Journal of Geophysical Research: Planets

Martian north polar layered deposits stratigraphy: Implications for accumulation rates and flow

Authors


Abstract

[1] We have used Mars Orbiter Camera (MOC) images and Mars Observer Laser Altimeter (MOLA) data to correlate specific layers within the upper ∼500 m of the Martian north polar layered deposits in many troughs. Using these correlation results, we derive relative accumulation rates across the polar layered deposits and through time. We identify two major layer sequences, one lying stratigraphically above the other, each consistent with an overall curving downward layer structure with shallow slopes but with significant localized variations in layer height. Major disruptions of stratigraphy (such as angular unconformities) do not appear within the correlated layer sequences. On local and broad scales, each layer sequence exhibits a different relative accumulation rate pattern, indicating that this rate has not remained constant through time and has been affected by localized processes. The overall pattern of the lower layer sequence is similar to that of a classic terrestrial ice sheet, with a decreasing relative accumulation rate away from the center of the polar layered deposits southward. The upper layer sequence exhibits no obvious overall trends. We also compare our correlation results to predictions of the effects of simple ice flow on layer structure, finding that mass balance patterns have overprinted any effects of large-scale ice flow. Flow has not been significant, compared to mass balance, in forming the overall structure of the correlated layers.

1. Introduction and Background

[2] Characterizing the past and current climate of Mars has been a major focus of Martian studies for many years. Since surface temperature and atmospheric water vapor pressure regulate the surface distribution of water ice, the polar layered deposits are intimately tied to the climate of the planet as a whole [e.g., Mischna et al., 2003; Haberle et al., 2003; Levrard et al., 2004]. Both the northern and southern deposits consist mostly of H2O ice and dust [Tanaka and Scott, 1987; Thomas et al., 1992], with each layer having a different dust to ice ratio. These polar layered deposits are exposed within scarps and shallowly sloping (a few degrees) trough walls. Overlying a small portion of the polar layered deposits in the south is a thin layer of CO2 ice, sometimes termed the “permanent cap” or “residual cap” [Thomas et al., 2000; Byrne and Ingersoll, 2003], juxtaposed with and underlain by H2O ice [Titus et al., 2003; Bibring et al., 2004]. The northern counterpart of the “permanent (residual) cap” consists of H2O ice [Kieffer et al., 1976; Bibring et al., 2004] which covers nearly the entire polar layered deposit surface. Within the polar layered deposits, there may be several geologic units of different origins and/or depositional histories [Tanaka et al., 2005; Tanaka, 2005]. Tanaka et al. [2005] have mapped the Boreum 2 unit, dated to <1 × 105 years, as material deposited mostly on flat portions between troughs. Underlying the Boreum 2 unit is the Boreum 1 unit, equivalent to the bulk of the polar layered deposits.

[3] Prevailing theories on the formation of the polar layered deposits revolve around the Martian orbital cycles, especially obliquity, influencing the climate and thus the amount of dust and ice in polar layers [e.g., Cutts and Lewis, 1982; Laskar et al., 2002]. What one means by “layer” can be confusing. For example, Fenton and Herkenhoff [2000] use “a dark and light stripe ‘pair’” whereas Laskar et al. [2002] consider each bright stripe to be one layer and each dark another, and it is this definition of layering which they tie to changing orbital parameters. What we term a “layer” in this paper is any stripe which is distinguishable by albedo and/or morphology from the stripes surrounding it and which is not resolvable by the Mars Orbiter Camera (MOC) into thinner stripes.

[4] To unravel the complex climatic record within the polar layered deposits, a better understanding of the geologic history of the polar layered deposits (PLD) is necessary. As one step in discovering this history, one must know the stratigraphic relationships and accumulation rates within the PLD. Howard et al. [1982] have performed an extensive study of the stratigraphy within both polar layered deposits using primarily Viking images. They have classified types of layered terrain and unconformities (breaks in the stratigraphic record) within them and have created detailed maps of northern layered deposit exposures within 11 study areas mostly concentrated near the PLD margins. From these observations, the authors are able to describe the complex patterns of erosion and deposition associated locally with troughs. However, this study does not present a stratigraphic cross section or correlation of individual layers across long distances. Fenton and Herkenhoff [2000] have used photoclinometry, stereogrammetry, and MOLA altimetry to correlate layers across and along a trough within the north PLD. They find that layer thicknesses change along the trough and thus are not constant throughout the PLD. Using Herkenhoff and Plaut's [1999] resurfacing rates and their own observations of layer thickness, Fenton and Herkenhoff [2000] find that one layer (by their definition) can form in ∼16,000 years (less than the period of one obliquity fluctuation).

[5] In one of two first attempts at a definitive correlation of individual layers across long distances, Malin and Edgett [2001] have described what they term a “marker bed” within the north PLD which has distinctive morphology and has been identified within 3 MOC images about 100 km apart within one trough (see their Figure 68); the authors mention that the stratigraphic sequence surrounding this “marker bed” is the same in all 3 images, though a figure illustrating this correlation is not presented. Kolb and Tanaka [2001] have also analyzed three pairs of images from adjacent north polar troughs which have similar layer sequences, with one pair exhibiting another distinctive layer, separate from the marker bed of Malin and Edgett [2001]. They find that the difference in elevation of the members of each pair decreases as distance from the PLD center increases.

[6] Two recent studies have determined that the internal layer structure of both PLD may be curving downward, away from the PLD center. Byrne and Ivanov [2004] have identified a bench-forming layer and mapped it across a distance of about 150 km within the south PLD, noting that other bench-forming layers have been identified during their study and could be used for further correlation efforts. They find that the overall shape of the bench-forming layer is Gaussian and nearly fits a parabolic dome in the center. Milkovich and Head [2005a] use the Match 1.0 program, developed by Lisiecki and Lisiecki [2002] for matching deep sea cores, to match the intensity profiles from one MOC image to the next. They find that four images across multiple troughs have good correlations which they define as having coefficients of determination (the “percentage of the [DN] variation within each data set that is related to variations in other data sets”) equal to 0.6–0.8,wherein 1.0 is a perfect match. The “marker bed” is found by Milkovich and Head [2005a] to have an apparent dip of about 0.5° so that, combined with the good correlations of several images, the north PLD, may also have a curved structure. In their case, the internal layers generally follow the surface shape.

[7] Figure 1a presents a generalized picture of downward curving layers, as previously suggested for both PLD [Byrne and Ivanov, 2004; Milkovich and Head, 2005a], which generally follow the PLD surface [Milkovich and Head, 2005a]; we have ignored local anomalies and specific curvature shape in this plot. To generalize the PLD structure by such a sketch, several conditions must be met.

Figure 1.

Generalized sketches of potential PLD internal layer structure. As discussed in section 4.1, the results of our layer correlations indicate that the structure of the northern PLD cannot easily be generalized in sketches such as these. All have downward curving layers. (a) Layers with nearly constant depth from the center of the PLD to the margin and net advance of the PLD margin. (b) Layers that all terminate at nearly the same latitude so that the lateral extent of the PLD has not undergone large-scale changes. (c) Lateral extent of the PLD, which has changed significantly through time, causing layers to terminate at various latitudes.

[8] 1. A curving downward surface shape will result from the increasing influence of ablation over accumulation near the margin, with zero net accumulation at the margin. Internal layers should also be expected to curve downward toward the margin since they are former PLD surfaces. Indeed, unless the layers were deposited as a flat-lying stack with the current convex-upward shape of the PLD being due entirely to processes (such as erosion) which occurred after all of the layers were deposited, flat-lying layers are not expected.

[9] 2. Additionally, deposition of the PLD on a preexisting mound will impart a curving downward shape [Byrne and Ivanov, 2004]. In the north, the polar basal unit underlying the PLD [Byrne and Murray, 2002; Edgett et al., 2003; Fishbaugh and Head, 2005] may provide such a mound, while the southern mound source is less obvious (possibly the rim of the Prometheus Basin or possibly older southern PLD).

[10] 3. Since the layers in Figure 1a generally follow the PLD surface and have the same thickness across the whole PLD, from center to margin, latitudinal trends in factors which affect mass balance, such as lower temperatures near the PLD center, have not affected the PLD layers in any significant way in this sketch. Mass balance is the sum of deposition (positive) and ablation (negative). One can measure the mass balance at particular points on a glacier's surface at particular times, or one can calculate the net mass balance over an entire year at particular points or for the glacier as a whole. A negative mass balance indicates a state of net erosion and a positive mass balance a state of net deposition. The thickness of a layer is determined by its deposition rate and the amount by which it has been eroded. Thus, if each layer has nearly the same thickness across the PLD from the center to the margin, the mass balance has been nearly the same at all latitudes. We find this to be an unlikely scenario.

