the base of layer 2A may be associated with an increased prevalence of massive flows, the first appearance of dikes (lava-dike transition zone), or with increased crack sealing by hydrothermal products. The upper portion of layer 2B, which begins at km bsf, may correspond to sheeted dikes or the top of the transition zone of lavas and dikes. Citation: Christeson, G. L., J. V. Morgan, and M. R. Warner (2012), Shallow oceanic crust: Full waveform tomographic images of the seismic layer 2A/2B boundary, J. Geophys. Res., 117,, doi: /2011jb Introduction [2] The seismic layer 2A/2B boundary maps a significant increase in seismic velocities in young oceanic crust. This boundary has now been imaged in multichannel seismic (MCS) reflection data from studies at slow-spreading ridges [Peirce et al., 2007; Seher et al., 2010], intermediatespreading ridges [e.g., Carbotte et al., 2000; Blacic et al., 2004; Baran et al., 2005; Canales et al., 2005; Van Ark et al., 2007; Christeson et al., 2010], and fast spreading ridges [e.g., Harding et al., 1993; Kent et al., 1994; Carbotte et al., 1997; Christeson et al., 2007]. Models for the nature of this boundary include a geological contact between high-porosity basaltic lavas and a lower-porosity 1 Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA. 2 Department of Earth Science and Engineering, Imperial College London, London, UK. Corresponding Author: G. L. Christeson, Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, J.J. Pickle Research Campus, Mail Code R2200, Burnet Rd., Austin, TX 78758, USA. (gail@ig.utexas.edu) Copyright 2012 by the American Geophysical Union /12/2011JB sheeted dike complex [e.g., Herron, 1982; Toomey et al., 1990; Christeson et al., 1992; Harding et al., 1993], an alteration boundary within the lava unit [Rohr et al., 1988; Harding et al., 1989; Vera et al., 1990], a lithologic transition from low-temperature hydrous alteration above to hydrothermal alteration below occurring near the top of the lavadike transition zone [Carlson, 2011], or a complex boundary that varies as the crust spreads laterally from the ridge axis to the ridge flanks [Karson and Christeson, 2003; Christeson et al., 2010]. [3] At all spreading rates the layer 2A/2B boundary is observed at m below the seafloor (bsf) away from the ridge axis [Harding et al., 1993; Kent et al., 1994; Carbotte et al., 1997, 2000; Blacic et al., 2004; Baran et al., 2005; Canales et al., 2005; Christeson et al., 2007; Peirce et al., 2007; Van Ark et al., 2007; Christeson et al., 2010; Seher et al., 2010], which strongly implies that a fundamental process is occurring at these depths in young oceanic crust. However, the details of this seismic boundary are still poorly constrained. Forward and inverse methods to match the seismic waveform have modeled the onedimensional (1-D) velocity structure of layer 2A and the layer 2A/2B boundary at a few locations [Harding et al., 1989; Vera et al., 1990; Christeson et al., 1994a; Kappus et al., 1995; Tolstoy et al., 1997; Hussenoeder et al., 1of25

2 Figure 1. (a) Generic velocity-depth function for young oceanic crust. Layer 2A consists of an upper low-gradient region and underlying high-gradient region. Layer 2B reaches velocities of 5 6 km/s. (b) Velocity plotted against depth bsf from studies of young oceanic crust at the northern (blue, Harding et al. [1989]; red, Vera et al. [1990]; green, Christeson et al. [1994a]; cyan, Kappus et al. [1995]) and southern (maroon, Tolstoy et al. [1997]; orange, Hussenoeder et al. [2002a]) EPR. 2002a, 2002b], but no equivalent two-dimensional (2-D) studies have been performed. [4] In this study we use full-waveform tomography [e.g., Virieux and Operto, 2009] to produce high-resolution 2-D velocity models of shallow oceanic crust along 4 profiles acquired over young crust produced at the intermediatespreading rate Juan de Fuca Ridge and the fast spreading rate East Pacific Rise (EPR). We compare the models with observations from nearby seafloor escarpments and two deep drill holes, and evaluate the models to determine if any properties evolve with distance from the ridge axis. We also use our results to ground-truth previous methods for determining layer 2A thicknesses along these profiles. One new result from our study is the observation of intermittent high velocities at km bsf which we interpret as massive flows present over 25% of our profiles. 2. Background 2.1. Seismic Layer 2A and the Layer 2A/2B Boundary [5] Compilations of seismic refraction results divide the ocean crust into layer 2 and layer 3, where layer 2 has a highvelocity gradient with velocities increasing from 2 to 4 km/s at the seafloor to km/s at 2 km depth, and layer 3 has a low-velocity gradient with mean velocities of 7.2 km/s at the base of the crust [White et al., 1992]. Houtz and Ewing [1976] used sonobuoy data to further subdivide layer 2 into a layer 2A (3.6 km/s), layer 2B (5.2 km/s), and layer 2C (6.1 km/s). The focus of our study is the structure of layer 2A and the layer 2A/2B boundary. [6] Several studies have used 1-D forward modeling [Harding et al., 1989; Vera et al., 1990; Christeson et al., 1994a] or inversions [Kappus et al., 1995; Tolstoy et al., 1997; Hussenoeder et al., 2002a] to match waveforms from seismic studies of young ocean crust on the northern and southern EPR. The resulting velocity models typically have a low-gradient layer at the seafloor with velocities of 2 3 km/s underlain by a high-gradient region with velocities of 5 6 km/s reached at depths bsf of km (Figure 1). The low-gradient seafloor layer and underlying high-gradient region are referred to as layer 2A [Harding et al., 1989; Vera et al., 1990; Christeson et al., 1994a; Kappus et al., 1995; Tolstoy et al., 1997; Hussenoeder et al., 2002a]. [7] Representative shotgathers from seismic reflection profiles over young ocean crust are displayed in Figure 2. Energy turning within the high-gradient region at the base of layer 2A forms a caustic observed after the seafloor reflection, and energy refracting through layer 2B is observed as a first arrival at the longer offsets. Although the caustic is not a true reflection, modeling indicates that proper processing while stacking data can place this energy near the layer 2A/ 2B boundary [e.g., Harding et al., 1993; Vera and Diebold, 1994]. The result is a reflection-like event which can be readily mapped in MCS reflection profiles over young oceanic crust (Figure 3) Geologic Setting [8] The Blanco study region is located near the intersection of the southern Juan de Fuca Ridge and the Blanco transform fault (Figure 4a). The Cleft segment is spreading at an intermediate rate of 30 mm/yr (halfrate) [Delaney et al., 1981], and exhibits a well-defined axial magma chamber reflector at a depth of km bsf [Canales et al., 2006]. The Hess Deep study region is located near the intersection of the fast spreading EPR (65 mm/yr half-rate) and the Hess Deep rift, which is a broad rift valley near the tip of the westward-propagating Cocos-Nazca spreading center (Figure 4b) [Searle and Francheteau, 1986; Lonsdale, 1988]. An incipient rift has been identified as forming a portion of the northern boundary of the Galapagos microplate near the Hess Deep study region [Lonsdale, 1988; Klein et al., 2005; Schouten et al., 2008], but seafloor fabric indicates that it does not yet intersect the seismic profiles used in this study (Figure 4b). Crust generated at the Juan de Fuca ridge and EPR is exposed along the 2of25

