A SEISMIC INVESTIGATION OF BASAL CONDITIONS IN GLACIATED REGIONS

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A SEISMIC INVESTIGATION OF BASAL CONDITIONS IN GLACIATED REGIONS

Abstract

Seismic amplitude analysis of the ice bottom reflector is an effective way to constrain the basal regime of glaciated regions and better capture the role of the bed in ice dynamics. The strength and phase of this observed ice bottom reflection, and its variations when analyzed over a range of source-receiver offsets, relate to a unique set of elastic properties at the ice-bed interface that highlight the material properties of the subglacial bed. These observations allow us to obtain a greater understanding its role in facilitating ice drainage from the interior of the earth’s ice sheets to the margins. This thesis builds upon the seismic amplitude variation with offset (AVO) technique to exploit seismic observations of the ice-bed interface to determine basal conditions. The primary goal of this thesis is to outline the overall approach for extracting the elastic properties of the subglacial bed from an observed seismic reflection, touching upon the various simplifications and shortcomings experienced along the way. The secondary goal is to highlight the robustness of seismic AVO analysis in glaciated regions by applying this technique to seismic reflection data from four locations in Antarctica and Greenland. Each example provides a different snapshot of the basal regime, revealing a subglacial system with various structural, mechanical, and hydrological components at work in shaping the evolution of ice dynamics within the earth’s ice sheets.

 

Table of Contents

List of Figures                                                                                                              vi

List of Tables                                                                                                               xv

Chapter 1

Constraints on basal conditions in glaciated regions through ap-

plication of the seismic amplitude variation with offset

(AVO) technique                                                                                 1

1.1                         Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           1

1.2    Seismic AVO theory                      . . . . . . . . . . . . . . . . . . . . . . . . . .                       4

1.3             Forward modeling of the seismic response . . . . . . . . . . . . . . .             11

1.4    Data collection                       . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                       17

1.5                        Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        20

1.6    Summary                         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         24

1.7                          References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         25

Chapter 2

Seismic observations of a hard bed in the onset region of Jakob-

shavn Isbrae, West Greenland, through application

of the seismic amplitude variation with offset (AVO)

technique                                                                                            30

2.1                         Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         30

2.2                         AVO Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         32

2.3                         Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        35

2.4                 Determination of basal reflectivity . . . . . . . . . . . . . . . . . . .                 36

2.5     A hard bed in the onset region of Jakobshavn Isbrae          . . . . . . . .         43

2.6                   Seismic attenuation in the ice . . . . . . . . . . . . . . . . . . . . .                   46

 

2.7                          Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         47

2.8                       Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      48

2.9                          References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         48

Chapter 3

Seismic detection of a subglacial lake near the South Pole,

Antarctica                                                                                           53

3.1                           Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           53

3.2                         Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         53

3.3                Amplitude Variation with Offset (AVO) . . . . . . . . . . . . . . . .                55

3.4                        Seismic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        60

3.5                       Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      61

3.6                          References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         61

Chapter 4

Extensive storage of basal meltwater in the onset region of a

major West Antarctic ice stream                                                 65

4.1                           Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           65

4.2                         Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         66

4.3     Data and Analysis                      . . . . . . . . . . . . . . . . . . . . . . . . . . .                      68

4.4                          Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                          71

4.5                       Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      74

4.6                          References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         75

Chapter 5

Subglacial conditions at a sticky spot along Kamb Ice Stream,

West Antarctica                                                                                79

5.1                           Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           79

5.2                         Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         80

5.3                         Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                        82

5.4                         AVO Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         83

5.5                          Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                          85

5.6    Summary                         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         87

5.7                       Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . .                      88

5.8                          References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         88

Chapter 1

Constraints on basal conditions in glaciated regions through application of the seismic amplitude variation with offset (AVO) technique

1.1      Introduction

Ice streams and glaciers play a major role in draining the inland ice reserves of the earth’s ice sheets, with fast ice flow being attributed to rapid basal motion over a potentially deformable subglacial bed [e.g., Alley et al., 1896; 1987]. The spatial extent of this soft lubricating bed influences the overall drainage capacity of these ice streams and glaciers, for continuous sediment cover can enhance ice flow, allowing the overlying ice to slide over a smooth bed [Blankenship et al., 1986; 1987; 2001; Anandakrishnan et al., 1998; Bell et al., 1998 Studinger et al., 2001; Peters et al., 2006]. Changes in both the extent and character of this subglacial bed can also have considerable impacts on the future drainage of these delicate systems, and an understanding of how these changes may occur will lead to better modeling of past, present, and future ice dynamics.

Glaciers and ice streams around the world have recently been undergoing rapid evolutions in their flow regimes and character, leading to much concern over their stability and contribution to global sea level [Oppenheimer, 1998]. Numerous mountain glaciers, which have persisted for millennia, are shrinking at unprecedented rates, with many on the verge of extinction within the next few decades [Mosley-Thompson et al., 2006; Thompson et al., 2006]. Collapse of the Larsen B Ice Shelf has tremendously altered the drainage of ice from that region of the Antarctic Peninsula, with surface velocities of the outlet glaciers flowing into the ice shelf increasing by two- to eight-fold after its collapse [Rignot et al., 2004; Scambos et al., 2004]. The outlet glaciers of Greenland have also exhibited accelerations in ice flow to varying degrees, with seasonal fluctuations in ice flow velocity [Zwally et al., 2002]. The ice streams draining the West Antarctic Ice Sheet (WAIS), on the other hand, reveal regions of both increased and decreased flow velocities in the past few centuries (and on decadal timescales), especially along the Siple Coast of West Antarctica [Retzlaff and Bentley, 1993; Joughin et al., 1999; 2002; 2005].