[11] 4. Since the margin of the PLD is advancing to lower latitudes in Figure 1a (as indicated by Figure 2 of Byrne and Ivanov [2004] and by Figure 13 of Milkovich and Head [2005a]) the extent of the PLD has been net increasing. Global climate models [e.g., Mischna et al., 2003; Levrard et al., 2004] suggest that polar ice deposits are unstable at high obliquities (e.g., >35°) and, according to models of surface ice stability, may even disappear [Jakosky et al., 1995]. Additionally, as stated above, it is generally accepted that changes in obliquity probably regulate the deposition of layers in the PLD. Given that that average obliquity has remained relatively constant for the last 5 Myr and was larger previous to that (which would decrease the PLD extent) [Laskar et al., 2004], we find it unlikely that the PLD extent should be net increasing.

[12] While neither PLD likely meet conditions 3 and 4, the suggestion that the layers may generally be curved downward [Byrne and Ivanov, 2004; Milkovich and Head, 2005a] is expected by conditions 1 and 2 (most likely 1). Such a structure could be more consistent with a scenario in which the extents of the polar PLD have remained at nearly the same latitude (with minor fluctuations) (Figure 1b) or in which the extents have undergone larger fluctuations (Figure 1c). In Figures 1b and 1c we have illustrated situations in which ablation increases near the margin as is true for a classic terrestrial ice sheet; thus the thickness of the layers does not remain constant from the center to the margin. Wind patterns, troughs, and major topographic variations (e.g., Chasma Boreale) may complicate this situation on Mars at the local scale.

[13] In this study, we correlate individual layers across the north PLD using MOC images and MOLA data, thus obtaining PLD-wide stratigraphic information which can be used to assess whether the layer structure of the northern PLD is consistent with any of the general sketches shown in Figure 1. Additionally, the mass balance at particular points on the Martian PLD surfaces has never been measured, but, using our layer correlations, we can derive relative average accumulation rates (multiplied by time) for entire layer sequences at various points. Thus this study adds important insight into the depositional history of the north PLD. There is not necessarily any reason to assume that the southern and northern PLD have the same structure and accumulation rates, so our results cannot be assumed to also be true of the southern PLD.

[14] From these correlations, we can also assess whether large-scale flow has ever significantly affected the north polar layer structure. Since flow rates depend partially on temperature, any signs of significant large-scale flow could indicate a warmer climate during the past history of the PLD. We compare the structure of the layer sequences we correlate to model predictions of the effects of flow on layer structure. For the south, Byrne and Ivanov [2004] conclude that the shape of the layer which they trace is not consistent with typical shapes produced by flow (e.g., a Vialov profile), but they do not rule out that large-scale flow may have occurred in the past, with the current shape being a product of postflow erosion.

2. Layer Correlation

2.1. Methods

2.1.1. Data Sets and Layer Sequences

[15] We have performed our layer correlations using MOC images of the PLD exposed in trough walls and MOLA data which provide the elevation of each correlated layer. Beginning with 3 MOC images identified by Malin and Edgett [2001] as exposing the same “marker bed”, we have identified a sequence of what we term “reference layers”. Reference layers are distinct from the rest of the layering in the images in which they are exposed and protrude from the other layers; thus they are probably erosionally resistant layers. The sequence of reference layers containing the “marker bed” constitutes what we term the “upper layer sequence” (ULS) because it generally lies stratigraphically above the “lower layer sequence” (LLS) (as explained in section 2.2). Using the Geographic Information Systems (GIS) software, ESRI Arcmap 9, we have overlain coregistered MOC image footprints on MOLA gridded topography data to extract the elevations of reference layers. After identifying the ULS in the original three images, we have searched for the ULS in images lying progressively farther away from the original three. The LLS has been identified in a similar manner, though using different layers.

[16] To correlate layers, we have examined all MOC images which meet the following criteria: (1) The image must be of sufficient quality to resolve each layer used for correlation (i.e., we did not use images in which the layers appeared too “fuzzy” or pixilated). (2) The image must have been taken before the E07 set (August 2001) since MOLA was not operating after that, and coregistration of those MOC images and MOLA data consequently has larger errors. The need for accurate coregistration is explained below. (3) We have not used overlapping images, but rather have picked the best quality images of those which do overlap. We list the images used for correlations in Table 1, and we map their locations in Figure 2. Throughout the text, we refer to the images by their number in Table 1.

Figure 2.

Maps showing locations of images used for correlation in this study. Crosses in the center indicate location of the pole. Images are numbered as in Table 1. See Table 1 for center latitude/longitude and resolution information for each image. Marks show image location and orientation but not image size. (a) Underlying image is a portion of the MC-01 MOC wide-angle image mosaic (image credit: NASA/JPL/MSSS). Red marks indicate images used for correlations of the ULS, and blue marks indicate images used for correlations of the LLS. (b) Underlying is the 512 pixel/degree gridded MOLA topography.

Table 1. MOC Images Used for Correlations in This Studya
Image LabelImageResolutionCenter LongitudeCenter Latitude
  • a

    Longitude is in °W, latitude is in °N, and resolution is in scaled m/pixel. Latitude and longitude information is for the center of the images; outcroppings of the ULS and LLS used for correlations in this study do not necessarily lie at the center of the image. Numbers in the first column correspond to the labels in Figure 2. Throughout the text, we refer to the images by these numbers.

ULS
1E01/0103412.981.4287.09
2E01/0096613.01167.3486.98
3E03/0041712.9658.4387.07
4E01/0109213.03264.3687.03
5E01/013584.88185.3986.98
6M00/017541.62281.9286.55
7M00/021001.62279.5486.48
8M00/020721.61258.8985.96
 
LLS
9E01/0142213.0082.0287.08
10M18/018973.47127.7686.23
11E02/015404.86193.3486.11
12M00/016461.61105.9084.48
13M03/017276.45100.5384.23
14E03/004614.8583.4083.81

2.1.2. Correlating Layer Sequences

[17] After eliminating images which have not met these criteria, we have identified the ULS and LLS primarily by matching sequences of layers. In other words, we have not based the correlation on being able to identify individual layers from one image to the next but rather on being able to match the sequence of individual reference layers. By our methods, a reference layer cannot be uniquely identified separate from the sequence of reference layers surrounding it. The same layer sequence in different images will have the same reference layers in the same stratigraphic order. No reference layers used for correlation are missing from between other reference layers. We have identified sequences by noting the presence of reference layers and ancillary features such as fine-scale laminations above or below particular layers, occurrences of sets of two layers stratigraphically close together (a double layer), prominent layers lying between reference layers (though these are usually less prominent than the references layers themselves) and the apparent albedo of individual reference layers and of the layers surrounding them. We term the albedo “apparent albedo” since we do not quantify the albedo and since the brightness of a layer is only relative to other layers in the same image; layer brightness cannot be directly compared to that of a layer in another image.

[18] The technique of matching layer sequences can best be understood through Figure 3 and in Figures A1 and A2, which show the full layer sequences and ancillary features. To consider an exposure of layers in an image to be part of the ULS, five reference layers must exist and at least three of the ancillary features must exist in the proper place in the stratigraphic sequence. Two ULS references layers have a distinctive bumpy texture: the MB (“marker bed”) and the U1. In the LLS, the L5 layer is prominent and readily visible. The L3 and L4 layers are always found close together in the vertical direction. In all images of the LLS but one, the seven prominent layers (L1 to L7) and at least 4 ancillary features exist in the proper stratigraphic order. Only image 14 is missing any reference layers (one from the top and two from the bottom of the sequence); however, the prominent L5 layer is visible in this image, the L3 and L4 layers are close together, and there is one ancillary feature.

Figure 3.

Illustration of identifying layer sequences in MOC images. Note that the pattern, or sequence, of layering is as important as individual layer morphology or albedo, as explained in the text. Colored lines denote reference layers which comprise the ULS and LLS and are labeled as in Figures 6 and 7. See Figure 2 for image locations. (a) Examples of the ULS. (left) Portion of image 6 and (right) portion of image 5. A, fine layering; B, fine layering; C, prominent layer; D, prominent layer; E, dark strips on left = prominent layer on right?; F, fine layering; G, prominent layer; H, fine layering; X, dark stripe; Y, fine layering; Z, prominent layer. X, Y, and Z are ancillary features also shown in several images in Figure A1. MB is the “marker bed” described by Malin and Edgett [2001]. Figure A1 shows the rest of the images used for correlating the ULS, with the layers and ancillary features labeled as given here. (b) Examples of the LLS. (left) Portion of image 13 and (right) portion of image 10. A, dark mantle and fine layers; B, finely layered; C, prominent layer; D, prominent layer; E, prominent layer. Figure A2 shows the rest of the images used for correlating the ULS, with the layers and ancillary features labeled as given here.