3 Figure 2. Representative shot gathers for (a) BL102, shot 1450; (b) BL302, shot 203. Data have been band-pass filtered with a low cut of 3 5 Hz and a high-cut of Hz. The amplitudes have been range scaled by a factor of R 1.0, where R is the distance of the shot from the receiver. Both shot gathers are at approximately the same location, except that BL102 was shot at 37.5-m (16-s) spacing and BL302 at 200-m (96-s) spacing. northern walls of the Blanco transform fault and Hess Deep rift, respectively. The geologic stratigraphy has been characterized at both study regions using manned submersibles and remotely operated vehicles [Francheteau et al., 1990, 1992; Juteau et al., 1995; Tivey et al., 1998; Karson et al., 2002a, 2002b]. [9] The uppermost unit at both locations is composed of undeformed basaltic lavas which are primarily intact pillow lavas, with lesser lobate and tabular flows [Karson et al., 2002a, 2002b]. This unit is underlain by a transition zone containing intensely fractured basaltic lavas and dikes where flow morphologies are only rarely preserved [Karson et al., 2002a, 2002b]. Underlying the transition zone is a sheeted dike unit that is variably fractured and where the dikes predominantly dip away from the spreading center [Karson et al., 2002a, 2002b]. Although the character of the units are similar at both study region their thickness is not: at the Blanco transform fault the lava and transition zone units are 450 m and 700 m, respectively, while at the Hess Deep rift the units are 300 m and 150 m, respectively [Karson et al., 2002a, 2002b]. The average depth to the top of the sheeted dike complex is 1150 m for the intermediate-spreading crust exposed at the Blanco transform fault, and 450 m for the fast spreading crust exposed at the Hess Deep rift [Karson et al., 2002a, 2002b] Seismic Profiles [10] MCS profiles were acquired by the R/V Maurice Ewing at the Hess Deep and Blanco survey regions in July 2003 and October 2004, respectively. The source for BL102, BL109, HD101, and HD111 (Figure 4) was an array of 10 air guns with a total volume of 3,050 cubic inches fired at 37.5 m intervals at a depth of 7 m (Hess Deep profiles) or 8 m (Blanco profiles). The eastern off-axis portions of these profiles were reshot with an array of 12 air guns with a total volume of 3,705 cubic inches fired at a longer shot interval of 150 m (HD311) or 200 m (HD301, BL302, and BL309) to minimize previous shot noise on ocean bottom seismograph data [Christeson et al., 1996]. Data were recorded on a 6 km long hydrophone cable with 480 channels towed at a 3of25

4 Figure 3. Migrated stacks for (a) BL102; (b) BL109; (c) HD101; (d) HD111. Stacks are plotted with a minimum phase time domain filter and a 2 s automatic gain control. The red line shows the picked layer 2A event. AMC, axial magma chamber reflector. depth of 8 m (Hess Deep profiles) or 9 m (Blanco profiles). The slightly different acquisition parameters on the Blanco survey were an effort to better image the deeper structure (deeper source depth) and to decrease noise on the hydrophone cable (deeper cable depth). Weather conditions for both surveys were similar with knot winds. Equipment failures and marine mammal mitigation measures resulted in data acquisition gaps of <2 km for profiles HD101, HD111, and HD311. [11] Processing of the profiles shot at 37.5 m shot interval is described in Christeson et al. [2010]. In brief, MCS data were binned, filtered, amplitudes were corrected for spherical divergence, a predictive deconvolution was applied, initial velocity analyses were performed to flatten the layer 2A caustic [Harding et al., 1993], a parabolic Radon transform was applied to enhance the signal of the layer 2A caustic [Christeson et al., 2010], velocity analyses were refined, a normal moveout was applied, data were stacked, and a poststack F-K migration was applied using a constant velocity of 1.4 km/s. The migrated profiles are displayed in Figure 3. [12] The layer 2A event is observed intermittently at a mean two-way travel time (twtt) beneath the seafloor of s on all profiles (Figure 3). The layer 2A event is observed over 80 90% of profiles BL102 (Figure 3a) and HD111 (Figure 3d), is absent or poorly imaged on the 4of25

