Journal of Geophysical Research: Solid Earth

Imaging the shallow crust with local and regional earthquake tomography

Authors


Corresponding author: C. B. Biryol, University of Arizona, 1040 E 4th street, Tucson, AZ 85721, USA. (cbbiryol@email.arizona.edu)

Abstract

[1] While active-source imaging (seismic reflection, refraction) is typically used to image the shallow crust, these techniques tend to suffer from energy penetration problems in complex tectonic regimes, resulting in poor imaging. Further, active sources (such as air guns or vibroseis) tend to be band limited, resulting in poor signal-to-noise ratio at low frequencies (1–10 Hz). Recent studies suggest that earthquake data may be able to solve these imaging problems. However, conventional earthquake tomography typically aims to image the upper mantle and lithosphere, where typical station spacing (tens of km) and array aperture (hundreds of km) have resulted in the maximum resolution. In this study, we take advantage of the small-scale and 250 m station spacing of the LaBarge Passive Seismic Experiment to determine whether local and regional earthquake tomographies can be used to constrain structure in the top 5 km of the crust. We also study how the inclusion of finite-frequency effects impacts the final images. Our results indicate that local and regional events provide substantial improvements over teleseismic events alone, with approximately 500 m resolution both vertically and laterally in the upper most 5 km. We also find that inclusion of finite-frequency data between 1 and 10 Hz plays a key role in maintaining resolution in the shallowest portion of the model.

1 Introduction

[2] The advancements in natural-source seismic tomography in the past couple of decades have made it possible to obtain higher-resolution images of the Earth's crust through use of broadband seismic sources such as earthquakes and ambient seismic noise. Local Earthquake Tomography (LET) and Ambient Noise Tomography (ANT) are the most rapidly emerging techniques that provide higher-resolution images of the crust through usage of passive-source, broadband seismic data [i.e., Thurber et al., 1995; Laigle et al., 2000; Shapiro et al., 2005; Lin et al., 2008, Yolsal-Çevikbilen et al., 2012]. However, the resolution of these images are limited by the seismic source distribution (tectonically controlled) and receiver coverage (instruments spaced typically tens of km apart, with total array aperture of hundreds of km) and usually poor in the upper 5 km section of the crust.

[3] On the other hand, active-source seismic surveying, including both reflection and refraction, is currently the standard tool for studying the shallow crustal structure and is ubiquitous in the hydrocarbon exploration industry. However, there are also limitations associated with active-source analysis. Attenuation and scattering of the seismic energy emitted by conventional controlled sources can reduce the quality of the acquired data and hence reduce the resolution and robustness of the resultant seismic images. These types of problems are especially accentuated when structural complexities are present in the shallow crust. The broadband nature of natural-source seismic energy, particularly in the band between 1 and 10 Hz, makes it less prone to such undesired effects.

[4] As the search for commercial hydrocarbon accumulations in the subsurface moves to more challenging geologic settings and environments, the need for reliable, high-quality data to control and mitigate risks increases. In particular, we wish to explore the hypothesis that natural-source seismic data can contribute information about the shallow subsurface (particularly the top 5 km, but including basement and Moho structure) and determine how to best collect and process this data. Products from natural-source data, including velocity models and structural images, can then be used as starting models for inversions or to develop scenarios for basin and oil reservoir system development. The LaBarge Passive Seismic Experiment (LPSE) provides an ideal dataset for testing these concepts. An array of 63 broadband seismometers from the EarthScope instrument pool managed by the IRIS-PASSCAL consortium was deployed in western Wyoming through collaboration between the University of Arizona and the ExxonMobil Upstream Research Company. The instruments continuously recorded from November 2008 to June 2009 at a rate of 100 samples per second. Fifty-five of these stations were deployed in the form of a dense, three-branched linear array with 250 m station spacing (Figure 1). The remaining eight stations were deployed across the Green River Basin between the dense array and the Wind River Range. The larger array was used in conjunction with neighboring US Array stations to study the larger-scale crustal structure of the region spanning the transition from the thin-skinned Wyoming fold and thrust belt to the thick-skinned Laramide foreland structures [Gans, 2011]. Our analysis focuses on the denser portion of the LPSE array.

Figure 1.

Map of study area also showing the seismic array configuration of LPSE. The station numbers increase with increments of one from west to east and continuing southward from the middle of the array. For clarity, only odd-numbered stations are labeled. The inset map shows the location of the study area in the western United States.

[5] While the geometry of the array is not at first glance ideal for a tomographic inversion, it does provide several advantages. First, the northwest/southeast branches are aligned along great circle paths toward earthquake sources in the Andes and Aleutian subduction zones. This helps improve ray sampling for teleseismic events [Schmedes et al., 2012]. Further, the east-west branch crosses a major structural feature. West of station L23 (Figure 1), the array overlies the Hogsback thrust, a shallow angle thrust fault where approximately 1–2 km of Paleozoic carbonates are emplaced above late Mesozoic clastics [e.g., Coogan, 1992; Royse, 1993]. This configuration results in a shallow, high-velocity wedge in an otherwise (relatively) homogeneous sedimentary basin. This thrust sheet provides an enticing target for testing the resolution of seismic imaging techniques. The LaBarge field has been continuously producing oil and gas field since the mid-twentieth century. Because of this, the shallow crustal structure in the study area is well studied and well constrained using active-source techniques and in situ logs from wells and therefore provides a useful natural laboratory for testing imaging techniques. Leahy et al. [2012] carried out Receiver Function (RF) analysis beneath the array and concluded that RFs of teleseismic broadband data can provide high-resolution images of the shallow crust beneath the LPSE array that agrees favorably with well-log data.

[6] Schmedes et al. [2012] used a teleseismic relative traveltime tomography method to image shallow structure beneath the dense array. Their results indicated that the close spacing of the receivers yields a good lateral resolution of the shallow crust (up to 3–4 km depth). However, the vertical resolution is poor due to the sub-vertical sampling pattern of the teleseismic body-wave arrivals. They hypothesize that by including more seismic phases in the inversion, particularly local and regional earthquake arrivals, it would be possible to obtain better resolution images of shallow crust.

[7] In this study, we test this hypothesis by comparing the relative contribution of local, regional, and teleseismic datasets in an inversion for a shallow velocity model. Our approach uses a joint inversion of traveltime data from earthquakes using a tomographic algorithm that incorporates calculation of volumetric traveltime sensitivity kernels through finite-frequency approximation. The usage of finite-frequency approximation in seismic traveltime tomography improves the sampling of the modeled volume by incorporating the volume around the theoretical ray path into the tomographic inversion [Hung et al., 2004]. Previous studies indicated significant improvement in resolution using this technique [i.e., Schmandt and Humphreys, 2010; Biryol et al., 2011]. While the finite-frequency approximation in seismic tomography is commonly used for imaging the Earth's mantle in regional and global scales, there exist LET studies [i.e., Husen and Kissling, 2001] that apply this technique to image crustal structure of much smaller regions incorporating traveltime data from local earthquakes. Our approach significantly differs from conventional LET analysis where the data come from earthquakes located within the modeled volume. In our case, the limited spatial coverage of the dense array mandated the use of data from earthquakes that are located outside of the modeled volume. We anticipate that treating the tomography in this manner will remove the uncertainty associated with event locations in traditional LET analysis, while maintaining the improved sampling and resolution compared to teleseismic data alone.