[19] There are two main reasons why we correlate sequences of layers rather than correlating each reference layer individually. Albedo (whether “apparent” or quantified) is not always a reliable indicator of a layer's identity since a visible image only samples the top few microns of a surface. The surface albedo of a layer may not represent the actual, inherent albedo due to deposition of dust lags during ice sublimation (possibly only microns thick), deposition of frost, shadowing, and formation of dust streaks. Thus one cannot always use albedo to correlate a particular layer across several images. Perhaps less obvious is the fact that due to different image resolutions and actual physical differences the morphology of a layer can also change from one image to the next. The characteristic bumpy appearance of the marker bed in the original three MOC images presented by Malin and Edgett [2001] (images 6, 7, and 8) does not appear as obvious as in image 5 (Figure 3a) wherein it has been identified by its position in the layer sequence. Thus one also cannot always use the morphology of an individual layer either to correlate it across several images.

[20] To ensure that our sequence correlation method is stringent and produces unique results, we have compared randomly selected MOC images of north polar layers and have been unable to correlate them using our methods. In other words, using our method, one cannot “find” layer sequence patterns where they do not exist. This is important because of the natural human tendency to find patterns, even when they are not related to any relevant physical process. Additionally, in Figure 4, we show 2 examples of images which contain both the ULS and LLS, ensuring that these are separate, rather than overlapping sequences. This also ensures that the ULS stratigraphically overlies the LLS, rather than the LLS characterizing the layering of one portion of the PLD and the ULS characterizing another.

Figure 4.

Illustration of the link between the ULS and LLS. (left) Portion of image 6 which has been used for correlations of ULS layers, (middle) portion of image 13 which has been used for correlation of LLS layers, and (right) portion of image 2 which has been used for correlation of ULS layers. A, faint double layer set; B, faint layer amidst fine-scale layering just visible at image resolution; C, finely layered section; D, double layer.

[21] The map in Figure 2 merely shows locations where we are able to positively identify the ULS and LLS. This map is not meant to illustrate where the ULS and LLS cannot be found. It is possible only to positively identify where a layer sequence exists but not to identify locations where it does not exist. The ULS and LLS may be present in locations of insufficient data coverage or where MOC images cover too small a fraction of either (or both) layer sequence to be identified.

2.1.3. Finding the Elevations of Correlated Layers

[22] In order to map the overall, PLD-wide structure of the ULS and LLS, we have noted the elevation of each reference layer in each sequence by overlaying the coregistered MOC images on the MOLA gridded topography data in ESRI Arcmap. We use gridded topography because it has nearly 3 times better spatial resolution (∼115 m/pixel) than individual MOLA profiles (∼300 m between shot points). Since we have taken the elevation from one point along each layer, we assume that the elevation of a layer does not change within its exposure in one MOC image (<10 km width). Even MOC images taken when MOLA was still operating (images before the E07 series) can have positioning errors of up to 10–100 m after coregistration with the MOLA data [Byrne and Ivanov, 2004]. While images can be adjusted for incorrect positioning by eye, as Byrne and Ivanov [2004] have done to south polar MOC images, there are essentially no features in the north PLD, such as pits, craters, or knobs, which can be used to line up the images with the topography with better accuracy. However, we have corrected for inaccuracies in coregistration by taking the following steps.

[23] 1. If the image has an error in horizontal positioning and the slope of the corresponding trough wall changes with horizontal position along trough strike, then the slope along the image (perpendicular to layering) as is recorded in Arcmap may not be correct. To correct for this, we have calculated the slopes along the MOC images as derived from MOLA gridded data in Arcmap and as derived from MOLA profile data along each MOC image. Since there is essentially no error in the coregistration of individual MOLA profiles with corresponding MOC images, we have adjusted the Arcmap-derived slopes so that they are the same as the MOLA profile slopes. The vertical distance between reference layers in each image used for correlation has then been adjusted accordingly. Through this process we are assuming that the slope does not change between the top and bottom layers of the ULS and LLS. We have made certain that there are no major breaks in slope either in the MOLA profile data or in the uncorrected profiles gleaned from the MOLA gridded data in Arcmap. The MOLA profiles and their position along the MOC images have been taken from the NASA Planetary Image Atlas online, using the function created by Anton Ivanov (http://pdsimg.jpl.nasa.gov/cgi-bin/Atlas/).

[24] 2. To correct for possible vertical positioning errors, we have then chosen a representative layer in the ULS (the MB) and in the LLS (the L5), marking the location of these layers on the MOLA profiles corresponding to each image used for the correlations. Each layer in the LLS and ULS has been shifted up or down vertically based on how much the MB and L5 layers have been shifted in each image to match their elevations in the MOLA profile, assuming that all layers need to be shifted by the same amount.

[25] 3. After adjusting for possible errors in MOC image positioning with respect to the MOLA gridded topography, we have checked the elevations of the U5 and MB layers and the L5 and L2 layers against the position of these layers on the MOLA profiles corresponding to each image. The elevations of the U5, MB, L5, and L2 layers plotted in Figure 5 all lie within ±5 m of their position on a MOLA profile. A layer may not lie directly on a MOLA profile data point, but for those which do not we interpolate between points. We consider ±5 m to be our best estimate of the error in elevation of those particular layers. Layers other than the MB and U5 and the L2 and L5 may have slightly larger elevation errors (at most ±15 m), but they are not used to derive relative accumulation rates as described in section 3.

Figure 5.

Elevation of the ULS (gray) and LLS (black) as a function of latitude (°N). Since MOC images and MOLA gridded topography cannot be coregistered with 100% accuracy, the elevations derived from the gridded data have been corrected as described in section 2.1.3. As explained in the text, we estimate a maximum vertical positioning error of about ±5 m, about the size of a data point in the plot. Each vertical stack of points comprises an exposure of the ULS or LLS in one MOC image. See Figures 6 and 7 for labeled close-ups of the ULS and LLS elevations, respectively.

2.2. Observations

[26] Figures 57 display our layer correlation results. All of the layers identified in this study are exhibited in Figure 5 so that one can see the entire structure at once. However, the layers and images are too close together in Figure 5 to label them, so we have created labeled close-ups of Figure 5 in Figures 6 (ULS) and 7 (LLS). Each labeled line represents one reference layer. Each vertical stack of points (outlined by gray boxes in Figures 6 and 7) comprises the reference layers within one image (as labeled in Figures 6 and 7). It is important to keep in mind that all of the plots discussed in this section are 2-D representations of 3-D layer structure; for instance, the ULS and LLS do not actually cross each other as implied by Figure 5. To ascertain the 3-D position of one image relative to another, one must compare these plots with the maps in Figure 2.

Figure 6.

Elevation of the ULS as a function of latitude (°N). Gray boxes outline layer exposures in each MOC image. MOC images are labeled by number as in Table 1 and Figure 2. Individual layers are labeled MB (“marker bed,” named by Malin and Edgett [2001]) and U1–U5. (a) Elevation of the entire ULS. (b) Close-up of the portion poleward of 87°N.

Figure 7.

Elevation of the LLS as a function of latitude. Gray boxes outline layer exposures in each MOC image. MOC images are labeled by number as in Table 1 and Figure 2. Individual layers are labeled L1–L7 (layers L3 and L4 are too close together to label in this plot). Note that images 10 and 13 contain the MB layer from the ULS.

[27] While not a true cross section, Figure 5 does illustrate that if one considered only the elevations of the LLS and ULS in the images nearest the pole and at lower latitudes, the layer structure of the upper portion of the PLD would appear to curve downward. Since the PLD thickness decreases to a minimum at the margin (and thus net mass balance here is smaller than at the pole), this should be expected. However, the layer structure also exhibits local variations in layer height characterized by shallow slopes. All of the slopes discussed below are minimum estimates and are not necessarily true dip angles since they were not necessarily measured perpendicular to layer strike.

[28] According to Figure 6, the marker bed (MB) varies in elevation by ∼200 m within images 6, 7, and 8 which all lie within one trough. In agreement with the results of Edgett et al. [2003] for some polar layers, the along-trough slope of the MB within that trough is extremely small, ∼0.1°. The closest one can come to a true cross-section view of the ULS is between the outcroppings in images 4 and 8; the slope of the MB between these two outcroppings is ∼0.2° (measured along a line connecting the two outcrops). Within the LLS (Figure 7), images 12 and 13 lie within the same trough; the along trough slope of the L5 layer here is ∼0.07°. The closest approximation to a cross-sectional view of the LLS is between the outcroppings in images 9 and 14, where the slope of the L5 layer between these is ∼0.3°. To first approximation, the layers follow the curvature of the PLD surface which also has a shallow slope (∼0.3°) from the center to the margin at 270°W. However, even at such low slopes, seemingly small-scale variations can be significant on a vertical scale. Layer U5 in image 3 lies very close to the local PLD surface but is covered by younger layers at other locations examined in this study. In the next section, we examine the changes in thickness of the ULS and LLS across the PLD and relate this to changes in accumulation rate.

