The architecture of subsurface magma plumbing systems influences a variety of igneous processes, including the physiochemical evolution of magma and extrusion sites. Seismic reflection data provides a unique opportunity to image and analyze these subvolcanic systems in three dimensions and has arguably revolutionized our understanding of magma emplacement. In particular, the observation of (1) interconnected sills, (2) transgressive sill limbs, and (3) magma flow indicators in seismic data suggest that sill complexes can facilitate significant lateral (tens to hundreds of kilometers) and vertical (<5 km) magma transport. However, it is often difficult to determine the validity of seismic interpretations of igneous features because they are rarely drilled, and our ability to compare seismically imaged features to potential field analogues is hampered by the limited resolution of seismic data. Here we use field observations to constrain a series of novel seismic forward models that examine how different sill morphologies may be expressed in seismic data. By varying the geologic architecture (e.g., host-rock lithology and intrusion thickness) and seismic properties (e.g., frequency), the models demonstrate that seismic amplitude variations and reflection configurations can be used to constrain intrusion geometry. However, our results also highlight that stratigraphic reflections can interfere with reflections generated at the intrusive contacts, and may thus produce seismic artifacts that could be misinterpreted as real features. This study emphasizes the value of seismic data to understanding magmatic systems and demonstrates the role that synthetic seismic forward modeling can play in bridging the gap between seismic data and field observations.

Subsurface networks of igneous intrusions compose a series of interconnected conduits and reservoirs. The architecture of these systems influences the physiochemical evolution of magma (e.g., Holness and Humphreys, 2003; Magee et al., 2013a), extrusion location (e.g., Gaffney et al., 2007), and the accumulation of economic resources (e.g., Bedard et al., 2012; Holford et al., 2012). Establishing the geometry of individual intrusions and their connectivity is thus crucial to understanding igneous processes. Resolving entire intrusion geometries in the field is, however, hampered by a lack of high-quality, fully three-dimensional (3-D) exposures and the 2-D nature of the Earth’s surface (Fig. 1). Geophysical techniques such as magnetotellurics, InSAR (interferometric synthetic aperture radar), and reflection seismology have therefore been employed to either constrain subsurface intrusions or track real-time magma migration (e.g., Smallwood and Maresh, 2002; Wright et al., 2006; Biggs et al., 2011; Pagli et al., 2012). Of these techniques, reflection seismology arguably provides the most complete and detailed imaging of individual intrusions and intrusion systems. In particular, intrusions within sedimentary basins can be easily identified and mapped in 2-D and 3-D seismic reflection data due to the large acoustic impedance contrast between igneous rocks and encasing strata (Smallwood and Maresh, 2002). Seismic studies have thus revolutionized our understanding of intrusion systems in sedimentary basins, providing spectacular images of vertically and laterally extensive complexes of strata-concordant and/or saucer-shaped sills (e.g., Fig. 1) (e.g., Symonds et al., 1998; Smallwood and Maresh, 2002; Thomson and Hutton, 2004; Planke et al., 2005; Polteau et al., 2008; Magee et al., 2013b, 2014a; Sun et al., 2014). Mapping of magma flow indicators in these data has led to an emerging consensus that magma can be transported over significant lateral (to hundreds of kilometers) and vertical (to several kilometers) distances via interconnected sills and transgressive inclined sheets (e.g., Cartwright and Hansen, 2006; Magee et al., 2014a). Detailed analyses of these intrusion systems has also shown that (1) the architecture of magma networks is influenced by the host-rock structure, in particular bedding discontinuities and fractures, and lithology (Schofield et al., 2012a; Jackson et al., 2013; Magee et al., 2013c); (2) igneous activity may be protracted (e.g., incremental intrusion over 15 m.y.; Magee et al., 2014a); and (3) sill-complex construction can affect the distribution and style of host-rock deformation (Magee et al., 2014a) and volcanism (Magee et al., 2013d). Constraining the validity of these observations is, however, difficult to accomplish because of the limited vertical and horizontal resolution of seismic reflection data (≥20 m for igneous rocks) and the lack of boreholes intersecting igneous intrusions.

To help provide a better understanding of the general seismic expression of intrusions, we conduct seismic forward modeling to examine how sill geometries observed in the field are manifested in seismic reflection data. By creating simple geometric geologic models and using real host-rock mechanical properties (e.g., Fig. 1), we examine (1) whether seismic data can be used to determine the connectivity within sill complexes, i.e., whether magma can migrate to the surface through a network of sills (Cartwright and Hansen, 2006); (2) what inclined sill limbs tell us about magma propagation and emplacement mechanisms; and (3) the utility of subtle geometric features interpreted in seismic data to constraining magma flow directions. Our results demonstrate that intrusion geometries observed in the field can be distinguished in (synthetic) seismic data. Interference between intrusions and the encasing host-rock reflections can, however, generate seismic artifacts that may be misinterpreted.