[8] We investigate the individual contributions of sub-datasets (i.e., local, regional, and teleseismic datasets in various finite-frequency bands) and their combinations on resolution and robustness of the imaged shallow seismic structure. In these analyses, we take advantage of the close station spacing of the dense LPSE array. Our results indicate that combinations of local, regional, and teleseismic datasets in multiple, closely spaced frequency bands improve the resolution and robustness of the results significantly compared to results obtained using individual sub-datasets or partial combinations. Our results also show that finite-frequency tomography, using local, regional, and teleseismic traveltime data, can yield reliable, high-resolution images of the near surface in the presence of structural complexities. In particular, we find that while the station spacing and teleseismic arrivals constrain the lateral resolution [Schmedes et al., 2012], the regional events best constrain vertical resolution above 2.5 km due to their steeper incidence angles. Further, the addition of local events best constrains structure between 2.5 and 5 km due to preferential sampling in this region. Our best models compare favorably to models derived from converted phases [e.g., Leahy et al., 2012] and available well logs. Additionally, the addition of finite-frequency measurements up to 8 Hz places key constraints on the shallow most portions of the model. These results indicate that all of these types of seismic sources can be used constructively in inversions for seismic properties.

2 Data and Method

2.1 Data Selection and Measurements

[9] Relative traveltime residuals of first P wave arrivals from local, regional, and teleseismic earthquakes constitute our dataset (Figures 2a and 2d). The Pg and Pn wave arrivals from local and regional earthquakes are picked in multiple frequency bands using Multi-Channel Cross-Correlation (MCCC) technique of Pavlis and Vernon [2010]. The event information for the local and regional earthquakes is available from the EarthScope Array Network Facility (ANF) catalog [Newman et al., 2008]. We only picked first arrivals with sufficiently high signal-to-noise ratios (SNRs) as determined by visual screening. The teleseismic sub-dataset that we used in our study was provided by Schmedes et al. [2012]. The traveltime residuals are calculated with respect to IASP91 [Kennett and Engdahl, 1991], which are then demeaned to obtain the relative residuals. Here we should note that the source parameters (i.e., locations and origin time) for local and regional events in the ANF catalog are with respect to a regional velocity model that is different than the global velocity model of IASP91. As a result of this, the magnitude of the calculated residuals with respect to IASP91 may be statically offset compared to the traveltime residuals associated with the local velocity model. However, such variations diminish when residuals are demeaned to obtain the relative residuals. The distances from these events to LPSE stations are quite large compared to the aperture of the array, and no reasonable variation between the velocity models would have a significant effect on relative residuals across the small span of the LPSE. Nevertheless, we can account for those affects through incorporation of additional parameters in the inversion if they should exist. These parameters are described in detail in the following section.

Figure 2.

Earthquakes that are recorded by the LPSE array in the period of the deployment. (a) Location map of earthquakes from multiple catalogs in the region. The red concentric circles indicate 1° increments of distance. The red dashed circle indicates the 1.8° distance from the LPSE array that marks the divide between observed Pn and Pg (regional and local) observations. Due to the lower signal-to-noise ratio, we used only arrivals from earthquakes located closer than 3°. (b) Backazimuthal distribution of earthquakes shown in Figure 2a. (c) Residual distribution of earthquakes shown in Figure 2a. (d) Location map of teleseismic earthquakes used in this study. (e) Backazimuthal distribution of the teleseismic earthquakes. (f) Residual distribution of earthquakes shown in Figure 2d.

[10] The regional (Pn wave) traveltime observations are obtained from earthquakes that are located between distances of 1.8° and 3.5°. Even though there are regional earthquakes with epicentral distances exceeding 3.5°, we did not pick those arrivals because the associated Pn arrivals have much lower SNR, drastically reducing the accuracy of the measurements. The local earthquakes that we used are located at distances closer than 1.8°. The magnitudes of the local and regional earthquakes range between 1.5 and 3.5 (ML). Our observations of SNR of Pn arrivals indicated that distance of the earthquake is the major factor controlling signal quality (rather than the magnitude), and therefore, we did not implement any magnitude threshold for event analysis. Because of this, a larger number of reliable measurements are obtained for regional earthquakes located close to the 1.8° distance (Figure 2a). On the other hand, for Pg arrivals, the magnitude emerges as a more critical factor controlling the SNR. Hence, observations from higher magnitude earthquakes (ML > 2) constitute the major part of the local sub-dataset. The backazimuthal coverage of local and regional data sets is well distributed over the four geographical quadrants with an overall gap of approximately 90° (Figure 2b). The teleseismic sub-dataset that we used consists of earthquakes located within 25 to 95° distance range (Figure 2d) with magnitudes Mb ≥ 5.0 (see Schmedes et al. [2012] for further details). The backazimuthal coverage of the teleseismic dataset is not uniform, but the majority of the earthquakes are located in two opposing directions (NW and SE) (Figure 2e), which also parallel the major linear trend of the LPSE array (stations L01-L17 and L42-L55 in Figure 1). Hence, the data from these two directions potentially balance each other out in our analysis without introducing major bias in the results. In addition, the incidence angles for the teleseismic arrivals are sub-vertical at shallow depths and less likely to introduce directional bias.

[11] The MCCC technique of Pavlis and Vernon [2010] involves a robust stacking algorithm for accurate picking of arrivals that have coherent waveforms and polarities across a regional or local seismographic network. Figure 3 illustrates an example of the picking procedure using this algorithm for a local event recorded by the LPSE. In this technique, a reference trace is picked (L24 in Figure 3a) for initial cross correlation (Figure 3b). Subsequently, the traces are aligned with respect to the cross-correlation maxima (Figure 3c) and compared with the overall stack in an iterative fashion. This is the stage of robust stacking, in which those signals that do not conform with the stack are down weighted while creating a new robust stack (Figure 3d). The cross correlation, alignment, and robust stacking continue iteratively until the improvement in alignment for each trace does not exceed a single sample (0.01 s for our 100 samples-per-second data). This multi-step iterative procedure assures accurate determination of lag times that would yield accurate estimates of signal alignment, data stack, and hence arrival time picks [Pavlis and Vernon, 2010]. Even though this algorithm was developed for picking mainly teleseismic arrivals, the small aperture of the LPSE network and the fine spacing of its stations enhance signal coherency (Figure 3a), making it possible for us to use this technique.

Figure 3.

An example of the picking procedure for a local earthquake recorded by the LPSE array. (a) Raw data record section with respect to the theoretical Pg wave arrival times (using IASP91). (b) Cross correlation of each trace with data for L24 (reference trace). (c) Aligned traces with respect to the lag time of cross-correlation maxima in Figure 3b. (d) Robust stack of aligned traces plotted together with the reference trace. The blue line indicates the picked Pg arrival time in this plot and also in Figure 3c.