These observed changes in flow regime have either been directly or indirectly linked to changes in basal conditions. Glacier surges in mountain glaciers have occurred when a rapid emplacement, or ‘surge’, of water at the base of the ice occurs, softening the subglacial strata and allowing enhanced ice flow [Richards, 1988; Nolan and Echelmeyer, 1999a; 1999b]. Seasonal variations in flow velocity along many Greenland outlet glaciers have been linked to enhanced flow via infiltration of surface melt to the bed and decreased flow during the winter months [Zwally et al., 2002]. The stagnation of Kamb Ice Stream, West Antarctica, has been hypothesized to be the result of the diversion of basal water from Kamb Ice Stream to Whillans Ice Stream [Alley et al., 1994; Anandakrishnan and Alley, 1997; Anandakrishnan et al., 2001], though growing evidence suggests the bed of Kamb Ice Stream is quite wet [Atre and Bentley, 1993; Bentley et al., 1998; Catania et al., 2003], which could lead to reactivation in the near future [Vogel et al.,2005]. Whillans Ice Stream is also in a state of deceleration, with the potential for stagnation in the near future [Joughin et al., 2005].

This thesis outlines the application of the seismic amplitude variation with offset (AVO) approach to constrain basal conditions in glaciated regions, with four examples of applying this technique in Antarctica and Greenland (Figure 1.1). Chapter 1 covers the basic approach for determining basal reflectivity from an observed ice bottom reflection and then relating this reflectivity to the elastic properties of the subglacial bed. Chapter 2 highlights the advantages of seismic

AVO analysis when both AP<em><sub>P</sub></em>´(<em>θ<sub>i</sub></em>) and <em>A<sub>S</sub></em>S´(θi) are observed over a range of sourcereceiver offsets, where a hard sediment bed is identified along the upper reaches of Jakobshavn Isbrae, West Greenland. Chapter 3 confirms the presence of a subglacial lake near the South Pole via amplitude analysis of a four kilometer section of the basal regime in that region [Peters et al., 2008]. Finally, Chapters 4 and 5 image variable basal conditions from two seismic profiles along the Siple Coast of West Antarctica [Peters et al., 2007; Peters and Anandakrishnan, 2007]. For each locale, a slightly different approach is used to constrain the basal conditions present, based on the ice bottom reflectors observed in each seismic dataset.

Figure 1.1. Location maps for each of the seismic AVO experiments presented in this thesis. A) The location of the wide-angle experiment performed along Jakobshavn Isbrae, West Greenland is given by the black star (Chapter 2). B) MODIS (Moderate Resolution Imaging Spectroradiometer) MOA (Mosaic of Antarctica) of the Siple Coast of West Antarctica [Haran et al., 2005], highlighting the locations of the Antarctic datasets: SPL = South Pole (Chapter 3), DL = upper reaches of Bindschadler Ice Stream (Chapter 4), CT2 = across a sticky spot along Kamb Ice Stream (Chapter 5). The inset map shows the location of the MOA image in relation to Antarctica. Further details on the data collected for each experiment are covered in the appropriate chapters of this thesis.

1.2        Seismic AVO theory

When a seismic reflection is observed, the phase and magnitude of the reflector results from the difference in elastic properties (compressional wave velocity, α; shear wave velocity, β; density, ρ) along the seismic interface. Since the sourcereceiver array is generally placed at the surface when collecting these data, the observed reflection from a given interface can be written as

AR(x,f) = A0(f)R(x)γ(x)ea(f)r(x),                                     (1.1)

which states that the observed amplitude from this interface, AR, is a function of the source amplitude, A0, the reflectivity of the interface, R, the energy losses due to the seismic raypath, γ, and the energy losses due to seismic attenuation through the medium above the interface, where a is the seismic attenuation factor and r is the raypath length, all at some source-receiver offset, x, and a given (or dominant) frequency, f. The observed amplitudes from this range of sourcereceiver offsets should be collected in such a manner to form a common depth point (CDP) gather along the seismic interface to avoid any lateral variability in elastic properties on either side of the seismic interface. The resultant reflectivity is dependent on the the seismic waves that created the reflection, and may arise from one of four wave types: 1) a pure compressional wave, RP`P´, 2) a pure shear wave,

RS<em><sub>S</sub></em>´, 3) a converted compressional wave, <em>R<sub>P</sub></em>S´), or 4) a converted shear wave, RS<em><sub>P</sub></em>´ (Figure 1.2). Here <em>P</em> and S` represent the downgoing (or incident) compressional and shear wave, respectively, while P´ and S´ represent the upgoing (or reflected) compressional and shear wave, respectively. This observed amplitude will vary with offset due to changes in the raypath geometry of the seismic wave, as well as the incidence angle (θi, where ) in the simplest case of a flat seismic interface and an isovelocity upper medium, with h being the thickness of the upper medium, and xi being the horizontal offset from the source to the reflection point) at which the seismic wave strikes the interface, which leads to variations in reflectivity at that interface (Figure 1.3). This is where the strength of seismic AVO analysis arises in constraining subsurface conditions, as the variations in reflectivity over a range of source-receiver offsets is unique to a specific set of elastic properties from the media at the seismic interface.