3. Derivation of Relative Accumulation Rates

[29] From our layer correlations across the PLD, we derive relative average accumulation rates for the entire ULS and LLS, rather than for individual layers. Since individual layers in MOC images are likely made up of many thinner layers not visible at MOC image resolution, we feel that our estimates are better defined accumulation rates than those which rely on the individual layer thickness for their calculation. As a first-order estimate, we can equate relative accumulation rate to the elevation difference between two layers in the ULS and two in the LLS.

[30] We do not tie this calculation to a timescale, so the elevation difference actually equals the product of accumulation rate and time. Since we are considering the average accumulation rate (multiplied by time) for entire layer sequences at a time, derived patterns in these rates are equivalent to patterns in mass balance (which is everywhere positive when averaged over buildup of the entire layer sequence). Each point in Figure 8 represents the elevation difference between two layers, normalized to the value for the images closest to the pole in the ULS (layers U5 and MB) and LLS (layers L5 and L2, since image 14 does not contain the layers above and below these). The relative accumulation rates for the ULS and LLS are calculated using different sets of layers and have not been tied to a timescale, so one cannot directly compare the absolute values for the ULS and LLS but rather the overall trends. The error bars shown in Figure 8 are maximum errors calculated by propagating the ±5 m error in elevation of the U5, MB, L5, and L2 layers, using average deviations.

Figure 8.

Relative accumulation rates for the ULS (a) as function of latitude and (b) as a function of longitude and for the LLS (c) as a function of latitude and (d) as a function of longitude. The relative accumulation rate values have been normalized to those of the images closest to the pole (note that their values equal 1). The right-hand vertical axis on all plots is the elevation difference used to obtain relative accumulation rates as described in the text. Values of relative accumulation rate cannot be directly compared between the ULS and LLS since they comprise different layers and are of different thickness. Only patterns can be compared.

Figure 8.

(continued)

[31] From Figures 8a and 8b, it is evident that the accumulation rates of the ULS vary significantly, the highest rate being ∼2 times the lowest. We have no data for the ULS at latitudes lower than 86°, but there appear to be no overall trends in accumulation rate at these high latitudes, either with respect to latitude or longitude. We cannot determine with these data whether the accumulation rate decreases at lower latitudes, toward the margin.

[32] The LLS (Figures 8c and 8d) also exhibit significant variation in accumulation rate (the highest rate being ∼3 times the lowest), but that variability is almost completely within the error bars. The lesser thickness of the LLS as compared to the ULS results in larger errors in calculated relative accumulation rate. With respect to latitude, even within the error bars, accumulation rates decrease away from the pole. The LLS data cover a smaller range of longitudes than do the ULS data, but within this range, no trend is evident. There is no LLS coverage between 0° and 60°W, so we cannot determine whether the low accumulation rates observed there within the ULS are also apparent within the LLS. Of course, the absolute maximum and minimum relative accumulation rates for the ULS and LLS may occur at locations not represented by the data points shown in Figure 8.

4. Discussion

4.1. ULS and LLS Structure

4.1.1. Layer Heights and General Structure

[33] In this study, the sparcity of data does not allow us to draw a generalized sketch of the PLD layer structure. However, we can use our data to assess the candidate sketches shown in Figure 1. Our analyses show that layer slopes along troughs are similar to the PLD surface slope; layers are not flat lying, even though slopes are extremely shallow. Ignoring variation between them, the ULS and LLS slope downward between the images closest to the pole and those at lower latitudes. Additionally, the ULS and LLS curve downward at slopes close to that of the PLD surface between images 4 and 8 and 9 and 14, the closest approximations to true cross-sectional views in this data set. However, the observed variations in layer height indicate that the layers of the ULS and LLS likely do not smoothly curve downward in cross section, so that Figure 1 should include more local variations in layer height. On a vertical scale, these height variations are significant compared to the ∼3000 m combined thickness of the PLD and basal unit. Since localized variations in layer height are not parallel between the ULS and LLS, these sequences have not been deposited conformably with each other. Mass balance patterns must therefore have changed between the two units.

[34] Near the margins, the stratigraphy is difficult to interpret (as described in section 4.1.3) so that we cannot determine from this study whether the southward extent of the north PLD has always been in nearly the same position, consistent with Figure 1b. Fishbaugh and Head [2000] have presented evidence for a once much larger northern PLD extending out to ∼75°N, so it is likely that some layers pinch out and unconformities have been created by this erosional episode (and any others which may have occurred). Since we have been able to correlate layers in several locations, major sections of layers do not appear to pinch in the part of the PLD which we have analyzed. However, we cannot rule out that layers lying between the ULS and LLS, stratigraphically above and below them, or farther south than the images in Figure 2, pinch out somewhere. As discussed in section 4.1.3, angular unconformities do exist within PLD exposures closer to the margin so that Figure 1c might best describe the situation near the margins, albeit possibly in exaggerated form.

[35] None of the sketches in Figure 1 appropriately captures variations in layer package thickness (relative accumulation rate). The ULS appears to exhibit no specific trend (at least at latitudes greater than 86°), and the LLS exhibits decreasing relative accumulation rates away from the pole.

[36] In summary, layers within the PLD may be curving downward as shown in all Figure 1 sketches, but local variations in layer height are significant on a vertical scale. Unconformities near the margin indicate pinching out of layers there, as illustrated in Figure 1c. Layer sequence thicknesses (relative accumulation rates) are not constant and cannot be summarized by any of the sketches in Figure 1; Figure 1b may come closest to illustrating the decreasing thickness of the LLS with decreasing latitude but possibly not the situation near the margin.

4.1.2. Effects of Basal Topography

[37] As explained in the introduction, net ablation at the PLD margin and the mound shape of the basal unit will contribute to downward curvature of PLD layers. Localized variations in mass balance will impose localized variations in layer height. However, if major topographic variations exist on the PLD bed (or on the basal unit surface in the places where it underlies the PLD), then layers could be draped over these, causing anomalies in layer height. Layers near the top of the PLD will only be affected if the bed topography is of a significant vertical scale. Given the generally smooth, flat nature of the north polar plains evident from MOLA data it is unlikely that any large topographic features other than impact craters exist beneath the north PLD. According to Garvin et al. [2000], the largest crater near the PLD (at 73°N, 163°E) is about 84 km in diameter with a 920 m rim height. This height represents a significant fraction of the PLD thickness which, if such a crater exists beneath the PLD, could affect vertical positioning of a layer by affecting accumulation patterns (perhaps a greater accumulation rate within the crater if it acts as a cold trap) and/or flow near the crater. The effect on layer position would decrease with height above the crater. Since we do not know the detailed topography of the PLD base, we assume that any major topographic features which would significantly affect the depth of layers in the upper ∼500 m of the PLD would also manifest themselves on the surface of the deposits. Near the locations of images used in this study, we have observed no significant topographic variations at the surface. Additionally, basal topography anomalies would be expected to affect the ULS and LLS in the same way, yet local variations in layer height do not follow the same pattern in the ULS as they do in the LLS, further supporting the fact that these variations are not due to basal topography.

[38] Deflection of the lithosphere beneath the PLD may also affect the bed topography. However, again, this would in turn affect the ULS and the LLS in the same way, possibly causing layers closer to the margin to be deflected upward and layers toward the center to be deflected downward. Johnson et al. [2000] estimate such a deflection to be about 500 m at maximum, and recent Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) results confirm that any deflection is indeed less than this amount [Picardi et al., 2005]. In any case, even with possible lithospheric deflection below the PLD, the layers we have analyzed still in general appear to curve downward toward the margin.

4.1.3. Angular Unconformities and Stratigraphy Near the PLD Margin

[39] We have not performed any correlations any further toward the margin than the images mapped in Figure 2 because of poor image quality and coverage and because of stratigraphy which is difficult to interpret. We have been unable to recognize with certainty either the lower or upper sequence in those areas. In several images layers appear highly eroded (Figure 9a), making them difficult to identify. In other images, local angular unconformities (unconformities wherein the layers above and below the unconformity are oriented at some angle to one another) disturb the stratigraphy (Figure 9b). Howard et al. [1982] have also described unconformities observed in Viking images taken near the margin. They tend to occur on pole facing trough walls (due to unconformable deposition of what the authors term “banded terrain” on top of preexisting layers), within north-south striking troughs (where the north and south facing walls may receive similar amounts of insolation, thus alternating between erosion and deposition), and at trough junctions. Within MOC images, Tanaka [2005] has identified 75 unconformities in MOC images near the margin east of Chasma Boreale, within deep layers, near an impact crater, and at a trough junction. Murray et al. [2001] also note localized angular unconformities within the south PLD. Angular unconformities can arise from complex cycles of local ablation, retreat and readvance of the PLD margin, and from unconformable deposition, all of which would preferentially affect the margin.