[12] We attempted to improve the quality of our overall dataset in two steps. In the first step, we eliminated the outlier and erroneous measurements by discarding the data that fall outside of the 2-standard-deviation threshold from the individual station means. In the second step, we eliminated the measurements that yielded a misfit exceeding 0.1 s after a preliminary inversion of the full dataset (local, regional, and teleseismic arrivals). We selected this threshold as it defines outlier misfits based on their normal distribution around 0 s with a standard deviation of 0.05 s. The raw data set was composed of 56,663 measurements from 184 local, 129 regional, and 215 teleseismic events. After the implementation of the two-staged quality improvement, the dataset size reduced to 52,007 measurements representing the same events (Figures 2a and 2d). Measurements from the local data subset make up the dominant part (59%) of the refined dataset with 30,663 picks. The rest of the dataset is composed of 12,804 regional and 8540 teleseismic relative traveltime residuals, making up 25% and 16% of the entire set, respectively. The number of residuals peak near 0 s for all three data subsets with slight shifts toward positive residuals for local and teleseismic sets (Figures 2c, 2f, and 4b). The distribution of residuals is broader for the negative values, indicating presence of significantly faster structure beneath a part of LPSE array. The Root Mean Square (RMS) of the local, regional, and teleseismic sub-datasets are 0.068, 0.049, and 0.082, respectively. These values are close to zero as the sampled volume beneath the array is small. Thus, the magnitude of the RMS is an indication of how the volume beneath the array is sampled, and consequently, the difference between the RMS of the residuals for individual data subsets indicates that the sampling pattern for each category of events is somewhat different.

Figure 4.

Measured relative residuals through the array and the correlation between these and station elevations. (a) Elevation map of stations. (b) Histogram of observed relative residuals. (c) Filtered seismograms at each frequency band for a local earthquake recorded at L17. The red lines indicate the picked Pg arrival times, and the dashed red line emphasizes the magnitude of their variation between frequency bands. (d) Observed relative residuals (blue open circles) and station elevations (gray x marks) with respect to station number for individual frequency bands. The elevations are shown on right-side axes. The error bars indicate standard error of means for individual stations. (e) Relationship between relative traveltime residuals and station elevations. There are two trends visible marked by blue and red dashed lines. The trend with the positive slope indicates that there is some control of station elevations on the arrival times. We make sure that this trend is removed by applying an appropriate elevation correction as shown in the plot on the right. The blue dashed line indicates a negative slope, and it is more likely that this is related to variations in velocity structure underneath the array. This is also seen in Figure 4d where the relative residuals vary with a trend throughout the array.

[13] We filtered the regional and local raw data using an acausal Butterworth filter in six overlapping frequency bands and picked the P wave arrivals using the MCCC algorithm for each frequency band. These bands have center frequencies (CF) of 1, 2, 3, 4, 6, and 8 Hz. The Butterworth filter is applied to raw data both forward and backward directions in time in order to assure zero phase distortion and hence accurate determination of phase onset times [Boore and Akkar, 2003]. Even though such acausal filters can result in ringing precursors for sharp first arrivals, these precursors have much smaller amplitudes compared to the arrival amplitude and we expect that any bias in picks that could be introduced due to such precursor signals would be removed when residuals are demeaned. An example of filtered data in six frequency bands for a local event recorded at station L17 is shown in Figure 4c. The picking of local and regional data in various frequency bands in the scope of finite-frequency analysis is rather uncommon. However, we observe that the travel time picks that are obtained for multiple frequency bands show significant variations for the LPSE array (Figure 4c). The magnitudes of these variations are larger than expected errors associated with the picking procedure (on the order of a few samples).

[14] The teleseismic arrivals were picked only in the CF = 1 Hz band [Schmedes et al., 2012]. We did not attempt to pick these arrivals in higher-frequency bands (i.e., >1 Hz) as the teleseismic arrivals are dominated by signals with frequencies 1 Hz and less. On the other hand, the teleseismic data with lower CF (i.e., <1 Hz) are sensitive to structures in a broader region that is comparable to the size of our array and would not have a significant contribution to resolution of fine-scale structures. The major contribution of the teleseismic data set is through improvement of the sampling pattern via arrivals with near-vertical incidences.

[15] The corner frequencies, number of picks, and data RMS associated with individual frequency bands are given in Table 1. An important part of the dataset is composed of picks with CF = 1 Hz as this band has observations from all three event categories. Picks in CF = 3 Hz band makes up another important portion of the dataset: the Pg and Pn arrivals in this band consistently have higher SNR. Bands with higher CF (CF > 3 Hz) yielded fewer measurements due to lower dominant frequency of Pn arrivals and cycle skipping of higher-frequency signals during picking with the MCCC algorithm. The RMS values of the residuals for individual bands are within the same range as the overall dataset but vary as a function of central frequency. We propose that the differences in volumetric P wave velocities sampled by each frequency band may be responsible for these variations in the RMS values.

Table 1. Frequency Bands Used in Picking the Relative Traveltimes of First P Wave Arrivals, Associated Number of Measurements and Corresponding RMS Values
CF (Hz)Low Corner (Hz)High Corner (Hz)Number of PicksRMS
1.00.51.515,0920.071
2.00.53.589710.066
3.01.05.010,8900.063
4.01.07.060770.069
6.01.011.054400.061
8.01.015.055370.065

[16] The variations between relative traveltime residuals in different frequency bands can also be seen in the distribution of mean station residuals for each CF (Figure 4d). We observe a consistent general trend of mean relative residuals for each band, which displays faster arrivals (negative relative residuals) for the westernmost stations (L01 to L19) and slower arrivals (positive relative residuals) for the eastern stations (L20 to L55). However, detailed examination of these distributions shows some fine-scale variations among the bands regardless of how close their center frequencies are. Hence, this may be an indication of differences between sampled structures by arrivals in various closely spaced frequency bands. Consequently, the incorporation of data from all of these bands in the tomographic inversion has a potential to improve the resolution of the resultant images and illuminate the finer-scale details of the subsurface.

[17] Finally, we observe that the station-based mean relative residual distribution is generally anti-correlated with the station elevation, where late arrivals are observed at stations located at lower altitudes (L20 to L55 in Figures 4a and 4d) and vice versa. This indicates that the observed traveltime residuals are mainly controlled by subsurface structure rather than the station elevation. However, in several isolated parts of the LPSE array, the abrupt increase in station elevations manifests itself as increase in observed traveltime residuals (i.e., see L32, L33, and L34 in Figures 4a, 4d, and 4e). This shows that there is likely some contribution of station elevation on some of the observed traveltime residuals. Hence, it is important that we apply elevation corrections in order to avoid any elevation related bias in inversion results. In order to establish the suitable correction, we first determined which mean station traveltime residuals display positive correlation with elevation (stations along red dashed line in Figure 4e, left panel). These stations are generally in the sedimentary basin portion of the array and are presumed to sample structure that is more or less laterally homogeneous. We find that a P wave speed (Vp) of 4.1 km/s best de-trends the positive elevation-residual dependence (Figure 4e, right panel). We then use this velocity to apply a residual correction to the entire dataset. This velocity is slightly faster than would be expected for basin fill in this area (see well logs below) and therefore may mask second-order lithologic changes or deeper structural features. Application of these corrections removed effects of differential elevation from the dataset (Figure 4e, right panel), resulting in a more pronounced fast anomaly in the western part of the array.

2.2 Inversion Method

[18] The lateral dimension of the dense LPSE array is small (8 km by 4 km) compared to the distances and areal distribution of the local, regional, and teleseismic earthquakes (Figures 2a and 2d) that compose our dataset (from approximately 100 km to 10,500 km). Thus, all events are located outside the modeled volume and can be treated as remote sources: the first P wave arrivals at the array share essentially the same path before reaching close proximity to the receivers (modeled volume). Consequently, we treat the tomographic inverse problem as a miniature teleseismic problem rather than a LET problem. In addition, the downscaled teleseismic character and size of our problem free us from the computational burden and uncertainty of earthquake relocations that complicate LET algorithms.