5 Figure 4. Bathymetry of (a) Blanco and (b) Hess Deep seismic experiment study areas. White lines mark plate boundary, and red lines mark seismic profiles presented in this study. BT, Blanco transform; EPR, East Pacific Rise; HDR, Hess Deep rift; IR, Incipient rift; JDF, Juan de Fuca spreading center. (c) Regional setting of the Blanco and Hess Deep seismic experiments. Red asterisks show the two study areas. southeast end of BL109 (Figure 3b), and is observed over 70% of HD101 (Figure 3c). The signal-to-noise of the layer 2A event is higher in the Blanco study area than in the Hess Deep study area. 3. Waveform Tomography 3.1. Method [13] Waveform tomography typically uses travel time tomography to obtain a starting model and then iteratively uses waveform inversion to minimize the misfit of synthetic and observed wavefields. Full-wavefield tomography has a potential resolution of around the seismic wavelength [Wu and Toksöz, 1987], which is typically an order of magnitude better than that of travel-time tomography. For our study we use a 2-D frequency domain viscoacoustic code [Pratt et al., 1996; Pratt, 1999]. The code computes the numerical solution of the wave equation by finite differences in the frequency domain, which generates all wave types within a given model and can be used to simulate very complex seismic wavefields. Imaging starts with the low-wave number model obtained from traveltime tomography, and at each imaging frequency, the synthetic response of the current model is computed. The model is iteratively built as the code steps through the frequencies, and the final velocity model includes all imaging frequencies. A full description of the underlying theory and codes can be found in Pratt et al. [1998], Pratt [1999], and Brenders and Pratt [2007a, 2007b]. This method has been successfully applied to marine data from various geologic environments, including North Sea gas sands [Hicks and Pratt, 2001; Prieux et al., 2011], the eastern Nankai subduction zone [Operto et al., 2006], Faeroe Basin basalts [Chironi et al., 2006], an oceanic core complex [Canales, 2010], Queen Charlotte Basin [Takougang and Calvert, 2011], the Chicxulub impact crater [Morgan et al., 2011], and the Scotian Slope [Delescluse et al., 2011]. 5of25

6 Figure 5. (a) Starting model for waveform inversion of a portion of profile BL109. (b) Waveform inversion velocity models for 20-km-long overlapping regions of BL109. White dashed lines outline the area that corresponds to full-fold CDPs for each inversion; these areas are considered well-resolved. (c) Merged waveform inversion velocity model constructed from well-resolved regions of BL109. [14] The full-waveform inversion code makes a number of approximations to the physics of wave propagation: (1) The wave equation is solved in only two dimensions; (2) Attenuation is included in the forward modeling step but not updated during the inversion process; (3) The forward code is acoustic and does not include elastic effects; (4) There is a fixed relationship between velocity and density; and (5) There is no form of anisotropy included in the inversion. These approximations have consequences for the preprocessing of the field data, and especially for the way in which we have handled amplitude information during the inversion process. Warner et al. [2012] have looked in detail on these effects on synthetic 2-D and 3-D fullwaveform inversions. They also studied the effects of various strategies for dealing with amplitudes during inversion in the presence of these approximations and uncertainties. They conclude that the best strategy for inverting pressure data acquired in 2-D was to use 2-D (not 3-D) inversion, to 6of25

7 Figure 6. Results from a suite of inversions testing different starting models for a section of BL109. (a) Inversion using preferred starting model. Dashed lines mark depth to top and bottom of 0.4-kmthick high-gradient region at the base of layer 2A in starting model. (b) As for Figure 6a, except that layer 2A/2B boundary in starting model is 0.1 km deeper than preferred starting model. (c) As for Figure 6a, except that layer 2A/2B boundary in starting model is 0.1 km shallower than preferred starting model. (d) Velocity plotted versus depth at distances of 8 and 11 km for the waveform inversion velocity models generated from starting models with layer 2A/2B boundary at preferred depth (green), 0.1 km deeper (red), and 0.1 km shallower (blue). (e) Errors at each iteration at 6 and 7 Hz for the inversions generated from starting models with differing layer 2A/2B boundary depths. Color scheme is same as Figure 6d. See text for description of the error values. (f) As for Figure 6a, except that thickness of high-gradient region at base of layer 2A in starting model is 0.1 km thick. (g) As for Figure 6a, except that thickness of high-gradient region at base of layer 2A in starting model is 0.3 km thick. (h) As for Figure 6a, except that thickness of high-gradient region at base of layer 2A in starting model is 0.5 km thick. (i) Velocity plotted versus depth at distances of 8 and 11 km for the waveform inversion velocity models generated from starting models with thickness of high-gradient region at base of layer 2A of 0.1 km (red), 0.3 km (blue), 0.4 km (green, preferred starting model), and 0.5 km (magenta). (j) Errors at each iteration at 6 and 7 Hz for the inversions generated from starting models with differing thicknesses of the highgradient region at the base of layer 2A. Color scheme is same as Figure 6i. 7of25