Figure 1.2. Four potential reflections can be observed for a given two-layer system when the source and receiver are within the same medium. In this example, the seismic source and receiver array are both located near the surface of the ice column for an icesubglacial bed system. The blue and red arrows indicate the raypaths for compressional waves and shear waves respectively, with the black arrows highlighting the direction of particle motion for each seismic wave. The left panel shows the two reflections resulting from a compressional wave source, and the right panel shows the two reflections resulting from a shear wave source. For a given source amplitude, A0, AP<em><sub>P</sub></em>´ and <em>A<sub>S</sub></em>S´ arise from the pure compressional and shear wave reflections, where θi = θr (θi is the incident angle and θr is the reflected angle). AS<em><sub>P</sub></em>´ and <em>A<sub>P</sub></em>S´ come from the converted wave reflections, where the particle motion of the seismic wave is converted to a different propagation orientation upon reflection, with θi r for AP<em><sub>S</sub></em>´ and <em>θ<sub>i </sub>&lt;θ<sub>r </sub></em>for <em>A<sub>S</sub></em>P´.

This reflectivity, R, is what we ultimately want to determine from the above reflectivity equation, as it contains information about the lithology, porosity, and overall geologic conditions at the seismic interface. When R is observed over a wide range of source-receiver offsets, the elastic properties for the media above and below that interface can be determined via the Zoeppritz equations [Aki and Richards, 2002] (Figure 1.3). The process for producing the seismic reflectivity curves shown in Figure 1.3 is described in Section 1.3 (Forward modeling of the seismic response).

The simplest approach for determining subsurface conditions is to make observations of a given interface at normal incidence (ie, θi = 0, or x = 0 m), where the

Figure 1.3. Forward models of seismic reflectivity for each of the four possible reflection types (upper left panel = RP<em><sub>P</sub></em>´; upper right panel = <em>R<sub>S</sub></em>S´; lower left panel = RP<em><sub>S</sub></em>´; lower right panel = <em>R<sub>S</sub></em>P´) from a series of ice-subglacial bed interfaces (bedrock = red; consolidated sediments = black; dilatant till = green; water = blue). For a given seismic reflection (RP<em><sub>P</sub></em>´, for example), the reflectivity is quite variable, in terms of both reflection magnitude and polarity, for each modeled subglacial bed.. When more than one reflection type is observed for the same subglacial bed, the resultant reflectivities of <em>R<sub>P</sub></em>P´, RS<em><sub>S</sub></em>´, <em>R<sub>P</sub></em>S´, and RS`P´ for that bed are also quite variable. The elastic properties used to produce these reflectivity curves are listed in Table 1.1.

interface reflectivity is just a function of the acoustic impedances (product of seismic velocity and density of a given medium) at that interface. These observations can be made for both compressional waves and shear waves, where

(1.2)

Medium α (m sec−1) β (m sec−1) ρ (kg m−3)
Ice 3840 1920 920
Bedrock 5400 2800 2600
Consolidated Sediments 2600 1100 2200
Dilatant Till 1700 150 1800
Water 1500 0 1000

Table 1.1. Elastic properties for the upper and lower media that were used to produce the reflectivity curves presented in Figure 1.3.

(1.3)

Here the subscripts refer to the upper (1) and lower (2) media at the seismic interface. In each reflectivity equation, only the seismic wave velocity for that reflection can be determined (α for RP<em><sub>P</sub></em>´, or <em>β </em>for <em><sup>R</sup><sub>S</sub></em>S´) due to the propagation of the given seismic wave. The advantages of this approach are that quick point measurements can be made, as only data from normal incidence need to be collected, and the equations are quite simple, giving straightforward approximations of the acoustic impedances at the interface. The main disadvantage, though, arises from the fact that only the acoustic impedances are determined, where a non-unique solution to the elastic properties along the seismic interface arises, as any number of seismic velocity-density pairs can yield the same acoustic impedance. Extension of the interface reflectivity beyond normal incidence alleviates this problem, as the variation in reflectivity with offset is unique to a single set of elastic properties and both seismic velocities can be simultaneously constrained.

When analyzing seismic data at non-normal incidence (ie, x > 0 m), three variables are present in the general reflectivity equation that must be determined or assumed to accurately constrain interface reflectivity: 1) A0, 2) γ, and 3) a. The source amplitude (A0) can be most easily constrained by taking the ratio of the primary interface reflection and its multiple [Peters et al., 2008], as shown below:

,                                               (1.4)

with AR representing the primary reflection from the interface and ARR the multiple reflection from that same interface, both taken at normal incidence, and r the raypath length for the primary reflection. This equation can be applied to either compressional waves or shear waves, as long both the primary and multiple reflections are observed. This approach is only valid at normal incidence, though, as both the primary reflection and its multiple reflect off the same region of the interface and travel along similar raypaths at this point. If extended beyond nonnormal incidence, these two reflectors begin to sample different points along the interface (resulting in different reflectivities) and travel along different raypaths (Figure 1.4).

Figure 1.4. Cartoon of the primary reflection (red) and its multiple (blue) from a seismic interface. At normal incidence (left panel), both reflections cover similar raypaths and reflect off the same point along the seismic interface, thereby allowing a simple correlation to be drawn between the two reflectors. For the same angle of incidence (middle panel), the raypath of the multiple is twice as long as that of the primary reflection, with the primary reflection being a carbon copy of the ‘first bounce’ of the multiple reflection, but the ‘second bounce’ of the multiple reflection occurs at a different point along the seismic interface. For the seismic source-receiver offset (right panel), the incidence angles for both reflections are different and reflect off different points along the seismic interface.