Figure 9.

Examples of layers near PLD margin that cannot be included in layer correlations due to such factors as erosion and the presence of angular unconformities. (a) Example of eroded layers located near PLD margin. Portion of image M02/04019, centered at 69.05°W, 83.21°N. (b) Example of a local angular unconformity (center, left) located near PLD margin. Portion of image E03/00812, centered at 328.04°W, 80.95°N.

[40] Given that layers within the troughs sufficiently far inward from the margin can be correlated and that we do not see local angular unconformities within the correlated ULS and LLS, it is unlikely that there are any widespread, major angular unconformities in these layer sequences within the latitudes we have studied. Such a conclusion has also been reached by Milkovich and Head [2005a] since their matching analysis (described in section 1) has revealed no major disruptions of stratigraphy. This observation implies that if the polar troughs migrate poleward as suggested by Howard et al. [1982], they may be relatively young; their past presence in older layers would be expected to leave scars in the form of angular unconformities as the former troughs which have since migrated poleward were filled in by younger layers. However, if the position of the troughs has always been the same, if the troughs migrate but their separation distance is always the same, and/or if deposition takes place mainly on the areas between troughs (as modeled by Fisher [1993, 2000]), then no scars in the form of angular unconformities would be expected to develop.

4.2. Relative Accumulation Rates

[41] In order to interpret the results in Figure 8 as illustrating relative accumulations rates, we must first assume that the vertical distance between the MB and the U5 and the L2 and the L5 layers is affected only by accumulation. Circumstances exist in which this assumption can break down. For example, if there has ever been any significant localized erosion of some of the layers exposed in an image (perhaps of less resistant layers, not used as reference layers for correlations), then the distance between layers will decrease, having nothing to do with a change in accumulation rate. We can at least be sure that no reference layers were eroded down to thicknesses unobservable in MOC images since we have been able to perform the layer correlations. Note that we are considering an average accumulation rate over the time during which the layer package under consideration was at the surface. If more erosion of a reference layer occurred one year and more accumulation the next, we would never know as these events would be averaged out. Deriving accumulation rates over a package of layers rather than for individual layers allows us to eliminate the possibility that a low accumulation rate indicates postaccumulation erosion. In other words, if Figure 8 showed accumulation rates for individual layers, then it would be possible that the decrease shown away from the pole in the LLS is due to the fact that in those localized areas, those layers underwent major erosion after their deposition, thus decreasing their apparent thickness. Since we are using layer packages, the vertical distance between layers cannot be decreased due to major erosion of the package; if this happened, then individual layers upward in the sequence might disappear, making it impossible to do the correlations. It is additionally important to remember that the accumulation rate patterns expressed in Figure 8 are not necessarily representative of the current accumulation pattern but rather of the pattern in existence when those particular layers were deposited.

4.2.1. Relationship Between Accumulation Rates, Layer Structure, and PLD Surface Albedo

[42] Decreasing accumulation rate with distance from the pole (or ice sheet center) is characteristic of a classic terrestrial ice sheet with an accumulation zone toward the center and an ablation zone toward the margin. Since the PLD have a limited extent, the accumulation rate must decrease away from the pole. This decrease could result both from warmer temperatures at lower latitudes and to a lesser extent from warmer temperatures at lower elevations. The seasonal CO2 cap also decreases in thickness with decreasing latitude [Smith et al., 2001]. As discussed above, such a decrease in accumulation toward the margin, leading to zero accumulation just beyond the margin, will produce a PLD surface and internal layers which curve downward. The results of our layer correlations are consistent with a general trend of layers curving downward, but the vertical scale of local variations is significant. Thus one might expect accumulation rates in the ULS and LLS to generally decrease away from the pole.

[43] Relative accumulations rates of the LLS do decrease away from the pole (Figure 8c), even taking into account the relatively large error bars. However, no trend with latitude manifests itself in the relative accumulation rates of the ULS (Figure 8a). Given that the pattern of accumulation rates of the ULS and LLS with respect to latitude do not mimic each other, the mass balance pattern (at least on the local if not PLD-wide scale) has probably changed over time. It is possible that the ULS accumulation rate decreases at latitudes greater than 86°N, but no data exist south of this latitude. What appears to be a decrease in accumulation rate toward the pole beginning at about 87°N cannot be confirmed due to lack of data at higher latitudes and due to the fact that the ULS in image 8 at a lower latitude also has a relatively low accumulation rate. It may be that the maximum in relative accumulation rate of the ULS lies further northward than the latitudes covered by the data in this study. One could attribute the apparently lower variability of the ULS accumulation rate as compared to that of the LLS to the lesser thickness of the LLS because the accumulation rate is averaged over fewer layers.

[44] The lowest accumulation rate of the ULS (in image 1) may be due to a local process in that region of the PLD, though what that process may be would require more detailed investigation. Image 3 does provide a potential example of local processes affecting mass balance after the ULS was formed. The U5 layer in this image lies essentially at the surface, from which we infer that the layers above have been eroded away. This area has a relatively low albedo in the MOC image mosaic in Figure 2. Of course, wide-angle MOC images which are each a snapshot in time comprise this mosaic so that it does not reveal the changes in albedo with time. Hale et al. [2005] have examined MOC images spanning three years and find that the area whose tip is near image 3 (their “region 4”) tends to darken at various times in the summer, possibly indicating that the relatively low albedo of that region is characteristic of the current PLD surface. If indeed the current mass balance is relatively lower in this region, then one might expect buildup of dust as ice sublimates, lowering the albedo. Alternatively, this could be a region of dust accumulation which in turn would lower the albedo and possibly increase ablation, creating a relative low mass balance. Models of near surface wind patterns (which use MOLA topography data and albedo from Christensen et al. [2001], and thermal inertias derived from TES [Putzig et al., 2005]) show relatively high speed winds in this low albedo region which could aid in sublimation in those areas [Tyler and Barnes, 2005]. Of course, this discussion of the potential relationship between low PLD surface albedo and low current mass balance is speculative without more data.

4.2.2. Estimation of Absolute Accumulation Rates

[45] Thus far, we have only discussed accumulation rates multiplied by time, as we have no absolute age measurements of the Martian polar layers, nor any superposed craters on individual layers which could be used for relative age dating. Herkenhoff and Plaut [2000] calculate a recent vertical resurfacing rate of ∼1.2 mm/yr for the northern PLD based on the fact that no 300 m diameter craters exist on the surface (and knowing how many should exist, given their crater production function). Laskar et al. [2002] have used an alternative method for assigning ages to polar layers. The authors compare the DN profile of image 7 to calculated insolation values over time given calculated fluctuations in the Martian orbital parameters, thereby dating the layers. For the upper 250 m of the PLD in image 7, Laskar et al. [2002] estimate an average accumulation rate of 0.5 mm/yr.

[46] Using Laskar et al. [2002] best fit match between the DN profile of Figure 7 and the calculated insolation values (illustrated in their Figure 3), our U1 layer dates to about 0.45 Myr and our U5 layer to 0.05 Myr. Below our U1 layer, Laskar et al. [2002] assume that the deposition rate was lower by a factor of 2 due to a major shift toward higher obliquity, but we prefer to keep such assumptions to a minimum for this study. Thus if we assume that the ULS, from the U1 to the U5 layer took 0.4 Myr to form, then the accumulation rates taken from the elevation differences between these layers become 0.28 mm/yr at the minimum (image 1) to about 0.50 mm/yr at the maximum (image 7), averaging to 0.39 mm/yr (Figure 10). The error bars in Figure 10 take into account only the ±5 m error in elevation of the U1 and U5 layers (by propagating this error according to average deviations), assuming no error in age estimates. Since the absolute accumulation rates reported in Figure 10 encompass only the U5 to U1 layers, the detailed shape of the plot does not identically match the relative accumulation rates plotted in Figures 8a and 8b which encompass the entire ULS set.

Figure 10.

Estimation of absolute accumulation rates for the ULS from the U1 to U5 layers, calculated using Laskar et al.'s [2002] estimation of layer ages in image 7. The accumulation rates of ULS exposures in each image are slightly different relative to each other from those in Figure 8 because a greater thickness of the ULS is included in Figure 8.