8 amplitudes, at a single frequency, trace-by-trace. We do not seek to model correctly, or to invert, relative or absolute amplitude between traces or between frequencies. Warner et al. [2012] show that this strategy recovers p-wave velocity from pressure data correctly. Its principal deleterious effect is that is loses some spatial resolution in comparison to the theoretical maximum, especially in deeper parts of a model when sub-surface coverage is less than optimal. It does however recover the correct absolute p-wave velocities, in their correct sub-surface locations, mapped from 3-D into the line of the 2-D section. Figure 7. Results from a suite of inversions with bottom mutes (a) 0.28 s; (b) 0.18 s; (c) 0.08 s after the top mute for the input data of a section of BL109. Dashed lines mark depth to top and bottom of 0.4-km-thick high-gradient region at the base of layer 2A in starting model. (d) Velocity plotted versus depth at distances of 8 and 11 km for the models with bottom mute 0.28 s (red), 0.18 s (green), and 0.08 (blue) after top mute in the input data. include an approximate model of attenuation whenever possible, and to include the kinematic effects of anisotropy where these are genuinely recoverable. They also conclude that it is not necessary or justified to include elastic or density effects because the uncertainties introduced by working in only two-dimensions are already larger than these effects. [15] Warner et al. [2012] also show that it is important to deal with amplitudes using a strategy that is consistent with the approximations that have been made in the forward modeling. We proceed therefore by flattening all the amplitude spectra of the field data so that all frequencies are present at the same amplitude, and normalizing all trace amplitudes to the same single value. We apply this trace and frequency equalization to both observed and predicted data during the inversion. This approach suppresses all amplitude-versus-offset effects, and all other variations of amplitude with position. We do model and invert 3.2. Implementation [16] An example shotgather from BL102 is displayed in Figure 2a; first arriving energy after the direct water wave include a seafloor reflection at near offsets and a layer 2B refraction at far offsets. As expected, the arrivals are more clearly observed on profile BL302 shot at 200-m spacing (Figure 2b). Christeson et al. [2007, 2010] carried out velocity analyses on selected CDP supergathers from the Blanco and Hess Deep survey regions using 1-D ray-tracing. They model a layer 2A with velocities of km/s directly beneath the seafloor underlain by a 100-m-thick high-gradient region where velocities of 4 5 km/s (layer 2B) are reached at a depths of m bsf. Thus we constructed a 2-D starting velocity model for each profile that included these layers (water column, upper layer 2A, high-gradient region at base of layer 2A, layer 2B). [17] We obtained water column velocities from the mean water sound velocity for each study region using a global database [Levitus, 1982] and the MB-System command mblevitus ( We calculated seafloor depths by picking the seafloor reflection on migrated MCS profiles and converting to depth using the water velocities. The crustal portion of the starting velocity model was constructed by using the Zelt and Smith [1992] inversion scheme. Layer 2B refraction first arrival travel times associated with layer 2B refractions cannot constrain layer 2A velocities or the thickness of the high-gradient zone at the base of layer 2A, and thus layer 2A velocity was set to 2.65 km/s and the travel times were inverted for variable layer 2A thickness (at a 1-km spacing) and a constant layer 2B velocity. Models were also tested that included variable layer 2B velocities, but the additional nodes were not required to fit the travel time picks to within their uncertainties. The layer 2A/2B boundary was then modified to include a 400-m-thick high-gradient region at the base of layer 2A; this thickness was chosen because smooth starting models are preferable to sharp boundaries for full-wavefield inversions [Morgan et al., 2011]. The final models fit the layer 2B refraction travel time picks to s for the Blanco profiles, and s for the Hess Deep profiles. Figure 5a displays a sample starting model. [18] Data preprocessing consisted of (a) bandpass filter with a low-cut of 3 Hz and a high-cut of 18 Hz; (b) resample to 16 ms; (c) top mute (0.1 s above the first arrival) and bottom mute (5.0 s); (d) trace equalize; (e) add water wave to real data; water wave is generated through the water column in the starting model using the source wavelet that is used in the inversion; (f) decimate 37.5-m shot spacing data to 75-m shot spacing; (g) decimate data to 25-m channel 8of25