[19] Based on this perspective, we adapted the finite-frequency, teleseismic tomography algorithm of Schmandt and Humphreys [2010] to image shallow subsurface beneath LPSE. This algorithm involves calculation of Born theoretical “banana-doughnut” kernels [Dahlen et al., 2000], which are used to approximate the traveltime sensitivities of grid nodes around individual ray paths within the first Fresnel zone. Schmandt and Humphreys [2010] designed this algorithm to compute sensitivities at grid nodes spaced 35 to 40 km apart from each other and for teleseismic arrivals with frequencies less than 1 Hz. The usage of higher-frequency arrivals from local and regional events as well as the small size and shallow location of the modeled volume for LPSE mandated the readjustment of spatial calculation intervals, spans, and frequency ranges of the original approximate sensitivity kernel computation routine. We show examples of approximate sensitivity kernels calculated on a fine computation grid for a local and a regional arrival at various depths in Figure 5b. Additional examples of computed kernels for various frequency bands are shown in the Supporting Information (Figure A1). We observe that the magnitude and shape of our approximate kernels are similar to the ones obtained for a shallow local study by Nolet et al. [2005].

Figure 5.

Parameterization and sampling of the model space. (a) The configuration of the parameterized model centered at station L22. (b) Computed traveltime sensitivity kernels for a local arrival and a regional arrival displayed in map and profile views. Blue open triangles are LPSE stations, and the blue lines are the theoretical ray paths. (c) Normalized Derivative Weight Sum (DWS) for the model in Figure 5a, sampled by the rays of the joint dataset.

[20] The frequency-dependent nodal sensitivities are expressed as normalized weights, which define the relative contributions of individual nodes to the partial traveltime derivatives for a given ray. The cumulative value of all weights at a given node is termed the Derivative Weight Sum (DWS) and is a convenient measure of how well each model node is sampled by all incorporated earthquake arrivals (Figure 5c). This normalized nodal sensitivity weighting implements an intrinsic smoothing constraint for the inversion because the approximated sensitivity kernel varies smoothly around the theoretical ray path. This both represents a more complete picture of the physical system and additionally contributes to the stability of the solution without sacrificing resolution. Further, utilization of data from various frequency bands enhances sampling and resolution due to variations in the thickness of the Fresnel zone. This results in a more detailed image of subsurface structure and a more robust solution.

[21] We preferred to use the tomographic algorithm of Schmandt and Humphreys [2010], as it allows us to incorporate observations from multiple frequency bands to make the best use of broadband data with a computationally efficient traveltime sensitivity kernel calculation subroutine that permits scaling of the kernels in proportion to the problem size (see Schmandt and Humphreys [2010], for details).

[22] In order to stabilize the solution, the inverse problem is regularized via application of model smoothing and damping. The smoothing factor is applied on the approximated sensitivity kernels to account for geometrical ray location uncertainty normal to the ray and along the ray path. Gradient and norm damping factors are also applied. The gradient damping governs ray path-normal nodal weights as a function of depth and regularizes the weight distribution between sampled nodes for the increasing angle of inclination of the mean ray path with depth. In this respect, this type of damping is well suited for our dataset, as we incorporate arrivals from various distance ranges with a variety of incidence angles. Norm damping, on the other hand, targets to dampen amplitude of calculated perturbations in order to obtain the model with the smallest possible norm. This sort of damping strongly down-weights those anomalies that are weakly sampled [Schmandt and Humphreys, 2010].

[23] To solve the inverse problem, we used the LSQR method of Paige and Saunders [1982]. This method has an objective of minimizing the least-squares misfit between calculated and observed data in an iterative sequence. We performed trade-off analysis between a Euclidian model norm and variance reduction [Menke, 1989] to determine the smoothing weight and the overall damping factor using the screened, joint dataset. Our tests indicated that we needed smaller absolute damping and smoothing factors for this “mini-teleseismic” problem in comparison to an actual teleseismic inversion because the partial traveltime derivatives associated with each node scale with the physical dimensions of the inversion grid and array. Our screened, joint dataset with 52,007 measurements has an RMS of 0.07, and we obtained an RMS of 0.03 for the data misfit after the inversion with favored values of damping (0.1) and smoothening (0.3), achieving a variance reduction of 80%.

[24] The RMS of the elevation corrections is 0.01, and this is as much as 14%of the RMS for the full dataset (0.07). This indicates the overall contribution of elevation differences between stations on observed relative residuals and importance of the elevation corrections. Even though we applied elevation corrections to the data set, we also included additional station terms in the inversion to account for small-scale heterogeneities that may be present beneath each station that are not resolved using this method. Incorporation of this term also provides a way for regularizing the applied elevation corrections. Event terms are calculated representing the adjustment of the mean arrival time for the set of stations that recorded each event. These terms account for the static relative traveltime residual differences between and within local, regional, and teleseismic datasets. Hence, the inclusion of event and station terms in the solution (model) space assures that none of the station or event based static traveltime residual differences (i.e., variations in theoretical traveltimes due to the differences between local velocity model used for event relocation and IASP91 or significant velocity perturbations outside of the model volume) erroneously map into the resolved model and introduce bias in the solution.

2.3 Model Parameterization

[25] The footprint of the LPSE array defines an area of 12 km by 6 km at the surface. The Fresnel zone radius associated with our six frequency bands ranges between 0.5 km and 3 km and hence assures a wider zone sampled around the theoretical ray. Based on this sampling constraint, we defined a model that has uniform grid spacing in horizontal directions, which expands with depth in accord with the spreading of the ray paths and the widening of Fresnel zones. We defined the bottom of the model to be located at 6 km depth. The lateral spacing of the grid nodes starts with 0.5 km at top of the model and dilates with depth up to 0.56 km at the bottom (Figure 5a). The vertical (depth) spacing of layers starts with 0.25 km at top and doubles below 4 km. This vertical change in node spacing also compensates the effects of spreading of geometric ray paths, which would otherwise under-sample densely spaced nodes at depth. This configuration defines a model volume composed of 5016 nodes with 22 longitudinal and 12 latitudinal nodes in 19 depth layers (Figure 5a). We defined the top of the model to be located at 0.5 km. The seismic velocity perturbations and heterogeneities above this layer are compensated through a combination of station static terms (representing very slow, un-lithified sediments) and elevation corrections (400 m across the array; see Figure 4a).

[26] Unfortunately, the LPSE array is configured linearly rather than in a grid, and therefore, a considerable portion of the surface of the model domain remains uncovered. This results in limited sampling of upper layers of the model by sub-vertical incoming rays. However, close station spacing and utilization of finite-frequency sensitivity kernels within the first Fresnel zones of the arrivals assures better sampling of the nodes that are located closer to the array at shallow depths. DWS values for various model layers show that parts of the model that are located further from the station array are not sampled, especially at the top of the model (Figure 5c). Hence, the norm damping for the upper layers is adjusted to be slightly higher than in the rest of the model. This suppresses poorly resolved anomalies in under-sampled parts of these layers. In accord with the spreading of the geometric ray paths, the node sampling becomes more diffuse and spreads over wider regions with increasing depth. Below 4 km, the DWS decays rapidly as the number of ray path crossings decreases (Figure 5c). We preferred to include layers located deeper than 4 km to account for out of model, event-side anomalies that may potentially leak into the model and cannot be compensated by event static terms. The norm damping for these bottom layers is therefore also adjusted to be higher than the central model domain. This suppresses anomalies within the model to be erroneously resolved in these under-sampled layers. The central parts of the LPSE array, where the station branches meet, consistently displays better sampling patterns throughout the entire model volume. This is also the region where major structural and geological changes take place in the study area. The enhanced sampling here reinforces confidence in the ability of the inversion to resolve structures in this zone.

