Grounding zone subglacial properties from calibrated active source seismic methods

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Seismic Velocity Model
Tracing seismic ray paths between the source and receivers requires knowledge of the firn and ice column's seismic velocity.

Amplitude Picking
Amplitudes were picked on frequency-filtered and amplitude-scaled shot records guided by common depth point stacked profiles(Figure 3).On every shot record we attempted to digitize the direct arrival, primary bed return, and first long-path multiple of the bed return :::::: (Figure :: 3).The low impedance-contrast at the ice-bed interface meant the long-path multiple could not be reliably picked in the grounded part of the profiles.Amplitude picking selected the zero crossing preceding the side-lobe of the wavelet.Amplitude extraction was then performed on shot records with only bandpass filtering applied.Amplitudes were extracted within the wavelet encompassing the first side lobe, the central lobe, and the next side lobe.Within this wavelet, peak positive, peak negative, and root mean squared (RMS) amplitudes were extracted.We avoided picking bed returns where direct arrival energy was interfering :::::::: interferes with the bed wavelet.Our data are from ice thicknesses of approximately 730-790 m and direct arrivals interfere with the reflection from the base of the ice beyond offsets of approximately 700 m.While the channels with 5-element georods showed better signal to noise ratios for imaging, we here present an analysis of the single-string geophones as their amplitudes exhibit less channel to channel variability :: the ::::: cause ::: of ::::: which ::: we ::::::: attribute :: to ::::: more :::::::: variability :: in :::::::: coupling ::::: when ::::::: burying ::: the :::::: georods.Our analysis also uses the RMS amplitudes, with the positive and negative peaks used to define polarity.We tested the use of peak amplitudes and fixed wavelet length approaches and found both resulted in a greater distribution of source sizes, and less robust estimates of basal reflectivity.