9 Figure 8. Results from a suite of inversions testing different input attenuation fields for a section of BL109. (a) Inversion using an input attenuation field of Q = 500 in ocean crust, and Q = in the water column. Dashed lines mark depth to top and bottom of 0.4-km-thick high-gradient region at the base of layer 2A in starting model. (b) As for Figure 8a, except Q = 50 in ocean crust. (c) As for Figure 8a, except Q = 25 from seafloor to top of high-gradient region within layer 2A, and then linearly increases to Q = 500 at the top of layer 2B. (d) As for Figure 8a, except Q = 25 from seafloor to top of high-gradient region within layer 2A, and then linearly increases to Q = 100 at the top of layer 2B. (e) Velocity plotted versus depth at distances of 8 and 11 km for the waveform inversion velocity models generated from different input attenuation fields with Q = 500 in ocean crust (red), Q = 50 in ocean crust (green), Q =25in layer 2A and Q = 500 in layer 2B (blue), and Q = 25 in layer 2A and Q = 100 in layer 2B (yellow). (f) Errors at each iteration at 6 and 7 Hz for the inversions testing different input attenuation fields. Color scheme is same as Figure 8e. See text for description of the error values. spacing; (h) apply an exponential decay to the data with a time constant of 2.4 s. [19] Inversions were run using a grid spacing of 12.5-m with 10 iterations of 7 different frequencies from 6 to 12 Hz. The source wavelet is computed using near-offset data of the seafloor reflection and first multiple using the method of Warner [1990]. Densities were calculated from velocities using Gardner s relation [Gardner et al., 1974]. Owing to computational limitations, each profile is divided into overlapping 20-km segments and the resulting velocity models are merged (Figure 5). Errors are measured by the mean squared difference between the observed and predicted objective function at each frequency. The absolute value of the objective function is dependent on amplitude values in the input data set and cannot be easily compared between differing frequencies or differing data sets, but can be compared at each frequency for each data set. For the Blanco profiles, the error reduction is 12 24% at frequencies of 6 7 Hz, 21 45% at 8 10 Hz, and 49 66% at Hz. For the Hess Deep profiles the error reduction is 17 50% at 6 7 Hz, 27 60% at 8 10 Hz, and 59 67% at Hz. The greater error reduction for the Hess Deep profiles compared to the Blanco profiles might be the result of adding heterogeneities to fit the noisier data present in the Hess Deep data sets Inversion Sensitivity Starting Model [20] We ran a suite of inversions to test the sensitivity of the inversion to our chosen starting model using a section of profile BL109. We varied both the depth of the layer 2A/2B boundary and the thickness of the high-gradient region at the base of layer 2A; results are displayed in Figure 6. Varying the depth of the layer 2A/2B boundary has a significant effect on the resulting waveform inversion velocity models; mean differences in the crustal velocities for the sections plotted in Figures 6b and 6c are km/s compared to Figure 6a. A comparison of velocities at distances of 8 and 11 km demonstrates that the layer 2A/2B boundary depths vary by km between the 3 models. All 3 inversions reduce the error at each iteration, but the inversions using the preferred starting model provides the best initial and final fit (Figure 6e). These tests confirm the importance of choosing a starting velocity model that matches the main phases in the observed data to within half a cycle at the lowest inversion frequency [Sirgue and Pratt, 2004; Virieux and Operto, 9of25

10 Figure 9. Waveform inversion velocity models for (a) BL102; (b) BL302; (c) BL109; (d) BL309. The top and base of high-gradient region at the base of layer 2A are shown by white lines. Black circles display picked layer 2A event from seismic profiles BL102 and BL109 converted to depth using the waveform inversion velocity models. 2009]. Our inversions start at 6 Hz, hence the travel-time match should be better than s; differences larger than this can result in cycle-skipping and convergence toward a local minimum [Virieux and Operto, 2009]. Shifting the layer 2A/2B boundary by 0.1 km results in differences by as much as 0.1 s for the calculated arrivals, and thus the differences in the inversion results displayed in Figure 6 are likely an artifact of cycle-skipping. We have generated phase plots for both the observed and synthetic data generated from the preferred starting model, following the methodology used in Shah et al. [2010]. These plots show that the phase varies smoothly from trace-to-trace, and therefore that our synthetic data are not cycle-skipped. [21] Varying the thickness of the high-gradient region at the base of layer 2A from 0.1 to 0.5 km in the starting model has a lesser effect on the inversion results (Figures 6f 6h). A comparison of velocity models at distances of 8 and 11 km (Figure 6i) shows that the thickness of the highgradient region is similar for all inversions except that of the 0.1-km-thick starting model, with thicknesses of km and km at distances of 8 and 11 km, respectively, for the km-thick starting models. Plots of the errors for frequencies of 6 and 7 Hz show that the best initial and final fits are obtained for starting models with high-gradient region thicknesses of km, confirming that smooth starting models are preferable to sharp boundaries for full-wavefield inversions [Morgan et al., 2011]. Mean velocity differences between the inversions derived from these starting models are km/s compared to our preferred starting velocity model. [22] The waveform inversion is weighted to increase the effect of later arrivals which have less energy; an artifact of this weighting is the appearance of heterogeneities in the deeper parts of the model. In Figure 6 the velocity anomalies in the uppermost crust are apparent in the different waveform inversion tests, whereas those in the deeper crust are not reproduced. The layer 2B refractions will constrain the average velocities in the upper part of layer 2B, but we consider the short wavelength heterogeneities in this region to be poorly resolved Data Preprocessing and Inversion Parameters [23] Our data is preprocessed with a top mute 0.1 s above the first arrival and a bottom mute at 5.0 s; this passes through the sea-bottom reflection, the 2A/2B caustic, and the 2B refraction which are the main phases in the observed data, but also passes through scattered energy. The scattered energy is random and inconsistent from shot-toshot, so the inversion should be fitting the main phases. To test this we ran inversions with data preprocessed with bottom mutes that were 0.8, 1.8, and 2.8 s after the initial mute. These mute windows still pass through the phases of interest, but should reduce the amount of scattered energy. The resulting velocity models are similar, with mean velocity differences compared to our original inversion result of km/s (Figure 7). We conclude that scattered energy is not driving the inversion. [24] The inversion requires an input density field, which were calculated from velocities using Gardner s relation [Gardner et al., 1974]. Gardner s formula was derived for sediments, and thus might not be appropriate for oceanic crust. Thus we also ran an inversion where we calculated densities using the relationship for basalts of Christensen and Shaw [1970], which predicts slightly higher densities ( g/cc). The mean velocity difference between this velocity model and the original velocity model is 0.02 km/s, and we conclude that the inversion results are not strongly dependent on the relationship we used for calculating density values. [25] Our inversions were run with no attenuation (infinite Q). Direct measurements of Q values in shallow ocean crust are difficult to obtain from conventional experiments, but have been estimated from experiments with both sources and receivers on or near the seafloor. A study of Ma EPR crust models a Q of in layer 2A and Q in layer 2B [Christeson et al., 1994a, 1994b], while a study of 0.4 Ma Juan de Fuca crust models a Q of to depths of 0.65 km [Jacobson and Lewis, 1990]. Thus we 10 of 25