The γ term captures the raypath the seismic wave travels from source to receiver and accounts for the energy losses that occur along this raypath. Its takes into account spherical spreading, energy losses due to velocity gradients present along the raypath (especially the surrounding source and receivers), and the angle at which the seismic waves arrive at the receivers, and is given as:

)                                       (1.5)

Here r0 is a reference distance taken near the source (usually treated as one), Γ is the path amplitude factor to account for velocity gradients [Medwin and Clay, 1998], and θrec is the angle at which the seismic wave arrives at the receiver (Figure 1.5). The path amplitude factor can be stated as follows to determine the deviation in energy loss for the seismic wave from spherical spreading,

,                            (1.6)

where ρrec and ρsrc are the densities at the receiver and source respectively, crec and csrc are the seismic velocities at the receiver and source respectively, θsrc is the takeoff angle from the source, and θrec is the angle at which the seismic wave arrives at the receiver (Figure 1.5). In an isovelocity medium, this equation simplifies to one for all x, meaning that the energy losses resulting from the raypath are solely due to spherical spreading, whereas a velocity gradient (especially one between the source and receiver depth) can produce deviations of up to several fold over a given range of x.

Amplitude losses due to attenuation of the seismic waves are dependent on the material through which the seismic waves travel and are generally the least constrained amplitude losses. The most straightforward means to accomplish this is by analyzing amplitude decay with offset for the surface waves (direct arrival) from source to receiver. Since no reflection is involved with the direct arrival, the general ‘reflectivity’ equation is stated as:

ADA(x) = A0γ(x)ear(x)                                                                                         (1.7)

Here ADA is the amplitude of the direct arrival (DA), and the other variables are the same as in the general reflectivity equation (Equation 1.1). In an iso-velocity, homogeneous medium, the observed amplitude decay of the direct arrival with offset becomes:

ln(xADA(x)) = ax,                                                (1.8)

where the attenuation factor, a, is the slope of the line observed in the data. Since the seismic waves are traveling right along the surface, the γ(x) term in Equation 1.7 can be treated as  and the r(x) term be treated as x, with the source amplitude taken to be constant for a given source-receiver array setup. For two receivers with offset x and x + δx, the approximate difference in raypath coverage between the

Figure 1.5. Cartoon of the parameters involved in determining the amplitude losses due to the raypath geometry of the seismic wave. At the source, ρsrc and csrc are the density and seismic velocity of the medium at the source depth, and θsrc is the takeoff angle of the seismic wave from the source. At the receiver, ρrec and crec are the density and seismic velocity of the medium at the receiver depth, and θrec is the angle at which the seismic raypath arrives at the receiver. r(x) is the raypath length for a given source-receiver offset, x.

two receivers is the extra δx to the farther receiver (Figure 1.6). Thus for a series of receivers, Equation 1.8 provides a simple means for extracting the seismic attenuation factor for the upper medium.

When a velocity gradient is present in the medium through which the seismic waves travel, these waves will begin to dip down through this gradient with increasing source-receiver offset until an iso-velocity region is reached (Figure 1.6). At ‘near’ offsets, the seismic raypath for the direct arrival spends all of its time dipping through the velocity gradient, resulting in a rapid loss in seismic energy with increasing offset due to the lower densities and non-uniform organization of the medium likely to be associated with lower seismic velocities. At ‘far’ offsets, the seismic raypath then begins to rapidly pass downward through this velocity gradient to the iso-velocity region, where it travels as a headwave before quickly

Figure 1.6. Cartoon of the propagation of the direct arrival from source to receiver. The left panel shows the iso-velocity case, where the seismic waves travel directly along the surface, as this is the fastest route from source to receiver. In this instance, the difference in raypath between two receivers is just δx. When a velocity gradient is present (right panel), the ‘near offset’ seismic waves will begin to dip through the gradient some before arriving at the receivers, as this is the fastest route from source to receiver. The ‘far offset’ seismic waves will quickly dip through the seismic velocity gradient, then travel along the iso-velocity zone as a head wave before quickly turning up to the receivers. In this ‘far offset’ instance, the difference in raypaths between two receivers becomes δx.

bending back upward to the receiver array. It should be noted that the exact source-receiver offsets for the ‘near’ and ‘far’ terms stated above can vary from situation to situation, and are dependent on both the thickness and velocity gradient of the medium, as well as source depth, in determining the offset at which the seismic raypaths will begin to take the ‘far’ offset route. Once this ‘far’ offset route is reached, Equation 1.8 can be applied to the observed amplitude-offset pairs, as the only difference in raypath coverage at these ‘far’ offsets is the extra distance the rays travel through this deeper iso-velocity portion of the medium [Bentley and Kohnen, 1976].

1.3         Forward modeling of the seismic response

Before going into the field to collect an active seismic dataset for AVO analysis, it is beneficial to run forward models to predict the seismic response for a given seismic interface. Forward modeling of such a two-layer system can be accomplished a variety of different methods, two of which are presented here. Since the phase and magnitude of the seismic reflection defines the materials lying along the seismic interface, the Zoeppritz equations can be implemented to model the amplitude response for a given seismic reflection [e.g., Aki and Richards, 2002]. Synthetic waveform modeling can also be applied to capture the seismic response of a source wavelet reflecting off a given seismic interface [e.g, Kennett, 1983]. Since the focus of this thesis is on determining basal conditions in glaciated regions, the modeling work presented here involves a layered ice-subglacial bed systerm.

The Zoeppritz equations calculate the amplitude response for the ice-subglacial bed system, provided the elastic properties of both the ice and a given subglacial bed are known. These equations form the scattering matrix, which accounts for the sixteen potential reflections and transmissions that can occur at a given seismic interface [e.g., Aki and Richards, 2002]. In the field, both the source and receiver array are at (or near) the surface, so only four reflections are of interest here: P<em>P</em>´, <em>S</em>S´, P<em>S</em>´, and <em>S</em>P´. When the elastic properties of the ice and a given subglacial material are input into the Zoeppritz equations, the amplitude response of that interface over a range of incidence angles can be determined, as shown in Figure 1.3. Here four different subglacial bed scenarios are presented, each defined by a unique set of elastic properties (listed in Table 1.1). These differences in elastic properties from subglacial bed to subglacial bed, along with the range of incidence angles over which the basal reflectivity is modeled, produce the observed variations in basal reflectivity that distinguish one subglacial setting from another.