Magmatic bodies are traditionally mapped in seismic data by picking high-amplitude reflections that are considered to correspond to the upper contact between an intrusion and the encasing host rock (Smallwood and Maresh, 2002; Thomson, 2005). Occasional underlying high-amplitude reflections are observed that may correlate to the lower intrusive contact (e.g., Hansen and Cartwright, 2006; Jackson et al., 2013). Where both contacts are discernable, the mapped intrusions resemble, at least geometrically, those observed in the field (e.g., Jackson et al., 2013). Most intrusions are, however, expressed as tuned reflection packages (e.g., Fig. 1) (Smallwood and Maresh, 2002). This tuning effect occurs when the vertical intrusion thickness is between the limit of separability and the limit of visibility of the seismic data (sensu Brown, 2004). In this scenario, the reflections emanating from the upper and lower intrusion contact interfere and cannot be distinguished (Widess, 1973; Smallwood and Maresh, 2002; Brown, 2004; Hansen et al., 2008). Although these tuned reflection packages broadly correspond to the 3-D intrusion geometry, the sill thickness can only be estimated to be between the calculated limits of separability and visibility (e.g., Jackson et al., 2013). The same is true for magma flow indicators, which are typically on the cusp of the vertical seismic resolution (Schofield et al., 2012a). By assessing how predefined intrusion morphologies (Fig. 2) are expressed in 2-D seismic reflection data, we aim to examine the validity of seismic-based interpretations concerning the development of intrusion systems and determine if further information can be recovered from real data.

Modeled Intrusion Geometries

Large-Scale Intrusive Features and Sill Connectivity

Field- and seismic-based studies indicate that many magmatic networks within sedimentary basins consist of interconnected, strata-concordant (Fig. 1A) and/or saucer-shaped sills (Fig. 1B) (e.g., Symonds et al., 1998; Smallwood and Maresh, 2002; Thomson and Hutton, 2004; Planke et al., 2005; Polteau et al., 2008). To assess the overall expression of such intrusions in seismic reflection data, we developed a simple 2-D geometric model (Fig. 2A). The model comprises a 100-m-thick strata-concordant sill (sill 1) underlain by a saucer-shaped sill (sill 2) (Fig. 2A). Because sills commonly taper toward their tips (Hansen and Cartwright, 2006; Hansen et al., 2011), sill 1 thins laterally (Fig. 2A). The left sill tip thins relatively gradually (top contact dip of 15°) while the right termination thins more abruptly (top contact dip of 40°) (Fig. 2A). In contrast, the 100-m-thick strata-concordant portion of sill 2 transitions laterally into inclined limbs, which dip inward at 25° (Fig. 2A). This simple framework model provides a context for further examination of the seismic imaging of connected and unconnected sills and inclined sill limbs that crosscut a homogeneous or interbedded stratigraphy.

Magma Flow Indicators

Sheet intrusions typically do not initially intrude as bodies of magma with significant along-strike extents (e.g., Rickwood, 1990; Schofield et al., 2012b). Instead, the initial phase of emplacement is commonly dominated by the propagation of thin, discrete magma segments, which may be vertically and/or laterally offset from each other (Fig. 3) (e.g., Rickwood, 1990; Schofield et al., 2012b). Dependent on the behavior of the host rock during intrusion, the inflation and eventual coalescence of segments as magma input increases can produce a range of structures (e.g., intrusive steps and magma fingers). These flow-related structures are superimposed onto the overall morphology of a continuous sheet intrusion (Fig. 3) (Schofield et al., 2012b). Although there are various magma flow indicators that can be observed in the field, for simplicity we focus on intrusive steps and magma fingers. Importantly, the long axes of these structures are a proxy for the primary magma flow axis (Fig. 3) (Magee et al., 2012; Schofield et al., 2012b). Identifying types of magma flow indicators can also constrain the synemplacement host-rock behavior; i.e., intrusive steps occur via brittle fracturing, whereas magma fingers form through nonbrittle processes (Pollard et al., 1975; Rickwood, 1990; Hutton, 2009; Schofield et al., 2010, 2012a, 2012b).