11 Figure 10. Waveform inversion velocity models for (a) HD101; (b) HD301; (c) HD111; (d) HD311. The top and base of high-gradient region at the base of layer 2A are shown by white lines. Black circles display picked layer 2A event from seismic profiles HD101 and HD111 converted to depth using the waveform inversion velocity models. White dashed lines mark regions with missing shots where velocity model may be poorly constrained. might expect Q values of within layer 2A, and similar or higher values in layer 2B. Our acoustic inversion does not invert for attenuation, but does allow an input attenuation field to be given. Therefore we tested the effects of varying Q on the inversion result, and display the results in Figure 8. For our input attenuation fields we set Q = in the water column, and tested four models for the ocean crust: (1) Q = 500 below the seafloor; (2) Q = 50 below the seafloor [Jacobson and Lewis, 1990]; (3) Q = 25 in layer 2A and 500 in layer 2B [Christeson et al., 1994a]; (4) Q = 25 in layer 2A and 100 in layer 2B [Christeson et al., 1994b]. For the models with a change in attenuation across the layer 2A/2B boundary we linearly increased Q within the high-gradient region at the base of layer 2A. The error plots do indicate that a Q of may be appropriate within layer 2A (Figure 8f), but the mean velocity differences between the models are small ( km/s compared to the original model). The patterns of layer 2A thickening and thinning are similar for all models; the major difference is a somewhat smoother Vp model for models with high attenuation. We conclude that the full waveform inversion result is stable and relatively insensitive to the poorly constrained attenuation parameter. [26] Our inversions were conducted using frequencies of 6 12 Hz. Waveform inversions often do not use high frequencies because nonlinearity increases with increasing frequency, owing to accumulated inaccuracies in the inverted velocity model at lower wave numbers [Sirgue, 2003]. We tested including frequencies up to 16 Hz, but mean velocity differences in the inversion results were <0.1 km/s compared to our original models. We therefore did not invert for frequencies higher than 12 Hz. 4. Results 4.1. Velocity Models [27] The waveform inversion velocity models are displayed in Figures 9 and 10. The waveform inversion velocity models are similar to the starting models with low velocities near the seafloor, an underlying high-gradient region, and velocities of km/s at depths of km bsf. However, the inversion results include more detailed structure with short-wavelength lateral variability in velocities; in 11 of 25

12 Figure 11. Layer 2A and high-gradient region thicknesses from the waveform inversion velocity models plotted against distance from ridge for (a) BL102/BL302; (b) BL109/BL309; (c) HD101/HD301; (d) HD111/HD311. The dashed lines are a linear fit to the BL102, BL109, HD101, and HD111 values; the correlation coefficient for each fit is labeled. addition, a velocity inversion is sometimes observed within the uppermost 0.3 km. The overlapping profiles shot at sparser shot spacing (BL302, BL309, HD301, and HD311) provide one estimate of the reproducibility of model features. Overall, there is good agreement in the major features of the velocity models for the overlapping profiles and hence, for the rest of our study, we will only present results from profiles BL102, BL109, HD101, and HD111. [28] For all profiles we picked the top and base of the layer 2A high-gradient region (white lines on Figures 9 and 10). These picks were done by hand, guided by closely spaced velocity contours. We then calculated highgradient region thickness (Figure 11), layer 2A interval velocities (Figure 12), and average velocity within the top 0.25 km of layer 2B (Figure 12). Note that we are only using velocities from the upper portion of layer 2B since this is the only region resolved by the layer 2B refractions. The mean value of these measurements are similar for all profiles, with no significant differences between the Blanco and Hess Deep study regions (Table 1). Layer 2A has an average thickness of km, composed of a km low-gradient region overlying a km high-gradient region. There appears to be more spatial variability in the thickness of the low-gradient region compared to the high-gradient region in the velocity models (Figures 9 and 10), which is confirmed by differences in standard deviations for thickness values (Table 1). Average interval velocities within layer 2A are km/s, and average velocities at the top of layer 2B are km/s. [29] Model thickness and velocity values are plotted against distance from the ridge axis in Figures 11 and 12. There is no systematic correlation of layer 2A thickness, high-gradient region thickness, or layer 2B velocity with distance from the ridge axis, with slight positive, negative, or 12 of 25