There are a series of advantages and disadvantages to predicting basal conditions via the Zoeppritz equations, which center around the simplifications made to both the ice column and the subglacial bed. The main advantage to this approach is that the seismic reflectivity of any material beneath the ice can be adequately modeled, as long as the elastic properties of that material are known. The disadvantages to this forward modeling approach lie in the details of the two-layer system in question, as the calculated basal reflectivity only captures the amplitude of the seismic response at the ice-bed interface. Heterogeneities within the ice column, which may further attenuate or distort the true reflectivity, are not taken into account. A further assumption of the Zoeppritz equations is that the modeled subglacial material is at least  seismic wavelength thick (where

is the seismic velocity of the bed, and fdominant is the dominant frequency of the basal signal), and that the ice-bed interface is both flat and smooth. The seismic response of basal layers less than thick cannot be accurately modeled with the Zoeppritz equations alone, and both dipping and rough ice-bed interfaces require proper constraints on the source and receiver geometries to know the appropriate experiment setups to capture the seismic response over a range of incidence angles (such as the case for a dipping reflector, shown in Figure 1.10).

Synthetic seismogram modeling captures the theoretical seismic response of a given source wavelet traveling from source to receiver. Here, a model of the elastic properties and attenuation factors throughout the ice column, subglacial bed, and deeper subglacial materials is created, with the locations of the sources and receivers set within the model. The moment tensor associated with the source is also input, which is a triple dipole source for an explosion. The specific synthetic seismogram code used here follows the technique outlined by Kennett [1983], where the modeled seismic response is calculated in the slowness-frequency domain through excitation of a solid layered system by a point moment tensor source. The results of three modeling exercises are shown here, each of which highlights the benefits of synthetic seismogram modeling to predict the seismic response that should be observed in the field.

The first exercise demonstrates the influence of the firn on the seismic response of a 400 m thick ice column over crystalline basement, shown in Figure 1.7. In each instance, the source is placed at 10 m depth, and the receiver array is placed at the surface with a 50 m spacing. The upper two plots show the vertical component (left = reflected compressional waves recorded) and radial component (right = reflected shear waves recorded) of a single-layer homogeneous ice column. The key points to note in these plots are that no shear waves are produced, as an explosive source does not generate shear waves, and that the modeled reflections come in quite strong, as there are no velocity gradients or variations within the ice column. The lower two plots give the seismic response for a heterogeneous ice column with an upper 100 m firn. Since the source and receivers are within the firn, near-surface reverberations are observed for the direct arrival, and the modeled reflections are weaker. Also, since the source is detonated within the firn, where the seismic velocity gradient is high, shear wave conversions occur near the source to produce the S<em>S</em>´ and <em>S</em>P´ reflections that are absent in the upper plots. These observations highlight the effects the firn can have on the observed basal reflectivity, and also presents a means to ‘produce’ shear waves if the seismic source is placed within the firn.

Figure 1.7. Modeled seismic response of a 400 m ice column over crystalline basement. The upper two plots show the seismic response due to a single-layer homogeneous ice column, with the vertical component response on the left and the radial component response on the right. The lower two plots show the seismic response due to a heterogeneous ice column with an upper 100 m firn. The source was placed at 10 m depth and the receivers were at the surface in each case. The elastic properties used here are listed in Table 1.2.

The second exercise shows what the seismic response of a heterogeneous 400 m ice column over a kilometers-thick subglacial bed (Figure 1.8). Here four different ice-bed cases are presented: ice over bedrock (black), ice over water (blue), ice over dilatant till (green), and ice over stiff till (red) (elastic properties listed in Table 1.2). Both the P<em>P</em>´ (upper) and <em>P</em>S´ (lower) reflections are shown. Similar to the results observed from the Zoeppritz equations, the bedrock and water cases produce quite different basal reflectivities, and all four cases produce results that are distinguishable from each other when taken over a range of source-receiver offsets. In this instance, where a thick subglacial layer is modeled, forward modeling of the Zoeppritz equations does a good job at matching the synthetic seismogram response.

PP Seismic Response for a Heterogeneous Ice Column – 5km Thick Subglacial Bed System

PS Seismic Response for a Heterogeneous Ice Column – 5km Thick Subglacial Bed System

Figure 1.8. Modeled seismic response of ice over four potential subglacial beds: bedrock = black, water = blue, dilatant till = green, stiff till = red. The upper panel shows the modeled P<em>P</em>´ response, and the lower panel gives the modeled <em>P</em>S´ response. For each response, the hyperbolic moveout with offset of the reflector has been removed to flatten the reflector. The elastic properties used here are listed in Table 1.2.

The final exercise demonstrates the advantage of observing converted wave reflections (P<em>S</em>´ and <em>S</em>P´) for a thin 1 cm subglacial layer (water, dilatant till, and stiff till) between the ice and crystalline bedrock (elastic properties listed in Table 1.2). Again, both the P<em>P</em>´ (upper) and <em>P</em>S´ (lower) reflections are shown. The P<em>P</em>´ response (upper panel) shows minimal variations between an ice-bedrock reflection and a 1 <em>cm </em>layer of either water, dilatant till, or stiff till sandwiched between the ice and crystalline bedrock. The <em>P</em>S´ response (lower panel) shows variations between the four presented cases, though, as a 1 cm water layer produces a reflection of similar magnitude, but with a 180phase shift, in comparison to the ice-bedrock reflection. The dilatant till case produces a weaker version of the water case in general, whereas the stiff till case is similar to the ice-bedrock reflection. This observation highlights the fact that water (either in the presence of a pure water layer, or a high porosity till layer) at the ice-bed interface can be detected at the centimeter-scale, given that converted wave reflections (P<em>S</em>´ or <em>S</em>P´) are observed.