Mapping magma flow indicators in seismic data such as intrusive steps and magma fingers (e.g., Figs. 1C–1D and 3) can provide important insights into how melt migrates through a basin and where major magma reservoirs and/or sources reside (Schofield et al., 2010, 2012a, 2012b; Magee et al., 2014a). Analyzing flow indicators is also crucial to reconstructing the magmatic history of a sedimentary basin (e.g., Schofield et al., 2012a; Magee et al., 2014a). However, the size of intrusive steps and magma fingers is typically at or below the limit of separability, which means that they are likely to only appear as small vertical offsets and amplitude variations in the mapped reflections (e.g., Figs. 1C–1D) (Schofield et al., 2012a; Magee et al., 2014a). It can thus be difficult to differentiate the type of magma flow indicator, if the mapped offsets actually correspond to flow-related structures, or if they are simply geophysical artifacts. Because of the uncertainty in the interpretation of magma flow indicators, it is pertinent to assess how such structures are expressed in seismic data.

The models of magma flow indicators represent a cross section through the inner portion of a centrally fed, saucer-shaped sill and oriented orthogonal to the magma flow direction (Fig. 2B). Figure 2C depicts a series of intrusive steps (Schofield et al., 2012b). In this model (Fig. 2C) we assume that there are small (20 m) lateral overlaps between each 50-m-thick magmatic segment, producing intrusive steps with vertical offsets of 25 m and a local intrusion thickness of 75 m (compare to geometry shown in Fig. 1C). Figure 2D shows a series of magma fingers, which are elliptical in cross section when isolated (Schofield et al., 2010, 2012b), or form a magma lobe upon finger coalescence (Thomson and Hutton, 2004). Magma fingers observed in the field typically have an average height/width aspect ratio of 0.27 (Table 1); this morphology was incorporated into the model (Fig. 2D). Hypothetical magma fingers with an aspect ratio of 0.65 are also modeled to test how alternate finger geometries may affect seismic expression (Fig. 2D).

Rock Properties

Seismic forward modeling of igneous intrusions requires attributing realistic physical properties to the igneous rocks and the sedimentary host rocks. In absence of well data, it is commonly assumed that seismically imaged igneous intrusions are basaltic and have a P-wave velocity (Vp) of ∼5.55 km s–1 and a density (ρ) of ∼2.8 g m3 (Skogly, 1998; Berndt et al., 2000; Bartetzko et al., 2005); we adopt these values in our models (Table 2). The composition, velocity, and density of igneous rocks can vary (e.g., Vp may range from 4 to 7.5 km s–1; Skogly, 1998; Berndt et al., 2000; Bartetzko et al., 2005). Regardless of potential compositional variations, the Vp of igneous rocks is typically significantly higher than those associated with the sedimentary host rock. The resulting acoustic impedance (density × velocity) contrast between intrusion and sedimentary host rock produces the characteristic high-amplitude reflections.

We derived the physical properties for sandstone and shale host rocks from the porosity, density, and elastic moduli of their individual components (water, quartz, and smectite, respectively). To create synthetic seismic sections corresponding to a typical depth of 2.5 km, we first derived the host-rock porosity (φ) according to Sclater and Christie (1980):
whereby the porosity depth coefficient (c) is equal to 0.51 km–1 for shale and 0.27 km–1 for sandstone, assuming that the surface porosity (φ0) of shale is 0.63 and of sandstone is 0.49. The porosities were then calculated for a typical intrusion depth of 2.5 km (sandstone 0.25, shale 0.18), which is representative of the subseabed depths of intrusions in real data. The density (ρ) of sandstone and shale at 2.5 km depth was calculated using averages of grain density (ρgrain) and fluid density (ρfluid) based on the previously calculated porosities (Table 2):
Density values of 2.24 and 2.19 g cm–3 were derived for the sandstone and shale, respectively. We then calculated the corresponding bulk (k) and shear modulus (µ) for each rock type from the elastic moduli of its components and their volume fraction (fi) (Table 2). We assumed the pore fluid to be water with a density of 1 g cm–3, a bulk modulus of 2.2 GPa, and a shear modulus of zero. Because the shear modulus of water is zero, the Hashin-Shtrikman lower bound can be used to calculate the elastic moduli (Hashin and Shtrikman, 1963) (Table 2):
Note that we adapted the notation of Mavko et al. (2009). We used the elastic moduli to calculate the P-wave velocity (Vp):

The resulting values, 1.92 km s–1 and 2.03 km s–1 for sandstone and shale, respectively, are within range of previously reported examples (Jaeger et al., 2009). Bed thicknesses are modeled at either 50 m or 25 m to test how they may affect the expression of igneous intrusions.