13 Figure 12. Layer 2A and Layer 2B velocities plotted against distance from ridge for (a) BL102/BL302; (b) BL109/BL309; (c) HD101/HD301; (d) HD111/HD311. Layer 2A velocities are interval velocities calculated from the waveform inversion velocity models (Figures 9 and 10) and the picked layer 2A thicknesses (Figure 11). Layer 2B velocities are average velocities in the uppermost 0.25 km of layer 2B. The dashed lines are a linear fit to the BL102, BL109, HD101, and HD111 values; the correlation coefficient for each fit is labeled. no correlations observed for the various profiles (Figures 11 and 12). However, a positive correlation between layer 2A velocity and distance from the ridge axis is observed for all profiles (Figure 12). The correlation is moderate for BL102, BL109, and HD101 (correlation coefficients ) and weak for HD111 (correlation coefficient 0.37). We also compared all parameters to each other, but found no consistent relationships. Table 1. Waveform Inversion Velocity Model Measurements Thickness (km) Velocity (km/s) Profile Layer 2A Low-Gradient Region Layer 2A High-Gradient Region Layer 2A Layer 2A Layer 2B, Upper 0.25 km BL BL HD HD of 25

14 Figure 13. Shot gathers for BL102 shot (a) Input data for waveform inversion. (b) Synthetic shot gather from the starting velocity model. (c) Synthetic shotgather from the waveform inversion velocity model. (d) Comparison of data and starting model shotgathers for the region marked by the red box in Figure 13a. (e) Comparison of data and inversion model shot gathers for the region marked by the red box in Figure 13a. (f) Error reduction from the starting model to the final model at each frequency. Shot gathers for HD111 shot 580. (g) Input data for waveform inversion. (h) Synthetic shot gather from the starting velocity model. (i) Synthetic shot gather from the waveform inversion velocity model. (j) Comparison of data and starting model shot gathers for the region marked by the red box in Figure 13f. (k) Comparison of data and inversion model shot gathers for the region marked by the red box in Figure 13f. (l) Error reduction from the starting model to the final model at each frequency. 14 of 25

15 Figure 14. BL102 Migration of stacks created from (a) original processed data; (b) data preprocessed for waveform inversion as described in text; (c) synthetic data calculated from waveform inversion starting velocity model; (d) synthetic data calculated from waveform inversion final velocity model. The yellow line shows the picked layer 2A event in the original processed data; the red line is the picked layer 2A event for each stack Layer 2A Event [30] The waveform inversion code iteratively builds the velocity model in the frequency domain, but traditional processing of the layer 2A event is performed in the time domain. Therefore, we computed shotgathers from the final velocity model, sorted them into CDP gathers, carried out velocity analyses to flatten the layer 2A event, stacked the gathers, and finally applied a poststack F-K migration using a constant velocity of 1.4 km/s. We performed the same procedure using the starting velocity model, and also stacked and migrated the input data shotgathers that had been preprocessed for the waveform inversion. [31] Figure 13 shows comparisons of synthetic shotgathers calculated from the starting and waveform inversion velocity models with the input data shotgather for shot 1320 from BL102 and shot 580 from HD111. There are clear differences between the synthetic shotgathers calculated from the starting and inversion velocity models, and the latter better replicates the structure of the 2A/2B caustic and has a lower error at most frequencies. It is difficult, however, to determine the quality of the match over the entire range of input shotgathers. This is easier to assess using the migrated images (Figure 14). The imaged layer 2A event is present over most of the profile, but there are some imaging gaps including a region near the northwest end and one near the center of the profile (Figure 14a). The layer 2A event is more poorly imaged in the preprocessed data migration (Figure 14b), primarily because the preprocessing removes 15 of 25

16 Figure 15. Migration of gathers created from (a) BL109 original processed data; (b) synthetic data calculated from BL109 waveform inversion final velocity model; (c) HD101 original processed data; (d) synthetic data calculated from HD101 waveform inversion final velocity model; (e) HD111 original processed data; (f) synthetic data calculated from HD111 waveform inversion final velocity model. The yellow line shows the picked layer 2A event in the original processed data; the red line is the picked layer 2A event for each stack. 16 of 25