PP Seismic Response for a Heterogeneous Ice Column – Thin Bed – Bedrock System

PS Seismic Response for a Heterogeneous Ice Column – Thin Bed – Bedrock System

Figure 1.9. Modeled seismic response of ice over four potential subglacial bed scenarios: bedrock = black, 1 cm water over bedrock = blue, 1 cm dilatant till over bedrock = green, 1 cm stiff till over bedrock = red. The upper panel shows the modeled P<em>P</em>´ response, and the lower panel gives the modeled <em>P</em>S´ response. For each response, the hyperbolic moveout with offset of the reflector has been removed to flatten the reflector. Minimal variations in the P<em>P</em>´ response are observed between the ice-bedrock case and any of the one-centimeter layers. A 180<sup>◦ </sup>phase shift is observed in the <em>P</em>S´ response of a one-centimeter layer of both water and dilatant till (with the water response being of greater magnitude) in comparison to the ice-bedrock case. As in Figure 1.8, the hyperbolic moveout with offset of the reflector has been removed to flatten the reflector for each seismic response. The elastic properties used here are listed in Table 1.2.

The seismic response due to a dirty basal ice layer was also explored to both predict the effect of such a layer on the seismic response of the ice-bed interface and determine the thickness at which a dirty basal ice layer can be seismically detected. Two cases were tested: a layer consisting of 10% sediment and 90% ice, and a layer consisting of 30% sediment and 70% ice (the elastic properties used for these two cases are listed in Table 1.2). Since the seismic properties (α and β) of the ice and sediment are not too dissimilar, it would take several tens of meters of 10% dirty basal ice to be detected from a P<em>P</em>´ response and ∼10 <em>m </em>from a <em>P</em>S´ response. If a 30% dirty basal ice layer is present, the detection threshold is lowered to <20 m and ∼5 m from a P<em>P</em>´ and <em>P</em>S´ response, respectively. Since a dirty basal ice layer basically raises the values of the elastic properties of the ice at the ice-bed interface ( ρ increases more than α or β decreases), the resultant seismic response is dampened in comparison to no dirty basal ice, with the magnitude of this effect dependent on both the sediment content and layer thickness of the dirty basal ice.

Medium α (m sec−1) β (m sec−1) ρ (kg m−3)
Ice 3800   1950 920
Bedrock 5500   2700 2750
Stiff Till 1900   900 1900
Dilatant Till 1600   150 1800
Water 1500   0 1000
10% Dirty Ice 3770   1930 1060
30% Dirty Ice 3710   1890 1330

Table 1.2. Elastic properties used to forward model the seismic response of the ice over a series of subglacial bed scenarios.

1.4       Data collection

Data collection is in many respects the most crucial component of seismic AVO analysis, as the type, quantity, and quality of data collected will dictate what information can be retrieved. Limits on the data collection may be driven by logistical constraints, time constraints, or a lack of a priori knowledge for the study region. Whatever the case, a clear plan of experiment goals and forward modeling of what one would expect in terms of basal reflectivity will pay off in collecting the appropriate data to constrain subglacial conditions.

In terms of seismic AVO analysis, the expected outcome from the experiment will greatly shape how the data are to be collected. The main tradeoffs are between the amount of logistics and time to be spent on the experiment, and the quality and quantity of data to be collected. Normal incidence data are easier to collect and necessary to determine source amplitude (given that the multiple reflection is observed as well), though they provide looser constraints on the elastic properties of the subglacial bed. A well-planned wide-angle experiment, specifically one involving both vertically and horizontally oriented geophones, provides much greater constraints on basal conditions, but it becomes a time intensive process. Also, if other seismic data are to be collected, the question of whether focus should be placed on fully constraining a small patch of the subglacial bed or providing loose constraint along the entire seismic profile(s) to be collected needs to be addressed, as a point observation of the bed may not be representative of the overall basal conditions of the region.

A priori knowledge of the study region can also drive how the data are to be collected. Information on ice thickness is useful, as thinner ice requires smaller source-receiver offsets than thicker ice to collect data out to a given incidence angle, which in turn influences the amount of logistics and time needed for the experiment. Whether or not the subglacial bed is dipping significantly is also important, as this can greatly affect the experiment design. A flat (horizontal) to shallowly dipping bed (< 30) requires a simple walk-away setup for wide-angle data collection, whereas a steeply dipping bed shifts the portion of the bed sampled at depth and the positioning of the sources and receivers for the same wide-angle data collection (Figure 1.10). On the logistical side, the type of source to be used and the maximum potential depth of the source beneath the surface will influence the data to be collected, as a shallower or weaker source may not produce the energy necessary to observe ice bottom reflectors at large offsets, whereas a deeper or larger source may produce better data at the cost of greater logistics.

Before going to the field, forward modeling of the reflectivity response for a range of ice-bed interfaces can be invaluable in the field planning and on-site quality checks of the collected data. If prior data have been collected in the study region that suggest a certain bed type, then forward modeling of that ice-subglacial bed interface can point to a key range of incidence angles that can confirm or deny the presence of that bed. Also, if there is high uncertainty as to what type of subglacial bed exists in the region, then forward modeling can highlight the range of incidence angles that would be most appropriate in determining the true basal conditions of the region, especially if logistical constraints will not allow for a proper wide-angle experiment over a continuous range of incidence angles.