Seismic Modeling

The input models were converted into synthetic seismic sections by simulating a zero-offset survey using the Zoeppritz equations and a zero-phase Ricker wavelet typical for seismic forward modeling studies (e.g., Schwab et al., 2007; Holgate et al., 2014; Osagiede et al., 2014). To assess the impact of seismic resolution, which is partially controlled by and therefore acts as a proxy for burial depth, on the expression of different intrusions, we varied the wavelet frequency; we chose peak frequencies of 13 Hz, 26 Hz, and 45 Hz, which correspond to dominant frequencies of 10 Hz, 20 Hz, and 35 Hz (Kallweit and Wood, 1982). Given a Vp of 5.55 km s–1 for the intrusions (Skogly, 1998), these frequencies can also be used to determine the limits of separability and visibility expected for the synthetic seismic data (Fig. 4). To assess the ideal seismic expression of different intrusion geometries using synthetic seismic forward modeling, parameters that are likely to further degrade the seismic imaging quality are not accounted for (including, for example, seismic noise and depth-dependent amplitude and frequency decay). The imaging beneath the modeled intrusions is therefore of relatively high quality, whereas a marked drop in reflection continuity and amplitude may be expected in real data (e.g., Hansen et al., 2008).

It is apparent from Figures 5 and 6 that the expression of intrusions in synthetic seismic data geometrically resembles the input models, particularly those that only incorporate a homogeneous sandstone host rock. In the 45 Hz homogeneous host-rock model, the sills display constant, moderate amplitudes when the intrusion thickness exceeds 51 m (Fig. 5B). Figure 5B shows that as the thickness decreases, constructive interference between the upper and lower contact reflections produces an increase in amplitude, which peaks at the limit of separability for the data (i.e., 31 m; Fig. 4). A continued decrease in intrusion thickness below the limit of separability corresponds to a reduction in the degree of constructive interference and a transition into destructive interference (Fig. 5B). This variation in the degree of interference is demarcated by a decrease in amplitude (Fig. 5B). The humped amplitude profile geometries characteristic of seismic interference between two lithological boundaries (Widess, 1973; Hansen et al., 2008) are developed at the lateral terminations of each sill (Fig. 5B). Amplitude variations are also observed in the basal sill 1 and top sill 2 reflections immediately adjacent to the sill-sill junction, which is characterized by a break in reflection continuity (Fig. 5B).

Similar amplitude profiles are associated with the sills in the 26 Hz homogeneous sandstone host-rock model (Fig. 5C). The sill junction is, however, more complex; the basal sill 1 reflection and top sill 2 reflection appear to extend upward into the package that defines sill 1 (Fig. 5C). Within the 13 Hz homogeneous sandstone host-rock model, the ≤100-m-thick sills (Fig. 2A) are below the limit of separability (i.e., 107 m; Fig. 4); there is thus no constructive interference or presence of humped amplitude profiles toward the sill margins, but simply a reduction in amplitude where the intrusion thickness decreases further below the limit of separability (Fig. 5D). Complexity occurs at the sill junction, where the cumulative intrusion thickness locally increases to 175 m (Fig. 5D). In this location, a subdued increase in amplitude is observed to the left of the junction along the top sill 2 reflection. The width of the poorly resolved connection is, however, characterized by abrupt decreases and increases in amplitude, particularly along the basal sill 1 reflection (Fig. 5D).

In comparison to those models containing a homogeneous host rock, Figure 6 highlights the influence that a heterogeneous host rock has on the seismic expression of the sills. In all models, the inclined limb reflections, which crosscut stratigraphy, appear to have a stepped morphology despite being planar (Fig. 6). Because these step-like structures are not related to magma propagation (cf. Fig. 3; cf. Schofield et al., 2012b), we refer to them as pseudosteps. The pseudostep geometry is most pronounced at lower frequencies (i.e., 13 Hz; Fig. 6D), where it is clear that they correlate to abrupt fluctuations in amplitude.