3 Inversion Results

3.1 Resolution Tests

[27] We tested the resolving power of our dataset using synthetic models to check for under-sampled regions, as well as regions with lateral and vertical smearing. The synthetic input model for these tests contains layers with alternating fast and slow velocity anomalies emplaced in the model volume in a checkerboard fashion (Figure 6). There are regions remaining between the alternating blocks that were left neutral with no velocity perturbations. The input anomalies have −3% and +3% perturbations, and each block is comprised of a cube of 27 nodes separated by two and three neutral nodes in the horizontal and vertical directions, respectively. The presence of intervening neutral nodes helps us to understand lateral and vertical limitations in resolution.

Figure 6.

Results of synthetic tests showing input and resolved models along various depth slices (a) and latitudinal cross sections (b). Results are shown for both neutral (unperturbed) slices and sections with checkerboard patterns. The recovered models clearly outline the central regions with better resolution. The black line at top of each cross section in Figure 6b depicts the topography (not to scale), and the blue upside-down triangles shows the projected locations of LPSE stations along the given profile.

[28] We used rays and sampling kernels from our joint dataset to compute the synthetic dataset associated with this checkerboard setup. Then we inverted this synthetic dataset in order to obtain the images to compare with the input model (Figures 6a and 6b). All the regularizations and parameterizations are kept the same for this synthetic inversion in order to simulate the real data inversion step as close as possible. Figures 6a and 6b show the input model and resolved model in map and cross-section view, respectively. Not surprisingly, the results indicate that the resolution is better beneath the center of the LPSE array. The outline of resolved anomalies gradually dilates and degenerates together with significant reduction in amplitudes towards the lateral edges of the model. We can see this most clearly at the uppermost layers of the model (Figure 6a) where none of the off-array nodes are sampled by the data. Dilation and smearing effects exist along-ray path, particularly in the resolved checkers located close to the edges and bottom of the model (Figure 6b).

[29] The widening of better-sampled regions in deeper parts of the model can be clearly seen in cross-section plots of the checkerboard test results. This widening pattern is primarily controlled by the increase in Fresnel zone radii with depth. The reduction in overall anomaly amplitudes and dilation of outlines is primarily due to the minimum-length solution objective of the inversion procedure as well as the imperfect ray coverage.

[30] We calculated that there is an average of nearly 70% amplitude recovery of the synthetic anomalies that are located in the central portions of the modeled volume. This well-recovered bulk makes up nearly half of the entire model volume. In this respect, with the current model parameterization, and ray coverage of joint dataset, we can confidently expect to recover major upper crustal structures beneath LPSE with dimensions on the order of half a kilometer. Of course, the reliability of these sorts of tomographic inversion results may be limited by the basic tomographic assumptions including elasticity, isotropy of the medium, and accuracy of the sensitivity kernels and ray paths. Uncertainties in all of these assumptions may lead to mislocation and incorrect amplitudes of velocity perturbations.

[31] The results of these tests and the sampling pattern revealed by DWS should be taken into account during structural interpretation of resolved velocity perturbations. This will help avoiding misinterpretation of ambiguous anomalies that are resolved at regions of poor sampling and resolution within the model. For simplicity in examining images from our non-uniform array, we have defined a contour of DWS = 0.1, beyond which we deem the inversion results unreliable. In subsequent figures, model values for these regions are masked out. We expect this effect can be better controlled in future deployments with a more regular geometry.

3.2 Inversion Results

[32] The results of tomographic inversion obtained utilizing the joint dataset are summarized in Figure 7. A variance reduction of 80% is obtained as a result of this inversion. We preferred to interpret our results along a curvilinear cross section that follows the trend of stations between L01 and L41 (Figure 7a) in order to provide a direct comparison with the results of Leahy et al. [2012] and Schmedes et al. [2012]. The regions of the resolved model that are associated with normalized DWS values of 0.1 and higher yielded a variance reduction of 70%. This indicates that most of the resolved anomalies belong to the better-sampled regions of the model and the remaining anomalies have higher ambiguity both in amplitude and in location. The results revealed large-scale, distributed, and localized fast and slow velocity anomalies throughout the model. These anomalies have perturbation amplitudes ranging between −30% and 30%. While these values are high compared to anomalies typically resolved by global tomographic methods; they are consistent with the rapid changes in seismic velocity associated with lithologic change (e.g., from sandstones to carbonates) that one would expect in the tectonically active shallow crust.

Figure 7.

Results of tomographic inversion shown on various sections. (a) Along-array (L01 to L41) section showing the resolved model, normalized DWS, input synthetic model, and recovered synthetic model from left to right. The regions marked by dashed arrows labeled “1” and “2” indicate effects of smearing near poorly sampled western edge and bottom of the model, respectively. (b) Various depth slices across the resultant model. Note that the regions with poor or no sampling are masked out. (c) Results shown along various latitudinal cross sections. The poorly resolved regions are masked. Similar to the case in Figure 7a, the regions with sampling problems are marked with labels “1” and “2”. Topography and projected position of LPSE stations (blue upside-down triangles) are also shown.

[33] The results of the tomographic inversion indicate presence of two distinct fast anomalies: one located at shallow, western parts (above 1.5 km depth) of the array and another in the deeper, central parts (below 3.5 km) of the model. These fast perturbations appear to be roughly planar, with some thickness variations (Figures 7a and 7c). On the other hand, there is only one major slow velocity anomaly in the model, which is localized at depths above 4 km in the eastern half of the study area (Figure 7b).

[34] The fast (positive) perturbations make up approximately 45% of the entire (unmasked) model volume with average perturbation amplitude of 10%. The shallow and deep fast anomalies accounts for two thirds of the entire volume of resolved fast anomalies. The mean perturbation amplitudes for these shallow and deep anomalies are 8 and 15%, respectively. On the other hand, the negative perturbations comprise 40% of the unmasked modeled volume with a mean velocity perturbation of −9%. This volume is almost completely taken up by the localized slow anomaly, which comprises 38% of the entire model volume. Half of these fast and slow anomalies are resolved in the central parts of the model with nodes having above average DWS (see second panel in Figure 7a). This shows us the robustness of these anomalies.

[35] Our results also show that the transition between the resolved fast and slow anomalies occurs rather sharply, both laterally and vertically in the shallower and deeper parts of the model, respectively. The transition at shallow parts occurs between station L17 and L22 (Figures 7a and 7b) and the magnitude of this transition is nearly 40% in perturbation amplitudes. The deeper, vertical transition in perturbations appears to be sharper with amplitudes changing by up to 45% within 1 km depth at central parts of the model. Both the shallow and deep sharp transitions point out presence of structural complexities in the modeled volume. This can also be seen via trends observed in relative residuals for individual stations (Figure 4d).

[36] The impact of imperfect sampling is also visible in the results, and these are best seen on along-array and latitudinal cross sections (Figures 7a and 7c). The results of the synthetic tests clearly show the effects of weaker sampling. Specifically, two regions recognizably display the consequences of this sampling artifact. These regions, labeled as “1” and “2” in Figures 7a and 7c, indicate smearing of resolved anomalies along-ray paths coming in from western edge and western bottom parts of the model, respectively. The anomalies that bleed along the ray paths appear to have weaker amplitudes than the major slow and fast anomalies. The impact of such sampling problem is less pronounced in the eastern limits of the model due to dominance of arrivals from local earthquakes located to the southeast (Figure 2b).