[47] It is important to note that these absolute accumulation rates are not an independent check of the estimates made by Laskar et al. [2002] since the layer ages are taken directly from their paper. They are meant to serve merely as a first-order estimate. The trends in relative accumulation rates discussed above and plotted in Figure 8 are more important for this study. To test whether the trends in accumulation rate which are reported in this paper (Figure 8) would also be predicted by the Laskar et al. [2002] method, one would need to perform a similar analyses to theirs for all images used in this study.

[48] Milkovich and Head [2005a] have used more MOC images (13) than Laskar et al. [2002], and have performed Fourier analyses of the DN values of layers. They posit that the resulting 30 m dominant wavelength in layer brightness corresponds to the 0.051 Myr insolation cycle driven by precession and obliquity. From this the authors obtain an accumulation rate of 0.6 mm/yr for the layers approximately corresponding to the ULS. As described in section 1, Milkovich and Head [2005a] use matching techniques developed for paleoceanography to derive relative accumulation rates from how much a brightness profile needs to be compressed or stressed to match that of another image. Using this technique, they find that layer thicknesses (and thus accumulation rates) vary by up to a factor of 2.5 (with one exception) which is more than the variation shown in Figures 8a and 8b. Since the 30 m wavelength of Milkovich and Head [2005a] does not directly correspond to specific layers, it is difficult to compare our results for absolute values, but their higher accumulation rates may be due to factors other than precession-dominated insolation cycles also affecting deposition of the entire ULS, while their greater variation could be attributed to specific individual layers varying in thickness more than does the overall ULS thickness or to the fact that the authors' calculation may include parts of the ULS and LLS. The deposition rates that Laskar et al. [2002], Milkovich and Head [2005a], and we calculate are lower (by 4 times at most) than the possibly more recent resurfacing rates estimated by Herkenhoff and Plaut [2000], though all lie within the range of ∼0.3–1.2 mm/yr.

5. Implications for Flow

[49] Our layer correlations can also be used to examine whether or not the ULS and LLS have been affected by large-scale flow. An ice cap will flow under its weight as a result of gravity. On Earth, ice flow can influence internal layers by thinning them, creating folds and faults in specific places, and by smoothing large-scale variations in layer depth originally influenced by the mass balance pattern. If an ice cap surface is close to steady state, surface flow velocities must be balanced by accumulation and ablation on the surface. In this way the shape and volume of the cap will both be constant over time. Terrestrial ice sheets maintain their shape by a combination of flow and accumulation in central parts accompanied by ablation in marginal areas.

[50] Ivanov and Muhleman [2000] find that the current surface profile of the northern PLD can be approximated by a sublimation model alone. Indeed, Greve and Mahajan [2005] have developed a thermomechanical ice sheet model for the north PLD and find low flow rates of 0.1–1 mm/yr at present. However, these authors have also included the effects of changing obliquity on the surface temperature since flow rates will increase with increased temperature, finding that the positive effects of past higher obliquity on flow are counterbalanced by the negative effects of a thinner ice sheet in the past. Therefore Greve and Mahajan [2005] find a maximum flow velocity of about 1.4 mm/yr at about 5 × 105 yrs ago (which is not concurrent with the highest obliquity value). Near troughs, the flow rates can be even higher, up to cm/yr [Hvidberg, 2003]. The formation of folds and faults by ice flow are as yet poorly understood and seem to result from localized instabilities in the flow field [e.g., Alley et al., 1997; Paterson, 2001]. Candidate fold and fault structures have been discovered in both PLD [e.g., Head, 2001; Murray et al., 2001; Herkenhoff et al., 2003; Brightwell et al., 2003; Milkovich and Head, 2005b], possibly indicating significant large-scale flow at some time in the past. To ascertain whether the layers of the Martian north PLD which we have observed have been significantly affected by flow (especially at higher than the current rates), we estimate the amount of thinning which may have occurred and compare the layer structure with the predicted effects of flow.

5.1. Effects of Flow on Accumulation Rate Estimates

[51] Under steady state glacial flow, internal layers grow thinner as normal stresses compress and stretch them. Deeper layers will have undergone the most thinning because they are the oldest and have been flowing for the longest, accumulating the most strain. In most glaciers, the cumulative percentage by which a layer has been thinned increases linearly with depth until a certain depth and then decreases as shear stresses become more important. However, if a glacier grows relative quickly (as is possible for the Martian PLD; see section 5.2), the amount of thinning for each layer will be smaller than under steady state flow since the layers only gradually begin to flow as the ice thickness increases. Also in such a case, the difference in the percentage of thinning will be nearly the same at shallow and deeper layers since most flow occurs in the late stages of the buildup, after the shallow layers were deposited.

[52] Since glacial flow will thin layers, accumulation rates could be underestimated in the presence of flow. In this section, we calculate an absolute maximum amount of possible thinning in the ULS and LLS in order to ascertain whether estimates of absolute or relative accumulation rates could be significantly affected.

[53] We constrain the maximum possible amount of thinning in the ULS and LLS by assuming that the PLD behave as a steady state ice sheet. In this case, during the time that flow is thinning the layers, the ice sheet thickness is not changing. Additionally, the vertical strain rate throughout the ice sheet is proportional to accumulation rate divided by ice thickness; annual layer thickness decreases linearly from the surface to zero at the base. This is the Nye model [Nye, 1953] which is the simplest approximation of ice thinning. Field observations from terrestrial glaciers show that the Nye model is sufficient to describe layer thinning in the upper, central part of an ice sheet. A more complex description, like the flow model used in section 5.2, would not change the result from the simple Nye model. Given that the dust content, the thermal conditions of the ice sheet, absolute accumulation rate through time, and detailed bed topography are poorly constrained, the Nye model with only two parameters is the best model to estimate maximum thinning.

[54] According to the Nye model the cumulative percentage of thinning increases linearly with depth,

equation image

where A′ = accumulation rate * time, corrected for layer thinning; VD = vertical distance (elevation difference) between the top and bottom layers of the ULS or LLS, h = local ice thickness; and z = height of the layer. At the shallow depths spanned by the ULS and LLS we can assume that the thinning effect will be nearly the same for the entirety of each sequence, thus we calculate the thinning effect using values for the middle layers in each sequence (U2 and L2). For h we use the height of the U2 or L2 layer plus the local depth of the U2 or L2 layer. We estimate the height by assuming that the elevation of the PLD base is −4950 m, measured at a point 600 km from the PLD margin in the north polar basin at 90°W. We estimate the depth by subtracting the elevation of the U2 or L2 layer from the maximum surface elevation just poleward of the trough in which the layer sequence is exposed.

[55] What results is that the largest theoretical percentage of thinning (∼20% over the entire LLS sequence) is experienced by layers in images 10 and 11 which are the deepest exposures of the LLS. Remember that this is an absolute maximum estimate for an entire layer sequence and that actual effects of thinning within individual layers will likely be much smaller.

[56] Laskar et al. [2002] calculate an average accumulation rate of 0.5 mm/yr for the upper 250 m of image 7. According to equation (4), when corrected for thinning at that location, 250 m becomes 277 m, making the corrected accumulation rate 0.55 mm/yr. Thus absolute accumulation rates at shallow depths, calculated using the Laskar et al. [2002] method, may change by only approximately 10% at maximum. The effects of thinning within the upper 500 m of the PLD are small.

5.2. Model Predictions of the Effects of Flow on Layer Structure

[57] Again, in order to make the fewest assumptions possible, we use a simple flow model for comparison with observed layer structure in the Martian north PLD. We have adapted the model of Fisher [2000], which is based on the flow law of ice simplified to shear stress only, wherein

equation image

where A(T) is a temperature-dependent flow rate parameter, T is the temperature measured relative to the pressure melting point, and n is a constant, usually set to 3 for glacial ice. The derivation of this flow law is beyond the scope of this paper, but is well explained in many textbooks sources, including those of Van der Veen [1999] and Paterson [2001]. In this model the flow law of ice is adjusted for Martian conditions, using a basal temperature of 225 K (derived by assuming a surface temperature of 160 K and a geothermal temperature gradient at the base of the ice of 0.02 K/m) and assuming that there has been no deflection of the lithosphere beneath the PLD and that the entire thickness of the PLD as measured by MOLA consists of water ice (thus not taking into account the presence of the basal unit or of dust; see Byrne and Murray [2002] for basal unit cross section beneath the PLD). The model solves the equation of continuity and takes into account the lower Mars gravity.