Figure 1.10. The influence of a dipping seismic interface on incidence angle for a given reflection. In the case of a horzontal interface (left panel), θi is simply arctan  for RP`P´. Calculation of θi becomes more complicated when the seismic interface is dipping, as [Slawinski, 1997].

In the field, quality checks of the data are necessary to make sure the experiment objectives are being met. The key components here are making sure that targeted reflectors (P<em>P</em>´, <em>P</em>P´P<em>P</em>´, <em>S</em>S´, etc.) are being observed, and that the experiment is design appropriately to account for any dip present at the bed and collect wide-angle data over the desired range of incidence angles. A shallow refraction experiment should be performed in conjunction to constrain the velocity gradient through the ice column [e.g., Shearer, 1999] and determine the appropriate energy losses that may be associated with the seismic raypaths for the observed reflectors [Medwin and Clay, 1998]. If the seismic sources are being placed at depth beneath the surface, this shallow refraction experiment will also aid in determining an ideal minimum depth for ensuring most of the energy from the source is not initially attenuated through the firn.

1.5       Data processing

The processing required to constrain basal conditions from the ice bottom reflection(s) observed is dependent on the data collected. The basic procedure is to determine basal reflectivity, either at normal incidence or over a range of incidence angles. This involves calculating or assuming some value for the three unknowns in the general reflectivity equation: A0, γ, and a. As long as the ice bottom reflection (AR), its multiple (ARR), and the direct arrival (ADA) are all observed, and a shallow refraction experiment is performed to constrain the velocity gradient through the ice column, it should be relatively straightforward to determine the basal reflectivity for each AR observation. The one reflector that is generally the most difficult to see, if at all, is ARR, as this reflection travels twice the distance of AR for a given incidence angle (Figure 1.4), thereby allowing any energy losses to weaken the reflector considerably more, and it can easily be distorted by other seismic signals or noise that arrive to the receiver array at the same time.

As shown in Equation 1.1, the magnitude of the observed ice bottom reflection is a function of the dominant frequency of the wavelet. The attenuation of seismic energy through the ice column or any medium is also frequency dependent, thereby meaning that a quoted value of attenuation may only apply to a certain frequency range. Since different seismic signals arrive at different times in a given shot gather

(such as AP`P´, DA,P , and ADA,S in Figure 1.11), analysis of the frequency spectrum of each observed signal is necessary to capture its dominant frequency, determine if there are any frequency variations with offset, and compare the strength of each signal the background noise (Figure 1.12). The example power spectra in Figure

1.12 show that the desired AP`P´, DA,P , and ADA,S signals all have a dominant frequency in the 60-200 Hz range, with the higher frequencies attenuated more at the larger offsets.

To quantify the uncertainties associated with the amplitude picks of a given reflector, the signal-to-noise ratio (SNR) of the data is determined as follows

,                                           (1.9)

where Psignal and Pnoise are the observed powers (in dB) shown in Figure 1.12. Here the power spectrum is used to get at the signal-to-noise ratio, as the noise amplitude (Anoise) is hard to pick, while the signal amplitudes (Asignal) are easily distinguishable in the shot gathers. By comparing the power spectra of the P<em>P</em>´ signal and noise (Figure 1.12), the observed <em>SNR </em>for all offsets is about sixteen (<em>P<sub>signal </sub></em>∼ −7 <em>dB </em>and <em>P<sub>noise </sub></em>∼ −19 <em>dB</em>), which equates to a <em>P</em><sup>P´ picking uncertainty of σP<em><sub>P</sub></em>´ ∼ 0<em>.</em>06. This technique can applied to an entire dataset to determine the uncertainty associated with each amplitude pick.
<h2>Source - Receiver Offset (meters)</h2>
<strong>Figure 1.11. </strong>The vertical component (compressional) data recorded during the Jakobshavn wide-angle experiment (<em>Chapter 2</em>). The main reflectors of interest here are the compressional wave direct arrival (<em>A<sub>DA,P </sub></em>(<em>x</em>)), shear wave direct arrival (<em>A<sub>DA,S</sub></em>(<em>x</em>)), and the primary compressional wave ice bottom reflection (<em>A<sub>P</sub></em>
P´(x)). These reflectors were used to produce the power spectra presented in Figure 1.12.

If only normal incidence data are collected, ARR must be observed, as there is no other means to determine the true magnitude of RP<em><sub>P</sub></em>´(0) or <em><sup>R</sup><sub>S</sub></em>S´(0). Without a source amplitude, the magnitude of the observed reflectivity can be taken to be any arbitrary value, and hence, be representative of a wide range of potential subglacial beds. γ can be constrained with high certainty, as both AR and ARR following similar raypath geometries at normal incidence, with ARR covering an extra ‘bounce’ to produce its observed amplitude (Figure 1.4). From equations 1.2 and 1.3, the observed normal incidence reflectivity is a function of the acoustic impedances of the ice and its underlying bed. As a result, only the acoustic impedance of the bed is determined, loosely constraining what type of subglacial bed may be present. This

Figure 1.12. Power spectrum for four different signals from the shot gather in Figure 1.11: P-wave direct arrival (upper left), S-wave direct arrival (upper right), P`P´ reflection (lower left), and noise (lower right). The total power spectrum for the entire range of offsets (black), as well as a series of individual offsets, is shown for each signal. The three desired signals possess a dominant frequency in the 60-200 Hz range, and are 5-15 dB above the noise on average.

approach has been heavily applied to constraining RP`P´(0) in glaciated regions, as most active seismic data collected consist of normal to near-normal incidence observations of the subglacial bed [Bentley, 1971; R¨othlisberger, 1972; Smith, 1997; 2007; Vaughan et al., 2003].