3.3 Recovery Tests

[37] We carried out realistic amplitude recovery tests in order to examine how precisely the amplitudes and locations of fast and slow perturbations can be recovered in the case where these anomalies resemble the structures resolved in actual tomograms. This test also helps us to obtain more realistic measures of inversion artifacts that can be helpful when interpreting the robustness of imaged anomalies.

[38] We designed the amplitudes and geometries of input anomalies to be similar to the actual tomograms that we obtain after inversion of the joint dataset. The input anomaly pattern is shown in Figure 8, and there are no variations in its geometry latitudinally. The input anomalies have homogeneous +30% and −30% perturbations. The fast anomalies are modeled assuming an over-thrust structure, forming a wedge geometry that thickens toward the west in the shallow parts and a uniform-thickness layer below 3.5 km. We defined a single slow velocity anomaly located at shallow depths, extending down to 2 km depth.

Figure 8.

Comparison of results of recovery test with actual tomograms obtained after inversion of joint dataset. All of the synthetic, recovered, and actual images are shown across the L01-L41 section of the study area. The fast synthetic structures have a constant perturbation of 30%, and the slow structure has a constant perturbation of −30%. The arrow labeled “1” indicates the regions showing smearing of fast anomalies. The inward arrows labeled “2” shows thinning of the deeper flat layer of fast perturbations as some of the fast anomalies are traded off to shallow depths. This occurs most clearly in the west as the effects of smearing are more pronounced there. The outlines of major anomalies are marked with white dashed lines in input and recovered models.

[39] Similar to results of the synthetic checkerboard resolution tests, the results of the recovery tests also indicated sampling-related limitations of the inverse problem. Like the synthetic test, these recovery tests revealed a clear pattern of along-ray path distortion of resolved anomalies (Figure 8). This artifact of the inversion is best seen in the western part of the model where the sampling is relatively poor due to lack of earthquakes in this direction (Figures 2b and 2e). The recovered amplitude of the anomalies rapidly decreases toward the off-center parts of the model.

[40] The input shallow fast velocity anomaly makes up nearly 11% of the entire model. However, the resolved anomaly has an expanded volume covering up to 15% of the entire volume. This is probably a good indication of the distortion of the resolved anomaly. Conversely, the bottom fast velocity anomaly makes up 37% of the input model where the recovered volume is reduced by nearly 4% at this depth. This also shows the impact of sub-vertical smearing of fast anomalies along the ray paths in the western section of the model. This can be seen in the recovered model in Figure 8. The thinning of the bottom fast anomaly, marked by “2”, shows how the fast anomalies at this depth trade-off with shallower portions of the model, where significant increase in coverage of fast anomalies takes place (labeled by “1”). Similar artifacts are seen in the actual tomograms also labeled by “1” and “2” in Figure 8. These observations caution us about limitations of the tomographic images especially at the western edges of the model. The recovery test also shows us that the mean amplitudes of the recovered perturbations are reduced nearly by half. This is a common limitation of tomographic inversion algorithms as these have an objective of obtaining the solution with the smallest possible energy (length). Even though artifacts exist related to model space sampling and array geometry, we were able to recover accurate locations and basic outlines of the input anomalies at the central parts of the model. We will discuss the accuracy of the inversion and implications for hydrocarbon exploration below.

4 Discussion

4.1 Contribution of Sub-datasets

[41] In order to assess the value of individual data types (e.g., local, regional, and teleseismic earthquakes) and data of different frequency band combinations in resolving shallow crustal structure above 5 km depth, we carried out individual inversions of these dataset subdivisions. We compare the results of these inversions as well as results of synthetic resolution tests and normalized sampling for individual dataset cases. Here we describe these tests and highlight the contributions from each data type.

[42] In the first step of these analyses, we inverted local, regional, and teleseismic datasets individually and compared the results. In these tests, we implemented only the 2-standard-deviation quality threshold for individual station residual means. In order to compare the test results, we applied the same values of damping (0.1) and smoothing (0.3) parameters for each test. While it is probable that the damping and smoothing values for each data type could be further optimized to obtain improved results, this provides a point of comparison for major features in the model volume. As expected and demonstrated by Schmedes et al. [2012], the sub-vertical ray paths of the teleseismic arrivals yield a sampling pattern that is vertically stretched. This resulted in elongated fast and slow velocity perturbations (Figure 9a). Hints of such vertical stretching can also be seen in results of the synthetic resolution tests. The resolved fast and slow velocity anomalies for this inversion test occupy nearly equal amounts of model volume (50%). The inversion resulted in a small RMS misfit, but the poor sampling pattern yielded a very high RMS of station static terms relative to the overall RMS of the teleseismic dataset (Table 2). This indicates the instability of the solution and shows the mapping of misfit and errors into the station static terms due to laterally localized sampling.

Figure 9.

Results of inversion tests with different subsets of data. (a) Results of tomographic inversion, DWS sampling patterns, and checkerboard tests, obtained using teleseismic local and regional datasets. Regions marked with bold dashed lines marked “1” and “2” point out major differences in resolved structures. (b) Results of tomographic inversion, DWS sampling patterns, and checkerboard tests, obtained using relative traveltime residuals measured in two separate sets of frequency bands (f) and the band with CF = 1 Hz. Regions marked with bold dashed-boxes marked “1” and “2” point out major differences in resolved structures. Note that the results for CF = 1 Hz band yields smoother anomalies, which define the general background of structures.

Table 2. RMS of Individual Datasets, RMS Misfits, and RMS Static Terms Obtained After Inversion of Each Dataset Individually
 RMS DataRMS MisfitRMS Station Static TermsRMS Event Static Terms
Teleseismic0.1050.0270.3280.053
Regional0.0810.0660.0490.047
Local0.0760.0310.0660.032

[43] The regional dataset, on the other hand, is composed of arrivals with ray paths that intersect at higher angles and yields a more homogenized sampling pattern above 2–3 km. This can be seen in better recovery of the checkerboard pattern of anomalies for synthetic tests. The results for this dataset also reveal vertically distributed fast and slow velocity anomalies with the presence of a fast velocity anomaly that extends down to 1 km depth on the west side of the model. This near-surface fast anomaly constitutes nearly 15% of the model volume. Unlike the results of the teleseismic dataset, the RMS misfit for this dataset is higher with a much lower value of station static RMS (Table 2). We attribute the higher misfit for this dataset to its limited size and imperfect backazimuthal coverage (Figure 2b).

[44] Arrivals from local earthquakes have intersecting ray paths at even higher angles than those from the regional earthquakes. This helps extend the bottom limit of the well-sampled portions even deeper than the regional dataset. This can be seen both in results of synthetic resolution tests and in the inversion results where a deeper fast anomaly is also revealed different than the results from the regional case. This deeper anomaly makes up approximately 25% of the entire model volume. We must keep in mind that the local dataset is the largest of the three and has better backazimuthal ray coverage. Hence, the RMS misfit for this dataset is small compared to its overall RMS, and it has a low RMS for the station static terms (Table 2).

[45] Event static terms for all inversion tests have relatively low RMS values for local, regional, and teleseismic datasets (Table 2). This indicates that the majority of variations in the observed relative residuals are due to velocity structure within the modeled volume. For all of these dataset inversion tests, resolved fast and slow velocity anomalies both occupy half of the entire model volume.

