Journal of Earth Science  2018, Vol. 29 Issue (6): 1380-1389   PDF    
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Impact and Solutions of Seawater Heterogeneity on Wide-Angle Tomographic Inversion of Crustal Velocities in Deep Marine Environments-Numerical Studies
Zhihui Zou1,2, Hua-Wei Zhou1,2,3, Harold Gurrola4, Aifei Bian5, Zhonglai Huang1,2, Jianzhong Zhang1,2    
1. College of Marine Geosciences, Key Lab of Submarine Geosciences and Prospecting Techniques MOE, Ocean University of China, Qingdao 266100, China;
2. Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266061, China;
3. Department of Earth & Atmospheric Sciences, University of Houston, Houston TX 77004, USA;
4. Department of Geosciences, Texas Tech University, Lubbock 79409, USA;
5. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
ABSTRACT: The seawater column is typically taken as a homogeneous velocity layer in wide-angle crustal seismic surveys in marine environments. However, heterogeneities in salinity and temperature throughout the seawater layer result insignificant lateral variations in its seismic velocity, especially in deep marine environments. Failure to compensate for these velocity inhomogeneities will introduce significant artifacts in constructing crustal velocity models using seismic tomography. In this study, we conduct numerical experiments to investigate the impact of heterogeneous seismic velocities in seawater on tomographic inversion for crustal velocity models. Experiments that include lateral variation in seawater velocity demonstrated that the modeled crustal velocities were contaminated by artifacts from tomographic inversions when assuming a homogeneous water layer. To suppress such artifacts, we propose two strategies:(1) simultaneous inversion of water velocities and the crustal velocities; (2) lay-er-stripping inversion during which to first invert for seawater velocity and then correct the travel times before inverting for crustal velocities. The layer-stripping inversion significantly improves the modeling of variation in seawater velocity when preformed with seismic sensors deployed on the ocean bottom and in the water column. Such strategies improve crustal modeling via wide-angle seismic surveys in deep-marine environment.
KEY WORDS: deep water    seismic tomography    wide-angle seismic survey    water heterogeneity    OBS    vertical cable    

0 INTRODUCTION

Marine seismic surveys are useful in interpreting the geologic formations (Chen et al., 2015; Tian et al., 2015) and surface mineral distribution (Yang et al., 2016) beneath the seafloor. In conventional marine seismic surveys, seawater column is usually assumed to have a constant velocity. In reality, seawater has a layered seismic velocity structure due to vertical variations in salinity and temperature (Han et al., 2012; Holbrook et al., 2003). In three dimensions, the seismic velocity of seawater varies horizontally as a result of multiscale eddy currents, where ocean currents mix seawater bodies that have different salinity and temperature (Ma et al., 2016; Biescas et al., 2014, 2008; Song et al., 2009; Holbrook, 2003).

In deep marine environments, such as those near the east coast of Japan, the large-scale marine eddy can be over 200 km in width and reach to over 500 m in depth (Ma et al., 2016). Those eddies can have 4 ℃ temperature difference with the surrounding seawater, and these eddies may be stable for tens of years (Ma et al., 2016). The typical mesoscale eddy is the Mediterranean eddy, also called meddy. The meddy is generated when the warm and salty Mediterranean water mix with the Atlantic water (Biescas et al., 2008). The meddies can be 50 km in width and around 800 m thick (Huang et al., 2011; Biescas et al., 2008), may exist for around 2 years and travel to distances of up to 1 000 km (Richardson et al., 2000, 1989; Armi et al., 1989). The meddy normally has a 2 ℃ temperature increase and over 0.5 psu salinity increase, which result in a 20 m/s increase of seismic velocity (Huang et al., 2011; Biescas et al., 2008). The small-scale turbulences, which are hundreds of meters vertically and several kilometers horizontally, were found in areas that have internal wave and seawater currents (Holbrook et al., 2013; Eakin et al., 2011; Bertrand and MacBeth, 2003). The pattern and location of the small-scale turbulences can change in time periods as little as days to as long as months (Bertrand and MacBeth, 2003).