Resolvability of Sill Connectivity

By examining the expression of sill junctions in detail (Fig. 7), we aim to establish whether amplitude variations or reflection geometries may be used to determine the connectivity of a sill complex. In order to isolate the impact of sill connectivity and not, for example, image amplitude variations associated with a heterogeneous host rock, we only use a homogeneous sandstone host rock. The connected sills within the 45 Hz model are distinguished by a break in the basal sill 1 reflection (Fig. 7B). However, when the two sills are separated by 10 m or 50 m, the basal sill 1 reflection is continuous (Figs. 7F, 7J). In each 45 Hz model, the amplitude of the top sill 2 reflection increases as it approaches sill 1 (Figs. 7B, 7F, 7J). Amplitude variations are only observed along the basal sill 2 reflection when a gap between the two sills is present (Figs. 7F, 7J) and not when the sills are connected (Fig. 6B). At 26 Hz (Figs. 6C, 6G, 6K), and particularly at 13 Hz (Figs. 7D, 7H, 7L), the detail of the sill junction becomes more difficult to resolve. Figures 7D, 7H, and 7L highlight that the top reflection of sill 1 in the 13 Hz models, denoted by a yellow line, is more perturbed when the two sills are connected. Although only three of the generated seismic sections correspond to a connected sill (i.e., Figs. 7B–7D), most of the synthetic reflection configurations, perhaps with the exception of Figure 7J, appear to resemble sill-sill junctions.

Seismic Expression of Inclined Limbs

Pseudosteps occur in the seismic sections of planar inclined limbs encased by an interbedded host-rock stratigraphy regardless of frequency, although they are more prominent at lower frequencies (Figs. 5, 6, and 8). Figures 8H and 8L demonstrate that the lateral extent of individual pseudosteps decreases as bed thickness decreases. A similar decrease in the lateral extent of pseudosteps occurs in response to a reduction in inclined limb thickness (Figs. 8H, 8P). In addition to the abrupt changes in amplitude associated with pseudosteps, the apparent thickness of an intrusion (i.e., the vertical distance between the maximum peak and trough positions of the prominent top and basal reflections) varies with respect to the vertical thickness of the input model (Fig. 8). For example, the apparent thickness measured at the top-left termination of each inclined limb is greater than the vertical thickness of the input models (Fig. 8). Within individual models, across the rest of the intrusion, regardless of whether the top and base reflections are discretely defined, the apparent thickness appears to fluctuate (Fig. 8). In some instances the apparent thickness decreases below the vertical thickness of the input model (e.g., Figs. 8F, 8G, 8H, 8N, and 8O), although most seismograms demonstrate that apparent thicknesses greater than the vertical thickness of the input model are dominant. Despite all synthetic seismograms modeled with a heterogeneous host-rock stratigraphy displaying variations in both apparent thickness and amplitude, there appears to be no systematic relationship between the two measured parameters. However, several observations are highlighted: (1) the apparent thickness of the inclined limb is greater than the vertical thickness of the input model (i.e., 75 m) for all synthetic seismograms generated from Figure 8I where the bed thickness is only 25 m (i.e., Figs. 8J–8L); (2) maxima in the amplitude of top reflection in Figure 8L correspond to increases in apparent thickness; and (3) conversely, peaks in apparent thickness along the inclined limb in Figure 8K correlated to amplitude minima.

Resolving Magma Flow Indicators

Intrusive Steps

Within a homogeneous host rock, intrusive steps are easily recognizable and the only fluctuations in amplitude occur at the magmatic segment connections (Figs. 9B–9D). Reducing the frequency of the data produces an increase in apparent thickness of the intrusion (Figs. 9B–9D). The presence of a heterogeneous host-rock stratigraphy, with beds parallel to the modeled intrusive segments, alters the seismic expression of the sill (Figs. 9E–9L). Depending on the bed thickness and the position of the segments relative to the different host-rock lithologies (i.e., whether segments are immediately overlain by sandstone or shale), there are significant variations in (1) the amplitude of each magmatic segment in individual models, with some segments seeming to blend into the background stratigraphic reflections (e.g., Figs. 9F–9H); (2) the apparent thickness of individual segments (e.g., Fig. 9H); and (3) the vertical offset, or step height, between segments (e.g., Fig. 9K).

Magma Fingers

Across all the models there are prominent variations in amplitude along the top and basal magma finger reflections, which spatially correlate to changes in the actual and apparent intrusion thickness (Fig. 10). Within homogeneous host rocks the true geometry of the magma fingers becomes less recognizable with a decrease in frequency, particularly for those with a higher aspect ratio (Figs. 10B–10D). The resolvability of magma finger geometries is further compounded by the addition of alternating sandstone and shale beds (Fig. 10). For example, the basal reflection of the magma fingers expressed in Figure 10H has a more prominent curvature than that of the top magma finger reflection. In Figure 10P it is the top magma finger reflection that displays a greater curvature. In both of these examples, the contact reflection displaying the greater curvature is primarily hosted by shale beds (Figs. 10H, 10P). From the models presented in Figures 10H and 10P, it is also difficult to discern the high-aspect-ratio magma fingers from the background stratigraphic reflections. Where the magma fingers crosscut lithological boundaries, the synthetic seismic reflections corresponding to the host-rock strata appear to onlap onto or are truncated by the intrusion.