Path effects
Path effects (γ i ) modify the source amplitude during its propagation to the receiver.We calculate :::::::: calculated : the total path effects as where θ i denotes the angle between the incoming ray and normal incidence, z 0 , z 1 denote the acoustic impedance at the source and receiver respectively, and s i denotes the path length traveled between the source and receiver.Equation 2 therefore accounts for the angle at which the incoming ray arrives at the vertical-component receivers (cos θ i ), amplitude scaling due to the different acoustic impedance at the source and receiver ( z0 z1 , e.g.Shearer, 2009), and geometric spreading along the ray path (1/s i ).We estimate :::::::: estimated all near-field effects using the 1D velocity model (Figure 2) and the density-compressionalwave velocity relationship of Kohnen and Bentley (1973).The high vertical gradients in density and velocity in polar firn lead to a cos θ i correction≈ 1, as θ i ≈ 0, and a significant z0 z1 correction (∼ √ 10) due to the different source and receiver burial depths.
Long-path multiples from shots in which the primary reflections were from the interface between ice and seismically thick (> 5 m, see Section 4) water resulted in 60, 19, 9, and 24 estimates of A 0 for Lines 1-4, respectively (left column Figure 4, A 0AR ::::: A 0M B : columns Table 1).
Both our direct path methods show :::::: resulted :: in : large standard deviations (Table 1) and correlate poorly with our known reflector estimates (r 2 (coefficient of determination) of 0.1 ::: 0.09 : for the direct pair method and 0.04 for the linear intercept method, Figure 5).The linear intercept method resulted in an average α = 1.4 ± 0.5 km −1 (mean and 1 standard deviation of the combined results for all 4 lines).Individual line average values range from 1.0-1.6 km −1 .These α estimates are an order of magnitude greater than commonly used published estimates and are not used in our analysis.The amplitude ratio ::::::: multiple :::::: bounce : method correlates well with the known reflector method (r 2 =0.45 ::: 0.46, Figure 5).Linear regression of the known reflector estimates with the amplitude ratio ::::::: multiple :::::: bounce : estimates results in a best fitting gradient of 2.0 :: 2.2 : with an intercept of 200.::: 180.: However, this relationship is dependent on our estimate of α and our γ estimates, and will be discussed in Section 4.
The poor correlation between our known-reflector and direct-path A 0 estimates (Figure 4) shows that further investigation of direct path methods is warranted.Both the direct path methods we present would benefit from a greater offset distribution, and the direct pair method would benefit from a greater number of path combinations where s 2 /s 1 = 2 than was available to us. :::: Trace ::::::::::: interpolation ::::: could :::: also :: be :::: used :::: here :: as ::: the ::::: direct :::::: arrival :::::: energy :: is ::::::: unlikely :: to :::::: change ::::::: rapidly.Also, the path effects (γ i ) experienced by the direct ray are likely to be inadequately captured by our approach due to the possibility of unaccounted for energy loss and more complex travel paths than those predicted within the firn.
Our Zoeppritz fitting methodology is skilled at recovering both V p and ρ as demonstrated in the floating portions of all lines where the recovered values are those expected for water (see Table 5 Group 2 estimates).The methodology is less skillful at recovering V s , likely due to the weaker dependence of the shape of the R(θ) curve on V s for the angles we observe.We ::::: Using :::::: average :::::: source :::: sizes ::: and ::: the :::::: known ::::::: reflector :::::: method ::: we : recover the near zero V s typical of water for 73 of the 112 floating shots in our survey.Estimating V s , along with ρ allows the shear modulus to be estimated, which can be used to calculate the effective pressure in the till (Luthra et al., 2016).This provides a more direct link between seismic observations and till properties than is otherwise possible from estimates of ::::: normal ::::::::: incidence reflectivity (R b ) alone.An acquisition geometry that covered greater angles would improve our ability to estimate V s ; however, limitations due to interference from direct arrivals would still exist.
These limitations could be overcome by observing much greater offsets, where direct arrivals no longer interfere with the bed return, or surveying in regions of greater ice thickness.
Using multiple charge sizes and configurations also highlights the importance of source configuration.Line 3, which consisted of the largest charges by weight (0.85 kg) resulted in the lowest A 0 estimates calculated from both the known reflector method and the amplitude ratio ::::::: multiple :::::: bounce : method.The charges for Line 3 were made up of a stack of a single 0.4 kg charge, and three narrower 0.15 kg charges.These narrower charges were likely less well coupled with the shot hole wall, and the longer linear configuration resulted in a less effective source.A shorter interval between shot loading and detonation may have also been a factor here as Line 3 was shot within 1-2 days of loading.
Our comparison of methods used to determine source size (A 0 ) shows that the commonly employed amplitude-ratio ::::::: multiple :::::: bounce method correlates well with the known reflector method available to us.However, our comparison also highlights that path effects (γ i ) are incompletely modelled by the methods employed here and elsewhere.Our findings also reinforce the need for consistency in source placement, configuration, and time between burial and detonation.Overall our methods are skilled at retrieving basal properties at relatively high spatial resolution where the thickness of the subglacial material is sufficient to prevent thin film effects (> λ/4).Both V p and ρ are reliably retrieved, while V s is recovered but less consistently.While we are currently unable to accurately recover :: all seismic properties for what appear to be thin water layers, our methods also :: do : show promise here.These thin layers are pertinent for ice flow, and techniques such as full waveform inversion are likely to prove useful here.These methods, which invert not just for a single amplitude of the basal return but the full time series, have been successful applied to other environments where thin layers with large contrasts in seismic properties have been investigated (e.g.Pecher et al., 1996).

Figure 2 .
Figure 2. One dimensional compressional wave velocity profile estimated using the τ -p method.

Table 1 .
Source size (A0) estimates.Line 1 used a single 0.4 kg charge.Lines 2 and 4 used two 0.4 kg charges in a vertical configuration.Line 3 used one 0.4 kg charge and three 0.15 kg charges in a vertical configuration.See Section 4 for discussion.