[58] Fisher [2000] uses “accublation” to describe the mass balance pattern wherein ablation takes place at the troughs and accumulation on the flatter areas between. However, our data suggest that the troughs may have formed relatively recently. If so, the possible flow effects associated with the troughs have only been active through a limited time. We run our model using a less complicated scenario in which the accumulation rate is positive everywhere (deposition) but decreases with distance from the center. While the accumulation patterns described in section 4 are rather more complicated than this scenario, the data coverage is not sufficient for use in this flow model. In any case, we find that the size of the accumulation zone and the absolute values of the ablation and accumulation rates do not significantly affect how flow qualitatively alters the layer structure.

[59] We run the Fisher model with two different deposition patterns. In both of these models, deposition of the PLD begins at 5 Myr ago so that we avoid obliquities which might increase temperatures enough not to allow PLD to form or which cause major erosion [Jakosky et al., 1995]. The PLD build up through the entire 5 Myr because of the assumed deposition everywhere. We simulate layers within the PLD by keeping track of past PLD surfaces at specific time intervals as they are buried and gradually begin to be affected by flow. Both model runs are compared to scenarios with the PLD building up but never flowing. In no model do the PLD reach steady state after 5 Myr without assuming highly unlikely accumulation/ablation and flow rates.

5.2.1. Model 1: Building up With Decreased Accumulation Toward the Margin

[60] The PLD build up with deposition rates decreasing toward the margin. We calculate deposition rate by dividing the present PLD surface elevation (as prescribed by a smoothed MOLA topographic profile through the pole and 90°W) by an assumed 5 Myr buildup time (as described above), giving us a maximum deposition rate at the pole of 0.583 mm/yr, decreasing to 0 mm/yr at the margin. We have run the model in two different modes: one without flow, and one wherein the PLD are allowed to flow throughout buildup. In the model without flow, the PLD build up to the current profile prescribed by MOLA. In the run with flow, we follow the effect of flow on the internal layers.

5.2.2. Model 2: Building up With an Oscillating Deposition Pattern

[61] This model is similar to model 1, except that the deposition rate oscillates around the deposition rate in model 1. The oscillation is sinusoidal with an amplitude of 5% of the local deposition rate and a wavelength of 100 km. In the run without flow, the PLD build up to a profile that oscillates around the current MOLA profile according to the assumed oscillations in the deposition rate. In the run with flow, the oscillations of the PLD surface grow until the PLD gradually become thick enough to have significant flow. We follow the effect of flow on the internal layers.

5.2.3. Model Results

[62] Our model results for both runs are plotted in Figure 11. Each shows the results after 5 Myr of evolution according to the scenarios described above. Under a mass balance scenario with decreased accumulation rates near the margin (model 1, Figure 11a), flow tends to smooth away the mass balance signature on layers, made clear by Figure 11b. Even the signature of an oscillating deposition pattern (model 2, Figure 11c) may be almost completely erased by flow (Figure 11d). In model 2, after 2.5 My, the surface oscillations decline, and after 5 My of evolution (the present), the PLD have built up to almost the same smooth profile as in model 1, as illustrated by Figure 11e.

Figure 11.

Flow model runs illustrating the effects of flow on large-scale layer structure. All runs show a snapshot in time of the layers after 5 Myr of PLD buildup. Simulated internal layers (i.e., former PLD surfaces) are labeled by their age. (a) Model 1 without flow. PLD builds up to present shape as measured by MOLA (smoothed by a Gaussian filter to remove the troughs) but does not flow. Accumulation rate is equal to the present surface elevation divided by 5 Myr, with a maximum at the pole (0.58 mm/yr) and a minimum (0 mm/yr) at the margin. PLD shape and layer structure are determined by mass balance alone. (b) Model 1 with flow. PLD build up to present shape as measured by MOLA but are allowed to flow as they build up. Flow smoothes the mass balance signature. Gray lines represent the no-flow case (as in Figure 11a) to allow easy comparison. (c) Model 2 without flow. Here we simulate a varying mass balance pattern by imposing sinusoidal variation on the mass balance pattern used in model 1. Accumulation rate is equal to the present surface elevation (with the sinusoidal variations) divided by 5 Myr, with a maximum at the pole and a minimum (0 mm/yr) at the margin. PLD shape and layer structure are determined by mass balance alone. (d) Model 2 with flow. The PLD builds up with the varying mass balance pattern but is allowed to flow as it builds up. Flow smoothes the mass balance signature. Gray lines represent the no-flow case (as in Figure 11c) to allow easy comparison. (e) Comparison of the results of models 1 and 2 with flow (i.e., Figures 11b and 11d shown on the same plot). Black lines are for model 1, and gray lines are for model 2. Note how, after flow, the layer structure and PLD surface shape are nearly the same, regardless of assumed mass balance.

[63] Our data show that the heights of the ULS and LLS layers are not smoothly varying with distance from the pole. Thus the ULS and LLS do not match the predictions of the effects of large-scale flow on layer structure under the conditions modeled in this study. However, large-scale flow may still have affected the layers by thinning and smoothing them, but our data cannot resolve these effects on the ULS and LLS layers compared to the effect of mass balance patterns. However, it should be emphasized that the effects of flow on layers can be less pronounced at shallower depths (like those of the ULS and LLS) than at deeper depths, where flow may have acted for a longer time. Thus one may need to know the deeper layer structure to better assess whether large-scale flow has ever affected any of the PLD's large-scale layer structure. The presence of possible folds [Milkovich and Head, 2005b] indicates that localized instabilities in the large-scale flow field have affected specific layers, but the flow rates have been so slow as to be overprinted within the ULS and LLS by the effects of the mass balance pattern.

[64] Several factors may encourage slow flow rates beyond what is implied by the apparently unsmoothed structure of the ULS and LLS. Model runs using a lower basal temperature of 200 K, and thus slower flow rates, exhibit less smoothing than those run at 225 K. Also a high dust content of the PLD could have a hardening effect and thereby change the flow law rate factor compared to pure ice, resulting in slower flow rates. There is no obvious evidence on the PLD surface of a basal topographic relief, but if part of the apparent thickness of the PLD is occupied by the basal unit, the ice thickness could be smaller than the ∼3 km we assumed in our models, resulting in slower flow rates.

6. Conclusions

[65] Using MOC images and MOLA data, we have correlated individual layers within the Mars north polar layered deposits across much of the PLD area and to a depth of ∼500 m, gaining a better understanding of internal PLD structure and relative accumulation rates through time. We also use a simple flow model based on the flow law of ice to assess the likelihood of flow having affected the observed layer structure. Our main conclusions are as follows.

[66] 1. The upper ∼500 m of the PLD, containing two correlateable layer sequences, the ULS (with the Malin and Edgett [2001] “marker bed”) and the LLS, does not match the simplified layer structures illustrated in Figure 1, but rather is more complicated as illustrated by Figures 57. Our correlation results are roughly consistent with a downward curving layer structure, but local variations in layer height are significant compared to the thickness of the PLD. Layer packages do not smoothly curve downward with nearly constant thickness as in Figure 1a, though along-trough and nearly cross-sectional slopes of the layers are shallow (less than 1°). At least within the portion of the PLD covered by the ULS and LLS, major layer sequences do not pinch out so that Figure 1c probably does not adequately describe the structure of the ULS and LLS at the latitudes covered by the images in Figure 2. That conclusion along with the fact that the PLD margin contains angular unconformities and eroded layers suggests that not all layers terminate at the same latitude (Figure 1b) or at vastly different latitudes (Figure 1c), but rather that the situation in the northern PLD may be between those two extremes. The latitudinal range of the area where major layers may pinch out and create unconformities is unknown.

[67] 2. The ULS relative accumulation rates display no trends either with latitude or with longitude and vary significantly (with the highest rate being twice the lowest). Insufficient data coverage at lower latitudes does not allow us to determine whether a trend (such as decreasing accumulation rate away form the pole) would be visible if more data existed southward of 86°N. Relative accumulation rates of the LLS, however, generally decrease with distance from the pole, as expected of a “classic” terrestrial ice sheet, with the highest rates being ∼3 times the lowest. The patterns in at least the local variations in relative accumulation rate of the LLS do not mimic those of the ULS, indicating that the PLD may not have ever been in a steady state and that accumulation rates and mass balance patterns have not remained constant through time.

[68] 3. Major angular unconformities do not likely spread throughout the upper portion of the PLD, but rather appear localized and concentrated near the margins. Therefore, unless the trough separation distance has always been the same, if troughs migrate poleward as suggested by Howard et al. [1982] then they may have formed relatively recently since scars of past troughs in the form of angular unconformities are not observed within the ULS or LLS.