While seismic data have revolutionized our understanding of magma plumbing systems within sedimentary basins, we rely upon qualitative visual comparison with field analogues to interpret the origin of intrusion morphologies imaged. For example, sill-sill junctions, subtle inclined limb geometries, and magma flow indicators, all of which are key to elucidating the connectivity and emplacement of entire sill complexes, are interpreted in seismic data based on field analogues. There are, however, two key problems associated with qualitative comparisons between seismic and field data: seismic data are restricted in resolution, such that smaller scale (typically <10–20 m) structures are not fully resolved, and the 3-D geometry of intrusions exposed in the field is commonly limited. By demonstrating that synthetic seismograms can generally reproduce the geometry of the input intrusion models, which incorporate a variety of field observations, our results represent an important first step in bridging the resolution gap between seismic and field data (Figs. 5–10).

We discuss the implications of our results in light of how the synthetic seismic data produced relate to both real seismic and field examples. Overall, if the host rock is homogeneous, individual intrusion geometries are particularly well defined (e.g., Fig. 5). In these models it is apparent that variations in the amplitude profiles correspond to interference between the upper and lower contact reflections (Fig. 5). This tuning response occurs below the limit of separability and is a function of the intrusion thickness and frequency content of the seismic data (Widess, 1973; Smallwood and Maresh, 2002). The seismic expression (i.e., geometry and amplitude) of different intrusions may vary in response to changes in the frequency, the thickness of the intrusion, and the presence of interbedded strata (Figs. 5 and 6). Addition of a heterogeneous host-rock stratigraphy complicates the seismic expression, i.e., the reflection configuration and amplitude, of igneous intrusions. These affects are considered in more detail in the following.

Can Seismic Data Be Used to Determine Connectivity in Sill Complexes?

Extensive sill complexes have been recognized in a variety of sedimentary basins (e.g., Karoo Basin, South Africa, Chevallier and Woodford, 1999; the Vøring and Møre Basins, offshore Norway, Cartwright and Hansen, 2006; South Yellow Sea Basin, offshore China, Lee et al., 2006; offshore northwestern Australia, Rohrman, 2013; Rockall Basin, northeastern Atlantic, Magee et al., 2014a). In seismic data, these intrusion systems consist primarily of strata-concordant and/or saucer-shaped sills (Cartwright and Hansen, 2006) that appear to be connected via a range of sill junctions (e.g., Fig. 7A) (Hansen et al., 2004; Thomson and Hutton, 2004). Although these junctions can also form in response to sill abutment, and thus may not be indicative of throughgoing magma flow pathways (Hansen et al., 2004; Thomson and Hutton, 2004; Galerne et al., 2011), sill complexes are typically considered to transport magma over significant lateral and vertical distances through the upper crust (e.g., Cartwright and Hansen, 2006; Svensen et al., 2012; Magee et al., 2014a). However, limited seismic resolution and a paucity of field exposures mean that the assumed connectivity of entire sill complexes can rarely be physically confirmed. Assessing the degree of connectivity between sills is crucial to understanding whether sill complexes can facilitate extensive lateral and vertical magma transport. This is important because mechanisms of magma migration in sedimentary basins can influence volcano distributions (Magee et al., 2013d), magma fractionation and contamination, and compartmentalization of fluids (Holford et al., 2012, 2013).

The modeled seismic expression of a junction between a strata-concordant sill and an underlying saucer-shaped sill reveals that the continuity and amplitude of intrusion-related reflections is sensitive to the frequency of the data (Figs. 5–7). Within synthetic models with higher frequency contents, where the sill contacts are clearly resolved, the presence of gaps between the two intrusions can be inferred from the continuity of the lower sill 1 reflection (Figs. 7B, 7F, 7J). It is important that our results highlight that slivers of host rock between the two intrusions, particularly when modeled with low frequencies (e.g., Fig. 7H), could easily be misinterpreted as a fully connected, sill-feeding-sill relationship (cf. Fig. 7D). However, there are several nuances in the imaging of the sill-junction zone that may allow connectivity to be assessed. For example, there is a greater deflection in the peak wavelet position of the sill 1 tuned reflection package where the intrusions are connected (yellow line in Fig. 7D) compared to those separated by host rock (Figs. 7H, 7L). Figure 11 presents a real seismic example of a sill (i.e., sill A) from the Rockall Basin, offshore northwestern Ireland, whereby a deflection in the peak wavelet position and a significant decrease in amplitude correspond to an inferred junction with the underlying sill B. Although it is difficult to determine whether this narrow zone of low amplitude and peak wavelet deflection in sill A corresponds to an intrusive step, the close proximity to and inferred trajectory of the underlying sill B bears a similarity to Figure 7D and suggests that sills A and B are connected (Fig. 11). However, Figure 11 highlights an issue with real seismic data, in that imaging immediately beneath a sill is typically poor due to the attenuation of energy in the intrusion. By determining the frequency content of the seismic data and analyzing variations in reflection configurations for a series of imaged sill junctions, it may be possible to establish connectivity across a sill complex. Interpreted connections could be tested by mapping magma flow indicators, if present, to see if sills were fed from identified connections.