Due to the 3D inhomogeneity of seawater, it is important to use models that include heterogeneity in seawater velocities when processing the marine seismic data, otherwise there will be distortion in the resultant seismic images of the crust due to the application of inaccurate traveltime corrections (Ji and Lin, 2013; Han et al., 2012; MacKay et al., 2003). Given the fluid nature of water, velocity anomalies in seawater can vary with time which will cause mismatch in reflectors in 4D seismic surveys, where the same reflectors are imaged at multiple times (MacKay and Fried, 2002). Therefore, to produce high quality images in deep marine seismic surveys, corrections must be done for velocity heterogeneity throughout the seawater column (Ritter, 2010).

Similarly, if the seismic velocity in seawater is assumed to be homogeneous during seismic tomography, the calculated traveltimes will be erroneous which may generate artifacts in the inverted seismic velocity model. Hence, an evaluation of the impact of 3-D variations in water velocities on seismic tomography modeling in a marine environment is necessary.

In marine seismic surveys, wide-angle seismic arrays, containing tens to hundreds of OBSs, are typically deployed to construct the velocity profile. In such cases, the distance between OBSs may be several kilometers, which may under-sample the seismic waveforms (Zou et al., 2016; Markris et al., 2012; Gailler et al., 2009). In shallow marine environments, seismic ray paths are nearly vertical through the seawater so the impact of water on travel times are typically removed by subtracting the delay times calculated using an average seismic velocity for the water. However, in deep marine environments, traveltime corrections using an assumed homogeneous velocity may introduce errors by not accounting for the lateral variation in the seismic velocity of a thick seawater layer. During traveltime inversion, errors in the assumed water velocity will leak along the raypath and generate artifacts in the inverted crustal velocity model (Zhou, 2011).

It is clearly a challenge to interpret seismic velocity models that were derived assuming a homogeneous seawater layer. Though some authors argue that shallow velocity structure may not significantly impact the inversion for deeper velocity structure (Zelt et al., 1999), the angular coverage of seismic ray paths decreases with depth in wide-angle seismic surveys, meaning an increased chance for generating artifacts in the deeper part of seismic velocity models. The additional resolution required by recently established 4-D seismic studies of temporal changes in crustal seismic velocities will require the inclusion of 4-D water velocities in the inversion (Ritter, 2010; Bertrand and MacBeth, 2003). Therefore, in deep marine environments, it is necessary to evaluate the impact of seawater velocity heterogeneities on the results from seismic tomography of crustal velocities.

In this paper, we first investigate the effect of water velocity anomalies of different sizes on the inverted crustal velocity models. Two different inversion strategies are employed to improve the estimation of seawater velocity structure in crustal tomography. The first is a simultaneous inversion of seawater and crustal velocities. The second is a strategy of layer- stripping by first inverting for velocity models of seawater and then invert for crustal velocity models. Finally, we discuss the efficiency of different acquisition strategies on the inversion for seawater velocities.

1 MARINE SEISMIC DATA ACQUISITION AND MULTI- SCALE TRAVEL-TIME TOMOGRAPHY 1.1 Acquisition Geometry in Deep Marine Seismic Surveys

Marine seismic acquisition usually employs streamers of hydrophones, ocean bottom seismometers (OBSs), ocean bottom cables (OBCs) and/or vertical cables (VCs) to sense and record seismic waves. As shown in Fig. 1, the hydrophone streamers and seismic sources such as air gun arrays are towed by ships near the sea surface. OBSs and OBCs are deployed on the sea floor. A VC is a hydrophone cable deployed vertically, similar to a vertical seismic profile (VSP) onshore.

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Figure 1. Marine seismic acquisition system. OBS/OBC. Ocean bottom seismometer/cable; VC. vertical cable.

Conventional local (and relatively shallow) marine surveys deploy hydrophone streamers as receivers and air gun arrays as sources towed near the sea surface. For crustal seismic studies, because streamers may not provide the required long offsets, wide-angle OBS arrays are typically deployed. VCs are another type of acquisition geometry that can be used to record long-offset seismic data. We will discuss the application of OBSs and VCs for deep-water seismic imaging in the following sections.

1.2 Multiscale Travel-Time Tomography

Real Earth velocity structure includes anomalies of many difference sizes (Fig. 2a). Multiscale parameterization decomposes those different-sized velocity anomalies and projects them onto the meshes of appropriate cell sizes (such as cartoon shown in Fig. 2). The multiscale seismic tomography parameterizes the study volume into cells of different sizes, called submodels (Figs. 2b2f), and inverts all submodels, simultaneously (Zhou, 2003, 1996). Multiscale tomography mitigates the non uniqueness and the smearing effect resulting from uneven ray path coverage of conventional single-scale tomography (Zhou, 2003). The stability of multiscale seismic tomography is also confirmed by both numerical tests and case studies (Zou et al., 2016; Zhou, 2003).