[69] 4. Neither observed layer sequence structure matches predictions of the effects of large-scale ice flow under a simple scheme of decreasing accumulation rate toward the margin (even if that accumulation rate varies locally). In other words, large-scale flow has been so slow, at least during formation of these layers, that mass balance patterns have overprinted its signature in the overall layer structure of at least the upper 500 m of the PLD. Since the effects of flow could be more pronounced at deeper depths (if the PLD have been flowing at significant rates for most of their history), further assessment of the effects of flow on layer structure should include the structure of deeper layers. The current data sets do not provide for such an assessment.

[70] With future MARSIS [Winebrenner et al., 2005] and Mars Shallow Subsurface Radar (SHARAD) [Ori et al., 2003] data, one can possibly ascertain the stratigraphy of the central portion of the polar layered deposits, albeit at lower resolution than in this study. This portion of the layers is least affected by ice flow and retreat and readvance at the margins, thus one obtains the closest approximation to a complete layer structure (with vertical resolution limitations in mind) down to deeper sections of the PLD not exposed by troughs. From these results, it may be possible to estimate relative accumulation rates for major layer sections, from the PLD base to the surface, as well as information about relative accumulation rates near the center of the PLD where layers are not exposed by troughs. Additionally, MARSIS data obtained further from the center at greater depths than the ULS and LLS could be used for better comparison with flow models.

Appendix A

[71] The purpose of this appendix is to present figures and tables to further illustrate the process of correlating layers and the results obtained. Figures A1 and A2 are similar to Figure 3 in that they show MOC images annotated with the layers of the ULS (Figure A1) and the LLS (Figure A2) and associated ancillary features. All MOC images used for correlations in this study and listed in Table 1 are presented in Figures A1 and A2 except for those presented in Figure 3. One can use Figures A1 and A2 as guides to locate the labeled features in full-resolution, contrast-enhanced MOC images.

Figure A1.

Illustration of identifying layer sequences in MOC images. Figure A1 displays all MOC images used for correlations of the ULS except for images 5 and 6, which are shown in Figure 3a. Ancillary features are labeled in the same way as in Figure 3a. Note that the pattern, or sequence, of layering is as important as individual layer morphology or albedo, as explained in the text. Colored lines denote reference layers which comprise the ULS as labeled in Figure 6. A, fine layering; B, fine layering; C, prominent layer; D, prominent layer; E, dark strips on left = prominent layer on right?; F, fine layering; G, prominent layer; H, fine layering. X, dark stripe; Y, fine layering; Z, prominent layer. MB is the “marker bed” described by Malin and Edgett [2001]. Scale bars are 500 m. Arrows show Sun angle. Images are labeled as in Table 1 and Figure 2. See Figure 2 for image locations.

Figure A2.

Illustration of identifying layer sequences in MOC images. Figure A2 displays all MOC images used for correlations of the LLS except for images 10 and 13, which are shown in Figure 3b. Ancillary features are labeled in the same way as in Figure 3b. Note that the pattern, or sequence, of layering is as important as individual layer morphology or albedo, as explained in the text. Colored lines denote reference layers which comprise the LLS as labeled in Figure 7. A, dark mantle and fine layers; B, finely layered; C, prominent layer; D, prominent layer; E, prominent layer. Scale bars are 500 m. Arrows show Sun angle. Images are labeled as in Table 1 and Figure 2. See Figure 2 for image locations.

[72] Tables A1 and A2 list all of the reference layers identified in the ULS and the LLS, respectively. The listed latitudes and longitudes are the locations of the approximate centers of the layer exposures. Note that these are different from the latitudes and longitudes listed in Table 1 which correspond to the centers of the MOC images. The elevations have been gleaned from MOLA data as described in section 2.1.3. When noting these elevations, we have assumed that the elevation of a layer does not change along the width of its exposure in one MOC image.

Table A1. Locations of Layers in the ULSa
Exposed InElevation, mLatitude, °NLongitude, °W
  • a

    Image numbers refer to the numbering system for the MOC images in Table 1. Latitude and longitude refer to the latitude and longitude of approximately the center of the ULS exposure in that image. Method of extraction of elevation for each layer is described in section 2.1.3. Note that layer MB has also been identified in images 10 and 13 used for the LLS. The elevations of layers MB and U5 have an estimated maximum error of ±5 m. The errors for the other layers are unknown but likely lie between ±5 and ±15 m.

Marker Bed
Image 1−297287.13359.71
Image 2−301287.13165.27
Image 3−284987.1258.22
Image 4−273187.07264.15
Image 5−309187.05184.69
Image 6−295886.61281.00
Image 7−297486.53278.94
Image 8−316986.00258.65
Image 10−281286.23126.93
Image 13−330484.2399.87
 
U1
Image 1−293487.13359.71
Image 2−295687.13165.27
Image 3−279187.1258.22
Image 4−269687.07264.15
Image 5−302487.05184.69
Image 6−289386.61281.00
Image 7−291886.53278.94
Image 8−312086.00258.65
 
U2
Image 1−290087.13359.71
Image 2−291887.13165.27
Image 3−272787.1258.22
Image 4−262387.07264.15
Image 5−297787.05184.69
Image 6−282586.61281.00
Image 7−286186.53278.94
Image 8−308086.00258.65
 
U3
Image 1−286487.13359.71
Image 2−288087.13165.27
Image 3−268387.1258.22
Image 4−256487.07264.15
Image 5−293587.05184.69
Image 6−275786.61281.00
Image 7−280486.53278.94
Image 8−304786.00258.65
 
U4
Image 1−284787.13359.71
Image 2−284887.13165.27
Image 3−263487.1258.22
Image 4−252287.07264.15
Image 5−286587.05184.69
Image 6−272186.61281.00
Image 7−276386.53278.94
Image 8−300386.00258.65
 
U5
Image 1−283587.13359.71
Image 2−282987.13165.27
Image 3−260787.1258.22
Image 4−249987.07264.15
Image 5−284287.05184.69
Image 6−269786.61281.00
Image 7−271786.53278.94
Image 8−297386.00258.65
Table A2. Locations of Layers in the LLSa
Exposed inElevation, mLatitude, °NLongitude, °W
  • a

    Image numbers refer to the numbering system for the MOC images in Table 1. Latitude and longitude refer to the latitude and longitude of approximately the center of the LLS exposure in that image. Method of extraction of elevation for each layer is described in section 2.1.3. Note that image 14 does not contain layers L1, L6, and L7. The elevations of layers L2 and L5 have an estimated maximum error of ±5 m. The errors for the other layers are unknown but likely lie between ±5 and ±15 m.

L1
Image 9−272087.0879.99
Image 10−314286.23126.93
Image 11−362286.10192.50
Image 12−351084.52105.58
Image 13−354684.2399.87
Image 14N/A84.0084.02
 
L2
Image 9−266887.0879.99
Image 10−311686.23126.93
Image 11−356986.10192.50
Image 12−347084.52105.58
Image 13−349684.2399.87
Image 14−347284.0084.02
 
L3
Image 9−264387.0879.99
Image 10−310286.23126.93
Image 11−354286.10192.50
Image 12−345284.52105.58
Image 13−348184.2399.87
Image 14−346184.0084.02
 
L4
Image 9−262987.0879.99
Image 10−307986.23126.93
Image 11−353686.10192.50
Image 12−344384.52105.58
Image 13−347784.2399.87
Image 14−346084.0084.02
 
L5
Image 9−259687.0879.99
Image 10−303486.23126.93
Image 11−351186.10192.50
Image 12−341584.52105.58
Image 13−345584.2399.87
Image 14−344384.0084.02
 
L6
Image 9−255587.0879.99
Image 10−298086.23126.93
Image 11−347886.10192.50
Image 12−338084.52105.58
Image 13−341784.2399.87
Image 14N/A84.0084.02
 
L7
Image 9−254487.0879.99
Image 10−296686.23126.93
Image 11−345386.10192.50
Image 12−336984.52105.58
Image 13−341084.2399.87
Image 14N/A84.0084.02

Acknowledgments

[73] We would like to offer extensive thanks to Shane Byrne (University of Arizona) for generously sharing an enormous amount of GIS data for use in Arcmap and to the USGS ISIS and PIGWAD support staff, especially Trent Hare, for efficient and friendly help. The early stages of this work benefited from many discussions with Jim Head (Brown University). Thank you also to Sarah Milkovich (Jet Propulsion Laboratory) for stimulating discussions concerning her work with Jim Head on polar layer package correlation using matching techniques derived from paleoceanography. Nicolas Thomas (University of Bern) and Michelle Koutnik (University of Washington) provided helpful suggestions. Finally, we wish to thank Shane Byrne and Stephen Clifford (Lunar and Planetary Institute) for incredibly insightful and thorough reviews which greatly improved the quality of this paper. This work was made possible by a grant to KEF from the American Scandinavian Foundation and by a grant to CSH from the Carlsberg Foundation.

Ancillary