What Do Inclined Limbs Tell Us about Magma Emplacement Mechanisms?

Inclined limbs provide important magma flow pathways in sill complexes, facilitating magma ascent through significant thicknesses (e.g., 2 km) of sedimentary strata (Thomson and Hutton, 2004; Cartwright and Hansen, 2006; Magee et al., 2013b, 2014a). Distinguishing whether emplacement of these limbs occurred via either the passive or forceful intrusion of magma intrusion is important because these mechanisms can result in different styles of host-rock deformation, and thereby potentially control surrounding fluid flow (e.g., of hydrothermal fluids or hydrocarbons). For example, the forceful intrusion of magma is typically considered to be associated with the development of new fracture sets (e.g., Rubin, 1995), which may locally increase the permeability of the host rock. Conversely, passively emplaced limbs are likely to exploit preexisting fractures and faults (e.g., Magee et al., 2012), potentially forming baffles to subsequent fluid flow or influencing later fault reactivation (Holford et al., 2012, 2013; Magee et al., 2014b). Furthermore, identifying whether magma exploits preexisting faults or fractures can provide important insights into the distribution of volcanoes (Gaffney et al., 2007).

A number of mechanisms, which can be subdivided into those resulting from either the passive or the forceful intrusion of magma, have been proposed to explain inclined limb formation: (1) emplacement of magma into tensile fractures generated by extensional strains applied to the host rock during intrusion-induced forced folding (Fig. 12A) (Thomson and Schofield, 2008; Galland and Scheibert, 2013; Magee et al., 2013c, 2014a); (2) exploitation of reverse faults instigated by overburden uplift (Fig. 12B) (Thomson and Schofield, 2008); (3) intrusion along preexisting faults (Fig. 12C) (Bedard et al., 2012; McClay et al., 2013; Magee et al., 2014b); and (4) forceful transgression of a subhorizontal sill, hosted within a homogeneous elastic media, in response to asymmetrical stress fields generated during emplacement (Fig. 12D) (Malthe-Sørenssen et al., 2004). The first three mechanisms commonly produce relatively planar inclined limbs in cross section (e.g., Fig. 2A) (e.g., Thomson and Schofield, 2008; Magee et al., 2013b), whereas numerical modeling suggests that transgression induced by stress field variations results in an inclined limb with a stepped morphology (e.g., Fig. 2C) (Malthe-Sørenssen et al., 2004). Malthe-Sørenssen et al. (2004) provided a real seismic example of a sill offshore northwestern Australia with stepped inclined limbs that they use to support their numerical modeling.

Our models demonstrate that planar inclined limbs that crosscut stratigraphy may appear to consist of prominent strata-concordant steps in seismic reflection data (Figs. 6 and 8). Figures 13A–13C illustrate that these steps are a geophysical artifact, which we refer to as pseudosteps, generated by the interference between the sill and crosscut bedding reflections. This crosscutting relationship between the sill and stratigraphy effectively produces a series of tuning wedges between the two interfaces (Fig. 13A) (cf. Widess, 1973; Brown, 2004). When the vertical thickness of each wedge decreases below the limit of separability of the data, the corresponding sill reflection is pulled up or pushed down relative to its actual position (Fig. 13C). This tuning effect also superimposes abrupt increases or decreases in amplitude and apparent intrusion thickness along the length of the inclined limb (Fig. 13). Figure 14A documents a real example from a 3-D seismic data set located in the Rockall Basin, offshore northwestern Ireland, whereby subtle changes in the dip of the inclined limb imaged coincide with reductions in amplitude, and approximately correlate to intersections between prominent stratigraphic horizons. While it is difficult to fully ascertain the true geometry of igneous intrusions expressed by tuned reflections, we suggest that the inclined limb imaged in Figure 14B is actually planar, based on comparison to synthetic seismic models of sills observed in the field.