17 Table 2. Layer 2A Event Picks Mean TWTT (s) RMS Error (s) Profile Observed Starting Inversion Starting-Observed Inversion-Observed BL BL HD HD every other trace and every other shot resulting in lower fold. The layer 2A event is strong and continuous in the starting model migration (Figure 14c), while in the inversion model migration it is more variable in amplitude (Figure 14d). The inversion model migration for BL102 appears to be a better match to the character of the imaged data than that of the starting model migration. For all profiles the amplitude and continuity of the layer 2A event is diminished in the waveform inversion model migrations in regions where it is absent or poorly imaged in the data migrations (Figures 14 and 15). [32] The layer 2A event is observed at a mean twtt beneath the seafloor of s on all data profiles (Figure 3 and Table 2), at s on the starting model synthetic sections, and at s on the waveform inversion synthetic sections (Figures 14 and 15 and Table 2). There are a few locations where a layer 2A event was picked on the original data stacks but is not clearly observed in the inversion stacks (e.g., BL km, BL km, HD km), or is located above or below the layer 2A event in the in the inversion stacks (e.g., BL km, HD km). These discrepancies are an estimate of the uncertainties involved in correctly stacking the layer 2A event during the conventional processing sequence. Overall, the RMS error between observed and synthetic twtts for the waveform inversion models is s, which is a decrease from RMS errors of s for the starting models (Table 2). The better fit of s for the Blanco profiles compared to s for the Hess Deep profiles is likely related to the higher signal-to-noise of the Blanco data set Comparison: Layer 2A Event Picks and Velocity Models [33] Previous 1-D modeling studies have indicated that proper processing of the layer 2A event can place this energy near the layer 2A/2B boundary [e.g., Harding et al., 1993; Vera and Diebold, 1994]. In order to test this on our more heterogeneous 2-D velocity models, we converted the twtts between the seafloor and the layer 2A event picks to thickness using the waveform inversion velocity models. Similar to previous studies, the results show that there is a good correspondence between the picks from the original processed data migrations and the layer 2A/2B boundary (Figures 9 and 10). The mean layer 2A thicknesses computed from the layer 2A event picks vary from 0.48 to 0.54 km (Table 3), with more scatter than observed in the velocity model (Figures 9 and 10 and Table 3). These values differ from previous layer 2A thickness estimates of the same profiles owing to more accurate interval velocities in the waveform inversion models; these differences will be discussed in Section 5.1. For 3 of the 4 profiles the thickness calculated from the observed picks is slightly greater ( km) than measured in the waveform inversion velocity model (Table 3). There is a good match between the variability observed in the layer 2A event picks and in the waveform inversion velocity models (Figures 9 and 10). 5. Discussion 5.1. Previous Profile Results [34] Velocity analyses were previously carried out on selected CDP supergathers (composed of 6 adjacent CDPs) from the Blanco and Hess Deep study regions [Christeson et al., 2007, 2010]. The analyses solved for a three-layer model (upper layer 2A, high-gradient region at base of layer 2A, upper layer 2B) using a 1-D forward ray-tracing algorithm to model the travel times of observed arrivals. Examples from two BL109 supergathers are shown in Figure 16. For both CDPs there is a good match between the observed and modeled travel times of the layer 2A/2B caustic; there is a better fit for the layer 2B refraction for CDP 4150 (Figure 16b) than for CDP 2848 (Figure 16c). There is no clearly observed layer 2A refraction on either supergather, and thus a velocity was chosen that modeled the travel times of the layer 2A refraction near those of the seafloor reflection. For both supergathers the thickness of the high-gradient region at the base of layer 2A is 0.10 km; a thicker high-gradient region will move the triplication Table 3. Calculated Layer 2A Thicknesses Profile Mean Inversion Model Thickness a Inversion Model Velocities Interval Velocities km/s b Best Fitting Interval Velocity Mean Thickness Calculated From Observed Picks BL km 0.48 km 0.43 km 0.48 km (3.0 km/s) BL km 0.54 km 0.49 km 0.51 km (2.8 km/s) HD km 0.53 km 0.43 km 0.50 km (3.1 km/s) HD km 0.54 km 0.45 km 0.47 km (2.75 km/s) a Calculated only over regions with observed layer 2A event. b From previous analyses: 2.65 km/s for BL102 and BL109; 2.6 km/s for HD101 and HD of 25

18 Figure 16. (a) Waveform inversion velocity model for BL109. The top and base of high-gradient region at the base of layer 2A are shown by white lines, and velocity models from travel time analysis of CDP supergathers are shown in black. (b) Supergather composed of 6 adjacent CDPS centered at CDP 4150 on BL109. Red lines display travel time curves predicted from 1-D ray tracing. Right panel compares velocity model from the starting and waveform inversion models at the position of CDP 4150 with the model constructed from 1-D ray tracing. (c) As for Figure 16b, except for CDP associated with the layer 2A caustic to a greater distance and will not match the observations. [35] In Figure 16 we compare the 1-D raytracing velocity models with the 2D waveform inversion velocity models at the locations of BL109 CDP 4150 (Figure 16b) and CDP 2848 (Figure 16c). At both locations the waveform inversion velocity models have the general character of the 3-layer 1-D raytracing velocity models, but the high velocity gradient region is thicker for the waveform inversion models. The thickness of the layer 2A high-gradient region in the waveform inversion velocity model is independent of its thickness in the starting model, as demonstrated in section and Figure 6. At the locations of the 9 BL109 velocity analyses the thickness of the high velocity gradient region in the waveform inversion velocity model is km, compared to 0.10 km for the 1-D raytracing velocity models (Figure 16a). As a result, layer 2A is on average 0.1 km thicker in the waveform inversion velocity model than in the 1-D raytracing velocity models (Figure 16a). [36] Velocity analyses were carried out on 64 CDP supergathers from the Blanco study area [Christeson et al., 2010] and 16 CDP supergathers from the Hess Deep study area [Christeson et al., 2007]; the mean layer 2A interval velocity from these analyses was 2.65 km/s and 2.60 km/s at the Blanco and Hess Deep study areas, respectively. In comparison, the mean layer 2A interval velocities are higher ( km/s) for the waveform inversion velocity models (Table 1). The interval velocity is an important parameter because it is commonly used to convert the TWTT between the seafloor and the layer 2A event picks into layer 2A thickness. For the observed layer 2A event picks the mean calculated layer 2A thicknesses are km if interval velocities of km/s are used, as compared to mean values of km in the waveform inversion velocity models for the same regions (Table 3). The previously estimated layer 2A thicknesses are km thinner than observed in the waveform inversion velocity models (but are 18 of 25