[46] These individual data types play an important role in higher quality of the joint results as the arrivals for each of these datasets sample the model volume differently. This can be clearly seen in differences in locations and amplitudes of the resolved anomalies (regions marked by “1” and “2” in Figure 9a). Hence, joint inversion of all three datasets aids better resolution of the actual structure.

[47] In addition to testing individual data types, we subdivided the six frequency bands into two groups each having approximately 28,000 relative traveltime residuals. The first group was composed of residuals picked in frequency bands with CF = 1, 3, and 8 Hz, and the second group was composed of bands with CF = 1, 2, 4, and 6 Hz. These bands were chosen to determine whether or not comparable results could be obtained with less initial effort in data collection. For example, measurements at higher frequencies are more difficult and time intensive to make. We included CF = 1 Hz band in both groups in order to equilibrate their sizes for a better comparison of the inversion results.

[48] Like in the case of data type tests, we used the same damping (0.1) and smoothing (0.3) parameters for each frequency band test. The relative traveltime residuals for both sets have similar RMS (approximately 0.08). The inversion of these sets yielded similar RMS misfits in the order of 0.05 and variance reduction of approximately 60%. The results for these tests are shown in Figure 9b.

[49] Even though the general outline of resolved anomalies is pretty similar for both tests, there exist finer-scale differences in distribution of these anomalies throughout the model volume (i.e., see region marked by “1” in Figure 9b). This is also true for the sampling pattern for both of these tests. The results indicate that the shallower fast velocity anomalies at the western half of the model (see region marked by “1” in Figure 9b) are resolved by the set that contains the 8 Hz frequency band while the smearing artifact of inversion at the deeper (>3 km), western edge of the model is less pronounced in the results of the test with lower frequency bands of CF = 1, 2,4, and 6 Hz (see region marked by “2” in Figure 9b).

[50] This shows that although the observed traveltime residuals, misfits, and general anomaly distributions for both inversion tests are similar, the differences in frequency band content results in varying width of ray based sampling zones throughout the vertical extent of the model, affecting the sampling patterns. Hence, it is necessary to incorporate both of these frequency band sets in the inversion, to be able to obtain the best sampling and resolve finer structures. The robustness of the joint inversion of data in all of the six frequency bands is indicated by higher variance reduction (80%) and lower RMS misfit (0.03) compared to results of these tests.

[51] As a comparison, we included inversion results using only the lowest frequency band (CF = 1 Hz), as might be done in a more traditional tomographic inversion (Figure 9b). The number of relative traveltime residuals associated with this band is almost half of the number of measurements for the other two frequency band subsets. The inversion of this dataset yielded similar locations of fast and slow velocities compared to the results of other frequency band tests. However, the outlines of the resolved anomalies are much smoother, and these are poorly resolved. These results show that the data with CF = 1 Hz provide a smooth background of resolved anomalies while the addition of the higher-frequency components to the dataset improves the resolution and recovery of finer-scaled structures throughout the model space.

[52] Here it is important to note that the contribution of the near- and intermediate-field terms on finite-frequency sensitivity kernels is neglected in the “banana-doughnut” approach of Dahlen et al. [2000] and hence in this study. Analysis by Favier et al. [2004] indicated that the intermediate- and near-field terms contribute significantly to the complete sensitivity kernels near the surface on the receiver side. Their study showed that these contributions affect the geometry and magnitude of sensitivity zones along the ray path down to depths that are significantly smaller than the wavelength of the observed arrival (approximately 5% and 17% of the wavelength for P and S waves, respectively). Similarly, Nolet et al. [2005] pointed out that the contributions by these terms may be important for low-frequency arrivals (<1 Hz) in the immediate area surrounding the receiver, near the surface. In our study, we use observations from incident P wave arrivals that are in the frequency band of 1 to 8 Hz and the dominant affect of the near- and intermediate-field terms in this band affects traveltime sensitivities only in the upper 250 m section of the volume beneath LPSE array (assuming a maximum wave length of 4 km for 1 Hz). As it is stated earlier, the top of our model volume is located at 500m depth and we do not calculate sensitivities and invert for structure above this depth. Thus, we do not expect exclusion of these contributions to have an impact on our results. Favier et al. [2004] also states that the intermediate-field term may have some second-order contribution to the calculated sensitivity kernels down to depths comparable to the wavelength of the P wave arrival. For our lower frequency data (CF < 4 Hz), the traveltime sensitivities may have some contribution from the intermediate-field terms between depths of 0.5 km and 4 km. Nevertheless, as shown by the results of Favier et al. [2004], these contributions are second order to the contributions from the far-field terms and our 500 m lateral model-grid spacing is rather coarse for these terms to have any significant contribution to the overall result of the tomographic inversion.

[53] As mentioned previously, we anticipate that application of equal smoothing and damping to each data type may result in sub-optimal resolution. We also postulate that the same applies to measurements at different frequencies. One could therefore envision a generalized joint-inversion problem in which weights are introduced to moderate the influence of the different earthquake sources and frequency contents. These weights would be highly dependent on the source geometry, array geometry, and signal-to-noise ratio of the recorded data. A careful study of such issues in the future will be necessary to obtain the best resolution images possible.

[54] In summary, the results of both dataset and frequency band tests indicates the necessity for incorporation of all available data into the inversion to improve the approximate finite-frequency sensitivity zone coverage within the modeled volume. Our tests indicate that the associated joint inversion is capable of reducing the unwanted effects of inversion artifacts due to imperfect backazimuthal ray coverage and hence produce robust images with better resolution.

4.2 Effect of Array Geometry

[55] In the previous sections, we argued that the irregular, linear outline of the LPSE array is partially responsible for irregular sampling of the model volume and hence inversion artifacts such as smeared anomalies. In order to estimate the magnitude of those effects on the resultant tomograms, we tested several array configurations through inversion of synthetic models and the same ray coverage that we have used. We tested array configurations such as a grid (Figure 10a), intersecting lines with a high angle (Figure 10b) and single line crossing perpendicular to the major structures (Figure 10c). The station spacing was 250 m for all these configurations, in accord with the actual LPSE array. We adjusted the general spatial coverage of the arrays to be similar to E-W extent of the LPSE; hence, there are different numbers of stations for each array. In addition, we used the same synthetic input model for all of these tests, which is the model that we used for our recovery test shown in Figure 8. We compared the results of these tests with our actual recovery tests along the section between station L01 and L41 (Figure 10d).

Figure 10.

Results of inversion tests with different array geometries. (a) Array geometry test with a rectangular grid configuration of 105 stations shown as blue stars on the map view (left panel). The sections of synthetic input structure and the recovered (output) structures are shown for the A-B line in the right panels. (b) Array geometry test with 55 stations configured in two crossing lines at high angles. Note the near perfect recovery of the input structure. (c) Array geometry test with a single line of 35 stations that intersects the boundary between shallow fast and slow anomalies (black dashed line on map) perpendicularly. (d) Results of our recovery tests for actual LPSE array configuration. The dashed black box outlines the regions of smeared fast anomalies.

[56] Not surprisingly, the results of these tests indicated that the best recovery of the structure is obtained for a grid configuration (Figure 10a). Obviously, this array has a better sampling of the shallow structure due to its wider spatial coverage on the surface and large number of stations. However, very similar results are obtained for the crossing-line array, which has a relatively limited spatial coverage with fewer stations (Figure 10b). This indicates that the structure can be effectively recovered with fewer stations as long as the surface coverage of the array is wide enough to provide decent sampling of the volume that is located directly beneath it.