When non-normal incidence data are collected, a series of approaches to analyzing the subglacial bed can be applied, dependent on the exact data collected. If a given ice bottom reflection (RP<em><sub>P</sub></em>´ or <em><sup>R</sup><sub>S</sub></em>S´) and its multiple are observed, absolute basal reflectivities can be constrained [Peters et al., 2007; Peters and Anandakrishnan, 2007; Peters et al., 2008]. Not that RP<em><sub>S</sub></em>´ and <em><sup>R</sup><sub>S</sub></em>P´ possess zero reflectivity at normal incidence, and thus A0 cannot be constrained from those data. If both RP<em><sub>P</sub></em>´ and <em><sup>R</sup><sub>S</sub></em>S´ are observed over a range of incidence angles, absolute reflectivities can be constrained with greater certainty, as multiple reflection types are observed [Chapter 2]. Finally, if no ice bottom multiples are observed in the data, then only the relative basal reflectivities can be determined [Richards, 1988; Atre and Bentley, 1993; 1994; Nolan and Echelmeyer, 1999a; 1999b; Anandakrishnan, 2003].

The collection of non-normal incidence data usually occurs as a series of shot gathers that are pieced together to form a continuous CDP gather from normal incidence to some incidence angle, dependent on the ice thickness and number of shot gathers acquired. Multiple shot gathers means multiple source amplitudes with potentially different receiver-firn couplings for each shot gather. As long as the CDP gather is continuous in terms of source-receiver offset from shot to shot and each shot was placed at a consistent depth within the ice column, the amplitudes of the direct arrival can be adjusted to essentially calibrate the entire dataset to one source amplitude. This approach is permissible, given the nature of the seismic waves propagating as the direct arrival. Since we collect seismic data over a range of source-receiver offsets, the amplitude decay of the direct arrival with offset is captured, with some correction needed to account for source-firn and receiver-firn coupling differences from shot to shot. The ‘near’ shot gathers essentially capture the seismic waves dipping through the firn, while the ‘far’ shot gathers capture the seismic waves traveling through the upper ice column (Figure 1.6). Because of the large seismic wavelength through the lower firn and upper ice column, and the general consistency in source and receiver depths for a given wide-angle experiment (λ ∼30-60 m, with the receivers within a meter of the surface, and the shot depths varying by ±10 m or less from shot to shot), any small variations in source or receiver depth from shot to shot fall well within the amplitude scatter from the direct arrivals for a given shot. Simple DC shifts can then be performed from shot gather to shot gather to produce a continuous amplitude decay of the direct arrival with offset. Taking both Equations 1.1 and 1.7, where the same source amplitude can produce a given ADA and AR, any DC shift to the direct arrival will also need to be applied to the primary reflection to produce a continuous amplitude curve of the primary reflection with offset.

Once the primary reflection data from the CDP gather are calibrated to produce a continuous amplitude curve, Equation 1.1 can be applied to determine the basal reflectivity curve that best fits these data, given that A0, γ, and a have all been constrained or assumed. In the instance where both RP<em><sub>P</sub></em>´ and <em><sup>R</sup><sub>S</sub></em>S´ are observed over a range of incidence angles, the approach outlined in Chapter 2 can be used to determine basal reflectivity. In equation form, basal reflectivity is summed up in the Zoeppritz equations as a function of the elastic properties along the ice-subglacial bed interface (αICE, βICE, ρICE, αBED, βBED, ρBED) for a given incidence angle [Aki and Richards, 2002]. Here the grid search method is employed to search all possible elastic property combinations for the subglacial bed and determine the least-squares fit to the observed data. By inverting for the bestfitting reflectivity curve to the observed reflection amplitudes, the elastic properties of the subglacial bed are constrained, highlighting the basal conditions present to influence the observed ice dynamics in a given study region.

When no observable ARR(0) is present in the seismic data, it becomes difficult to place constraint on the source magnitude with high certainty. Nevertheless, if a continuous amplitude curve for a range of incidence angles is collected, loose constraints on the basal regime can still be made. Since A0 is constant for a given reflectivity curve,  will be the same if A0 is known or not. While the absolute reflectivity cannot be determined, the relative reflectivity can, allowing for modeling of the observed amplitude variation to see what subglacial bed reflectivities mimic this type of is unknown, this will not alter the incidence angle at which extinction or polarity changes in the reflectivity may occur. Forward modeling of various basal conditions to determine what bed types reflect the observed  in the data or the incidence angle at which a polarity change occurs can point to a subset of possibilities and the observations to be narrowed to a range of potential subglacial beds for the study region.

1.6      Summary

Seismic AVO analysis in glaciated regions is a powerful tool in identifying the basal conditions that promote or prohibit streaming ice flow. Dependent on the type and amount of data collected, the end results produced can range from loose constraints on the acoustic properties of the subglacial bed in a spot location to full analysis of the basal regime along a cross section of the study region. The seismic AVO technique detailed here in Chapter 1 has been applied to the four seismic datasets outlined in the following chapters, providing the reader with examples of how this approach is applied to a given dataset. The goal here is for the reader to note what is needed to perform a proper wide-angle experiment in glaciated regions, how to process the data, and how to interpret and infer basal conditions, even when constraints on the data collected are limited.

1.7      References

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Chapter 2

Seismic observations of a hard bed in the onset region of Jakobshavn Isbrae, West Greenland, through application of the seismic amplitude variation with offset (AVO)

technique

A SEISMIC INVESTIGATION OF BASAL CONDITIONS IN GLACIATED REGIONS

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