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Figure 2. Cartoon showing the multiscale parameterization. (a) Velocity model, color blocks indicate the velocity anomalies; (b)–(f) decomposed submodels.Cartoon showing the multiscale parameterization. (a) Velocity model, color blocks indicate the velocity anomalies; (b)–(f) decomposed submodels.

In the following sections, multiscale seismic tomography is first used to invert for the entire velocity model including the water layer on top and the shallow crustal layers at bottom. The inverted velocity models are compared with the true model to show the impact of inaccuracies of water velocities on the crustal velocity model. Then, to mitigate the impact of inaccurate water velocity, the multiscale tomography method is used to invert for a more accurate seismic velocity structure in the water layer.

2 IMPACT OF WATER HETEROGENEITY ON SEAFLOOR SEISMIC VELOCITY MODEL BUILDING

Variations in salinity and temperature in seawater can result in perturbations in seawater velocity of up to 200 m/s, which is more than 13% of the average water velocity of 1 500 m/s (Huang et al., 2011; Holbrook, 2003). In different marine environments, turbulence can result in salinity and temperature heterogeneity that can cause velocity anomalies of different magnitudes and sizes (Ji and Lin, 2013; Huang et al., 2011; Holbrook, 2003). In this section, we will evaluate the impact of small-scale and mesoscale anomalies in seawater velocity on crustal velocity model building.

2.1 Small-Scale Turbulence

Our synthetic model includes a 2 km thick crustal layer beneath a 2 km water column. The crustal layer in this hypothetical model is 2 km thick and has a 1-D velocity gradient from 2 to 4 km/s (Fig. 3b). To simulate velocity anomalies from small-scale turbulence in seawater, we introduce a low-velocity, 1 400 m/s, rectangular body (4 km wide and 1 km thick) in a 2 km thick seawater layer with a P-wave velocity of 1 500 m/s (Fig. 3a). In the numerical simulation, 12 OBSs' and 14 air gun locations were used to produce a data set of first arrival times using the shortest-path ray tracing method (Moser, 1991). The distributions of shots, receivers and ray paths are shown in Fig. 3b.

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Figure 3. (a) "Test" 2-D velocity perturbation in our hypothetical model used to generate the synthetic seismic travel-times. (b) Acquisition geometry and ray path projected on top of the hypothetical background velocity model. The black square shows the boundary of velocity anomaly of sea water. (c) Inverted velocity model. Panels (b) & (c) share the same colorbar. (d) Velocity perturbation relative to the "hypothetical" 1-D background velocity model. The dashed lines circle the velocity artifacts in crust due to the inaccurate assumption of uniform seawater velocity.

To demonstrate the impact of inaccuracies of seawater seismic velocities, we set the water velocity to be a constant 1 500 m/s in the tomographic inversion process. By assuming an inaccurate, uniform seawater velocity body (excluding the low-velocity rectangular body), the inversion resulted in 2-D crustal velocity anomalies in the inverted model (Fig. 3c). To elucidate 2-D variations in the inverted velocity model, we subtract the reference 1-Dhypothetical velocity model from the inverted (Fig. 3d). Three erroneous velocity bodies are clearly seen near the bottom of the crustal layer (Fig. 3d). A significant high velocity anomaly is observed in the middle and lower part of the crustal layer with two flanking low velocity anomalies. These velocity anomalies are artifacts resulting from using an erroneous assumption of a uniform velocity in the water column. Both the high and low velocity anomalies have magnitudes of about 150 m/s, which is a little higher than the 100 m/s velocity anomaly in seawater of the hypothetical model. The magnitudes of the three velocity artifacts are more than 5 % relative to the hypothetical crustal velocity model. Since the ray paths near the bottom of the model are nearly horizontal and subparallel to each other, the lateral resolution of tomography is poor at those depths. Comparison of the size and magnitude of the artifacts in synthetic data computed from a plausible velocity model demonstrate that the assumption of a uniform water layer in seismic tomography can cause significant errors in the interpretation of crustal structure. Such artifacts are very harmful in a 4-D survey where anticipated temporal velocity variations may be smaller than those artifacts that leaks into crust and can be totally obscured by them.