[57] This is further clarified, when we compare the results here with the results from the linear array (Figure 10c). In the case of the linear array, we begin to see the effects of poor lateral sampling near the surface. Here the recovered amplitudes are less, and we see considerable vertical smearing of the recovered fast and slow anomalies when compared to the actual structure (see region marked by “1” in Figure 10c). Obviously, poor lateral sampling due to linear configuration of the array introduces inversion artifacts and results in relatively poor recovery. However, when we compare the locations and trends of these amplitude losses and smearing artifacts, we can see that they correlate with those that we see for the actual LPSE array configuration (Figure 10d). We therefore propose that the configuration of the LPSE array is the major reason for the inversion artifacts that we observe in our actual tomograms and synthetic recovery tests.

[58] Nevertheless, we cannot (and do not) assume that dataset imperfections (i.e., gaps/bias in backazimuthal ray coverage) have little impact on the inversion results. These imperfections act together with the poor lateral coverage of the LPSE array to generate similar artifact patterns in actual tomograms marked by “1” and “2” in Figures 7a and 7c. With the help of these tests, we believe we are able to identify erroneously resolved anomalies in our actual tomograms. The determination of the problematic anomalies in the tomograms will aid us when comparing our results with other studies.

4.3 Comparison of Results With Other Studies

[59] Regional geological studies in the vicinity of the study area indicated the presence of a thrust sheet of high-velocity Paleozoic carbonates emplaced onto lower velocity late Mesozoic clastic strata [e.g., Coogan, 1992; Royse, 1993]. The associated thrust subdivides the study area into two geomorphologically different terrains to the east and west (Figure 11). Receiver function analysis by Leahy et al. [2012] and Gans [2011] as well as the well logs in the region indicates presence of faster Precambrian granitic basement at 3–4 km depth. Analysis by Leahy et al. [2012] indicated the presence of a gradational transition below 3 km from lower velocity clastics to higher velocity basement units. This transition zone is marked by Paleozoic carbonate formations.

Figure 11.

Comparison of our calculated Vp models with results of well log measurements, receiver function analysis, and geological observations in the study area. Top panel shows the 1-D Vp structure at stations L12 and L19, obtained from our Vp model (blue line), RF analysis (red line) [Leahy et al., 2012], and well log measurements (magenta line). Regions marked by “1” and “2” correspond to parts of the resolved model with smearing problems which are also shown in Figures 7a, 7c, and 8 with the same labels. Middle panel shows a 3-D layout and morphology of the study area, together with along-array Vp structure inferred from our results. Same labeling as 1-D Vp plots is used for the problematic regions with smearing. Bottom panel shows generalized geological layout of the study area based on regional geological studies [Coogan, 1992; Royse, 1993].

[60] In order to compare our results with results of receiver function studies and well logs, we need to convert the resolved P wave perturbations into absolute P wave speeds (Vp). We chose to use a Vp of 4.1 km/s as the reference value and calculated absolute velocities for our preferred tomographic model. As discussed above, this reference Vp was obtained via the elevation corrections and is consistent with the results of Leahy et al. [2012]. A section of the resultant Vp model is shown in Figure 11. This model has a maximum Vp of 6 km/s located at nearly 4–4.5 km depth, where Precambrian granitic basement exists. Lower to minimum values of Vp (3–3.5 km/s) are observed at the shallower eastern half of the study area, where younger sediments occur. We can also observe a 1–2 km thick volume at the shallower western half of the model with an average Vp of approximately 5 km/s, corresponding to the western thrust sheet bound by the Hogsback thrust fault. These observations are in accord with results of receiver function analysis of Leahy et al. [2012].

[61] In general, our Vp model is in agreement with Vp structure obtained from well logs and structure inferred from geological surveys (Figure 11). However, there are portions of our model that deviates from receiver function results and well log measurements as well as structural observations. These regions are marked with labels “1” and “2” in Figure 11. Our model displays higher Vp than RF results and well logs in the western, shallower parts of the study area (regions marked by “1” in Figure 11). Based on our aforementioned tests and observations, we attribute these to sub-vertical smearing of fast anomalies in the west due to imperfect sampling pattern and linear configuration of the LPSE array (see regions marked with “1” in Figures 7a, 7c, 8, 10c, and 10d). In addition, at deeper western central parts of the model, Vp from other studies are significantly higher than our resolved Vp at depths between 3 and 4 km (regions marked by “2” in Figure 11). Similar to the case in shallow western parts, we attribute this misfit to sub-vertical smearing of the central slow velocity anomalies, which results in thinning, disappearance, and depression of fast anomalies that are located below 3 km (see regions marked with “2” in Figures 7a, 7c, and 8).

[62] Despite these discrepancies and limitations, the general agreement between results of other studies/surveys and our tomographic model shows that we can retrieve robust first-order shallow crustal structure in the region using broadband earthquake tomography. Because the tomographic inversions are sensitive to slightly different properties than the RF model, we anticipate that an improved model might be obtained if the data types were combined in a joint inversion.

5 Conclusions

[63] We were able to illuminate first-order shallow crustal structure above 5 km depth beneath the LPSE array using broadband earthquake traveltime data. Our tomographic inversion tests of local, regional, and teleseismic datasets revealed different strengths and weaknesses for these when determining the subsurface structure. Through joint inversion tests with all three datasets, we determined that these datasets complement each other to produce robust and better-resolved tomographic models. Our study suggests that proximity to seismic sources may be an issue if earthquake tomography is the desired imaging method. This may provide challenges for hydrocarbon exploration, given that historically, most industry activity has focused on seismically quiet passive continental margins. While this problem might be avoided with the addition of receiver function data, the industry continues to move into more tectonically active settings both on land and in marine areas, suggesting many possible application areas.

[64] We evaluated the value of finite-frequency approximation and utilization of arrival time data in multiple, closely spaced frequency bands by testing various data subsets with different frequency content. The results of these tests indicated the need for joint inversion of data in all available frequency bands in order to enhance the robustness of the solution and improve the resolution of the acquired tomographic images. In addition, we were able to constrain the major causes of the inversion artifacts within our resolved model, through recovery tests and testing of different array geometries with the same set of data. The results of these tests indicated imperfect sampling of the model domain mainly due to the linear configuration of the LPSE array. Hence, we were able to identify the regions of the resolved model with such problems and the probable magnitude of the associated artifact. We take these observations into account when comparing our results with results from other studies.

[65] Even though minor deficiencies in our resultant tomographic model exist, we observe that the first-order configuration of the resolved structures is in good agreement with the independent outcomes of receiver function studies and well log measurements. Like these studies, we were able to identify a thin, fast thrust sheet in the western half of the study area, as well as a deeper, fast crystalline basement below 4 km. This is a good indication of how broadband earthquake data can prove useful in constraining shallow crustal structure for similar studies. We therefore anticipate that this sort of joint analysis of available earthquake data can provide robust starting models and framework structures for higher-resolution active-source studies.

Acknowledgments

[66] We would like to thank Christine Gans, Ryan Porter, and other members of the field crew for their help and efforts during deployment of LPSE array; Jan Schmedes for providing the teleseismic dataset; and Rebecca Saltzer for useful discussions in the earlier stages of this study. We also thank members of the Pinedale office of the BLM and ExxonMobil field operations office for their assistance in permitting this experiment. The seismic equipment for this project was provided by the EarthScope program through the IRIS-PASSCAL consortium. The seismic data are available through the IRIS Data Management Center. Figures 1, 2, and portions of Figure 11 were generated using Generic Mapping Tools [Wessel and Smith, 1998].

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