Although the arrangement of the intrusive steps in Figure 8 was designed to test the seismic expression of magma flow indicators, the model configuration may also be considered similar to that of the stepped inclined limbs modeled by Malthe-Sørenssen et al. (2004) (Fig. 12D). In contrast to the planar inclined limb modeled in Figures 5, 6, and 8, inclined limbs that originally have a stepped morphology and crosscut stratigraphy (i.e., Figs. 2C and 9) appear to consist of discrete, geometric segments with apparently different properties (e.g., apparent thickness, amplitude, and vertical offset). The expression of these segments is dependent on their position and actual thickness relative to bedding (Fig. 9). However, such variations in the apparent thickness, amplitude, and vertical offset of inclined limbs have not been reported in seismic reflection studies. It is therefore possible that the natural example of apparently stepped inclined limbs from offshore northwestern Australia, provided by Malthe-Sørenssen et al. (2004) to support their numerical model, may actually represent a planar inclined limb emplaced passively. This challenges models suggesting that inclined sill limbs are forcefully emplaced (cf. Malthe-Sørenssen et al., 2004). Numerical modeling of sill transgression in a layered medium, as opposed to a homogeneous host rock (Malthe-Sørenssen et al., 2004) and further comparison to seismic and field examples are required to test this implication of our results. In particular, analyzing the geometry of the wavelet across an inclined limb may allow interference between inclined limb and host-rock reflections to be distinguished (Fig. 13C).

Can Subtle Geometric Features Be Interpreted as Magma Flow Indicators?

Figures 9 and 10 indicate that magma flow indicators can be discerned in seismic reflection data. However, their original morphology may be difficult to distinguish depending on the frequency of the seismic data and the thickness and composition of strata truncated by the intrusion (Figs. 9 and 10). For example, the variable expression of intrusive steps in the synthetic seismic sections is discussed herein (Fig. 9). Comparing our results in Figure 9 to the intrusive steps imaged in Figure 1C, we suggest that the real example constitutes a sill within a thinly bedded or host rock (cf. Figs. 9K and 9L). A thinly bedded host rock, relative to the intrusion thickness, would explain the consistently higher amplitudes of the sill imaged in Figure 1C relative to the host rock. However, we note that the actual vertical offset of the steps is difficult to evaluate (Fig. 1C). It is clear that the apparent morphology of magma fingers in seismic data can vary greatly. Magma fingers hosted in homogeneous host rock and imaged in high-frequency data may be well resolved (Fig. 10). In contrast, interference with bedded stratigraphy, particularly at lower frequencies, causes the magma fingers to have a conical appearance if they have a low aspect ratio, and blend in with the background stratigraphy if their aspect ratio is relatively high (Fig. 10). The apparent onlap onto the magma fingers or truncation of underlying reflections (Fig. 10), produced by the intrusion of stratigraphic horizons by the magma, may mean that they are misinterpreted as extrusive features such as eye-shaped hydrothermal vents (e.g., Hansen, 2006; Magee et al., 2015). Although our results suggest that magma flow indicators can be interpreted, albeit with caution, constraining the seismic frequency and the relative bed thickness can help improve certainty.

We present a series of synthetic seismic forward models that examine how igneous intrusions observed in the field may be expressed in seismic reflection data. Our results demonstrate that the appearance of intrusions in seismic data is controlled by a range of parameters, including the intrusion thickness, frequency of the data, and the style of the host rock (i.e., whether it is homogeneous or interbedded). While the majority of the modeled geometries are relatively well defined in synthetic seismograms, geophysical artifacts generated by the interference between intrusive contact and bedding-plane reflections can affect image quality and, thereby, interpretations. These issues particularly arise when the sizes of the intrusive structures imaged (e.g., sill-sill connections or magma flow indicators) are on the cusp of or below the limit of separability. The broad correlation between field observations and synthetic seismic models strengthens the importance of seismic reflection data to the study of igneous systems and suggests that seismic forward modeling provides a useful method for testing interpretations.

We thank Ikon Geoscience for providing the synthetic seismic forward modelling software and continued technical support. We are grateful to Geoscience Australia for seismic data provision and to Schlumberger Limited for seismic interpretation software. We also thank Katarina Roele for conducting initial tests on the synthetic seismic forward modelling of intrusions, Shanaka de Silva for the editorial handling of the paper, and Craig Jones and two anonymous reviewers for constructive reviews.