Based on the ray path distribution, we believe the two low-velocity anomalies are the first-order artifacts caused by the seismic rays crossing the low-velocity rectangular water body. The high-velocity body, between the low velocity bodies, is the second-order artifact that was necessary to correct the traveltimes of the longer seismic rays that cross all three anomalous bodies.

2.2 Mesoscale Eddy

The size of mesoscale eddies known to occur in the ocean can be more than 50 km horizontally and around 0.6 km vertically (Ji and Lin, 2013; Huang et al., 2011). As a second test of the impact of assuming a uniform seawater velocity, we construct another synthetic model similar to what can be expected by taking account of mesoscale eddies (Fig. 4a). A rectangle-shaped anomaly of seismic velocity was set at 0.7 km depth in the seawater (the orange-colored rectangle in Fig. 4b) with a velocity departure of +20 m/s departure from the background 1 500 m/s. The sea floor is at a 2 km depth. The crust of our hypothetical model was assumed to be the 1-D seismic velocity model of South Yellow Sea which has a layer of low velocity sediment rock at the shallowest depths underlain by a basement layer with seismic velocity increasing to 6 km/s at 4.5 km depth (Zou et al., 2016).

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Figure 4. (a) "Hypothetical" background velocity model. (b) True velocity perturbation relative to the "hypothetical" background model. (c) Velocity perturbation inverted using the homogeneous seismic velocity of water. (d) Velocity perturbation constructed by simultaneous inversion of seismic velocities in the water and crust. The curve to the right of panel (a) represents the variation of 1-D background velocity along depth. The red and blue curves to the right of panels (b)–(d) represent the velocity perturbation along depth at the location 10 and 45 km, which are marked by the vertical dashed lines in cross sections. The absolute velocity is generated by the summation of the background velocity and the velocity perturbations.

In this experiment, to simulate errors caused by velocity anomalies in the water column, we produced first arrival times using the shortest path ray tracing method (Moser, 1991). To compute the synthetic data, we adopted a commonly used acquisition geometry in wide-angle seismic surveys, which included 19 OBSs' with a 5 km horizontal spacing and 109 sources shooting on sea surface with a spacing of 200 m. The acquisition geometry and the corresponding ray paths are shown in Fig. 5a.

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Figure 5. (a) Raypaths of OBS acquisition. The background color shows the seismic velocity perturbation. Stars: seismic sources. Triangles. OBSs. (b) The raypaths of an example OBS. The shots are sparsely marked to clearly show the raypaths.

In conventional tomographic inversion, the velocity of seawater is typically assumed to be a uniform 1 500 m/s throughout all iterations of the inversion. As shown in Fig. 4c, the resulting seismic velocity model has significant deviation from the 1-D hypothetical velocity model (Fig. 4b), especially beneath the edge of the eddy. The high (right) and low (left) velocity artifacts in Fig. 4c correlate to positions the high and low velocities of the seawater in the hypothetical model (Fig. 4b). The erroneous velocity anomalies in crust have values of about 20 m/s, similar to the velocity perturbations of the seawater in our hypothetical model (Fig. 4b). This test reinforces the conclusion that relatively small perturbations in seawater velocity will leak into the inverted crustal velocity when tomography is performed with an assumed uniform and constant water velocities.

3 STRATEGIES OF CONSTRUCTING SEISMIC VELOCITY MODEL

To suppress artifacts in the inverted crustal velocity model, such as those shown in Fig. 4c, we need to invert for the velocity structure of seawater as well as the crustal velocities in tomographic inversion. We will test two different strategies to mitigate errors in the inverted crustal velocities by correct seawater velocities. One strategy, called simultaneous inversion, inverts for the seawater and crustal velocities simultaneously. The second method first inverts for the seawater velocities and then invert for the crustal velocities. This second strategy is effectively a "layer-stripping inversion" (Bian and Yu, 2011).

3.1 Simultaneous Inversion

In this strategy of simultaneous inversion, all first arrivals including those of direct waves in seawater, refraction waves from sea floor and crustal interfaces are used. As shown in Fig. 4d, the velocity artifacts in the shallow crust of the tomographic model are significantly reduced as compared to the anomalies in the model assuming constant seawater velocities (Fig. 4c). While the magnitude of most crustal velocity anomalies was reduced when seawater velocities were included in the inversion (Fig. 4d), significant velocity anomalies are still present in the center of the model where there is a large horizontal change in the seismic velocity of seawater. These erroneous velocity anomalies at the center of the model are artifacts that result from poor resolution of the internal structure of seawater.

To understand the inversion results, we plot the seismic raypaths on the velocity perturbation profile for several shots recorded by a single OBS (Fig. 5b). The raypath segments within the seawater are nearly parallel with each other beneath the sources (at the surface) and have a very narrow range of angular coverage. The poor angular coverage in the raypaths through the seawater is mainly due to the strong velocity contrast between the seawater and shallow crust, which results in near vertical raypaths through the water column. These near vertical raypaths fail to provide sufficiently crossing raypaths necessary for the inversion to accurately model heterogeneous velocity anomalies in the seawater and crust at the same time.

In field OBS data, we can often, clearly identify the first-arrival waveforms through seawater in near-offset traces (Markris et al., 2012). Including such direct arrivals in the inversion for seawater velocity provide more diversity of raypaths than illustrated in Fig. 5 and may improve the accuracy of the models of seawater velocities. An inversion that includes these first arrivals will be particularly effective in the layer- stripping strategy.

3.2 Layer-Stripping Strategy

The layer-stripping strategy of inversion was designed to cope with the uneven resolution of tomographic inversion at different depth (Bian and Yu, 2011). Therefore, layer stripping should be effective in reducing artifacts of crustal velocity models due to anomalies in a marine environment, which contains a layer of low-velocity seawater on top. In layer-stripping inversion, the seawater velocity structure is modeled using the seismic phases that travel only in seawater and then these modeled seawater seismic velocities are fixed when inverting for the deeper, crustal velocity structure. Thus, determining the accuracy of the inverted seawater velocity is a key step in the success of the layer-stripping inversion.

To constrain seismic velocities in the seawater, we need the seismic raypaths to span the seawater body with sufficiently dense coverage. One simple method to increase the raypath coverage of the water body is to distribute sources and receivers both horizontally and vertically throughout the seawater body. However, marine seismic sources, such as air gun and spiker, may not be able to generate appropriate seismic waves in the high pressure environment of very deep water. Therefore, it is more common to place the seismic sources at the sea surface and receivers, such as OBS and vertical cable (VC), at multiple depth to record the direct waves that span the seawater volume, and hence, have the potential to image seismic velocity of seawater.

To facilitate a comparison between the methods using layer stripping and simultaneous inversion, we adopted the same OBSs and seismic source geometry as well as velocity models used in Fig. 4. We found that, when we use the first arrivals of the direct waves in seawater for this source-receiver geometry, the inverted seawater velocity model (Fig. 6b) has strong vertical and lateral velocity variations, but these velocity anomalies are significantly different from those of the hypothetical velocity model shown in Fig. 6a. To improve the resolution of the inversion for seawater velocities, we added ten VCs, each contains seven receivers with a 250 m vertical spacing. The horizontal distance between these VCs is 5 km.

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Figure 6. (a) True velocity of seawater. (b) The velocity model inverted using only first arrivals from the OBS data. (c) The velocity model from the inversion of both OBS and VC data. The dashed line marks the boarder of the high-velocity eddy. The vertical exaggeration is 12 times.

We find that the velocity model inverted from all first arrivals including the OBSs and the VCs (Fig. 6c) matches the hypothetical velocity model (Fig. 6a) more accurate than the model using only OBS data (Fig. 6b) but there are still flaws in both of the inverted models. The model inverted using only OBS data cannot recover the shape of the layer and has significant leakage of high velocities into neighboring regions. The model from the receiver array geometry consist of OBSs and VCs recovers the rectangular shape of the low velocity body relatively well but it maps the low-velocity anomaly to a depth that is about 0.25 km shallower than that in the hypothetical model.

The difference in the performance of the inversions that use OBS data from the inversion using the combined acquisition geometry can be explained by the analysis of raypath coverage (Fig. 7). The distribution of raypath in Fig. 7 suggests two possible factors that would improve the recovery of the seawater velocity anomalies when VCs data are combined with OBS data. First, the VCs have more sensors and higher raypath density than does the OBS acquisition system. Second, the VC acquisition system has wider angular coverage. The second factor is quite important for tomography, because wider angular coverage will help reduce artifacts and enhance the horizontal resolution of the inversion. More precisely constrained seawater velocity means less errors introduced into the inverted crustal velocity model. So, using the seawater model from the combined acquisition geometry should yield higher resolution in the velocity model when we invert for the crust velocity models.

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Figure 7. Raypath coverage. Top. OBS; Bottom. vertical cable (VC); Stars. seismic sources; Triangles. receivers.

The layer-stripping method in seismic tomography is applied by downward continuing the seismic sources from sea surface to the sea floor. This process is similar to the tomo-datuming that is used for onshore static corrections (Zhu et al., 1998). The contribution of errors in traveltimes due to errors of seawater heterogeneities can be determined by evaluating the accuracy of traveltimes at the datum, which is sea floor in our case. Fig. 8 shows the traveltime errors at the sea floor for different velocity models, which are calculated by subtracting the model traveltime from those estimated for the seawater velocity models. The traveltime errors from the homogeneous seawater velocity model, which can be more than 10 ms at wide offset, are much larger than those from the 2-D velocity models. The traveltime errors for the combined acquisition (red lines in Fig. 8) are less than those computed by using only OBS data (black lines in Fig. 8), especially at wide offset.

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Figure 8. Traveltime errors of example shot gathers (left: shot at 13-km distance; right: shot at 40-km distance) at the seafloor for the homogeneous seawater velocity model (dashed line) and the velocity models inverted by OBS (blue line) and OBS+VC (red line). Left and right panels are the results for shots at different locations, which are marked by arrows.

The artifacts in crustal velocity models due to the inaccurate seawater velocities can be qualitatively estimated by analyzing the magnitude of near-offset traveltime errors at datum, i.e., sea floor. The traveltime errors at the datum for the layer- stripping inversion are much smaller (1/2 on the left side and 1/7 on the right side) than those computed using a homogeneous water velocity model. These small values in traveltime errors from the layer-stripping method (less than 1 ms) are significantly smaller that than the residuals in typical traveltime tomography, and are not likely to cause observable artifacts in the tomographic crustal velocity profile. Therefore, smaller traveltime errors at the seafloor for the dual acquisition geometry should results smaller artifacts in the crustal velocity model for the inversion using the dual acquisition geometry.

4 DISCUSSION AND CONCLUSIONS

In deep marine environments, crustal seismic tomography using an assumed homogeneous seawater velocity model will generate artifacts in the tomographic solutions of crustal velocities. Although a simultaneous inversion of seismic velocity of seawater and crust may improve the recovery of crustal velocities, the internal velocity heterogeneity of the seawater can still produce some artifacts in the inverted crustal velocity model. We propose a layer-stripping strategy to solve this problem by first accurately constraining the velocity structure of the water layer. The acquisition geometry is another important factor influencing the accuracy of velocity model building. By using the first arrivals of seismic waves recorded by a combined OBS and VC acquisition system, the seismic tomography recovers the seawater velocity structure better than that by the OBS system alone.

To further improve the accuracy of the velocity model building of the seawater layer, several approaches deserve to be tested in future numerical tests and field-data applications. First, improving the regularization of tomography may be helpful to resolve the layer structure. Since the water velocity tends to have large-scale, layered (rather than flat) structures, we suggest adopting some types of layer-based regularizations in tomographic inversion, such as the deformable layer tomography (Zhou, 2006). With the addition of vertical cable (VC) sensors that penetrate the high-velocity eddy, the deformable layer tomography will recover the layered velocity structure with greater accuracy (Liu et al., 2010). Second, full waveform in version may resolve more internal details of the seawater velocity layering than the inversion of arrival times alone (Bian et al., 2015; Bornstein et al., 2013). Third, using additional but different seismic phases, such as sea-bottom reflections, multiples and refractions, may increase the ray coverage and hence the accuracy of the recovered velocity models. Finally, improved acquisition geometry, such as using an integrated marine acquisition system that includes streamers, OBSs and VCs, may perform better in resolving the lateral variation of the seawater velocity.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (No. 41230318), the Natural Science Foundation of Shandong Province (No. ZR2014DM006), the China Postdoctoral Science Foundation (No. 2015M582138), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education. The final publication is available at Springer via https://doi.org/10.1007/s12583-017-0816-7.


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