Application of full waveform inversion to OBS data acquired in an active-source seismic survey: a synthetic test for the 2020 Bungo-channel profiles

Jensen DeGrande1,2 and Kimihiro Mochizuki1

1Earthquake Research Institute, University of Tokyo, Japan, 2Texas A&M University – Corpus Christi

Abstract

Slow earthquakes occur along the boundary of megathrust earthquakes, which makes the interactions between slow earthquakes and megathrust earthquakes of particular interest in Japan. Specifically, the Bungo-channel has been an area of interest because of the amount of shallow tremor activity occurring in the region. In 2020, an active seismic survey and the deployment of new Ocean Bottom Seismometers (OBS) profiles are planned for the area. As OBS units are limited in number, it is important to determine the most efficient placement of these units for the upcoming survey. The most efficient placement is defined as one that allows obtainable accuracy of the visualization of the subsurface structure, as well as the subducting plate’s topography, while using the least amount of physical resources, OBS units. This can be related to the overall spacing interval of units, variation in placement of units, profile spatial distribution/angles along the area interest, and number of units used for each profile.

This study takes an existing profile from the study area and executes various synthetic tests with changes in OBS locations to compare the resolutions of the visualized subsurface structure using waveform inversion. Waveform inversion techniques are a fairly new method providing higher resolution than previously used methods. This synthetic test will help determine the approximate profile of the 100 OBS units to be deployed in 2020 so that the subsurface structure of the new profile can be visualized in a similar method.

The optimal profiles for the upcoming deployment will be described along with a comparison of the results from various synthetic tests of OBS placement of an existing profile within the area of study. As more is learned about the subsurface structure and the subducting plate’s topography, more conclusions can be drawn between slow earthquakes and megathrust earthquakes related to the physical properties of the plate interface, the effect of subducting seamounts, and the overall relationship between these two types of earthquakes. By knowing more about the relationship, the effect of slow earthquakes on megathrust earthquakes can be studied in the sense of whether slow earthquakes are a cause or predecessor of megathrust earthquakes. This could aid the field of megathrust earthquakes and increase efforts of disaster mitigation in the future. 1. Introduction

1.1. Slow Earthquakes Slow earthquakes are a new phenomenon and a particular interest in Japan

because they occur along the boundary of megathrust earthquakes. Seismology, in general, is a widely studied field across the country due to its geographic location in relation to plate boundaries. The spatial relationship between slow and megathrust earthquakes was first identified in Japan and continues to be the best studied in Japan. The family of slow earthquakes consists of tectonic tremors, long-term / short-term slow-slip events, and very low-frequency earthquakes, each of which has unique

qualities that differ from one another and megathrust earthquakes. As more is learned about the field of slow earthquakes, more relationships can be understood and concluded between slow and megathrust earthquakes to relate the physical dynamics between the two.

Figure 1. Diagram showing subduction zone dynamics and the location of megathrust

earthquakes and slow earthquakes (transition zones). (Obara and Kato, 2018) 1.2. Active Seismic Surveys

This study uses the data acquired through wide angle active source seismic survey. Active source seismic surveys are one way to obtain seismic data through simulation and used for learning more about the plate interface. The second method is passive source which utilizes natural regular earthquakes as seismic sources to study the structure and the earthquake generation mechanisms. Resolution of structure obtained by this method is, however, much more coarse. In active source seismic surveys, Ocean Bottom Seismometers (OBSs) on the seafloor of the study area collect the data from the survey. The data obtained by the OBSs will be discussed in further detail in a later section. During active source seismic survey, a research cruise fires airgun shots to propagate energy down to the OBSs and through the subsurface structure. The OBSs record those bursts of energies as they travel through the medium, recording aspects such as travel time, amplitude, and phase. The data can then be used to obtain the subsurface structure represented by elastic properties such as seismic velocities and density beneath those OBSs by methods of travel time inversion or waveform inversion to learn more about the plate interface and the subduction dynamics in the area (refer to Figure 1. for a typical subduction zone representation).

1.3. 2020 Bungo – Channel Profiles The study area for this project was the Bungo-channel region off the coast of

southwest Japan in the Kyushu Peninsula.

Figure 2. Google Maps satellite imagery of Bungo channel in reference to Japan

Specifically, the Bungo-channel was selected as the main study area because

various types of slow earthquakes, ranging from a large amount of shallow tremor

activity (e.g. Yamashita et al., 2015) to deep long-term slow slip events, (e.g. Hirose and Obara, 2005) occur in the region. Such along-depth variation of slow earthquakes can be considered as manifestation of changes in frictional properties along the plate interface.

Figure 3. Geographic representation of variety of slow earthquakes in Bungo Channel area.

(modified from Obara and Kato, 2018)

Figure 4. Shallow tremor activity around Bungo Channel (Yamashita et al., 2015)

In order to reveal structural factors that control such frictional properties, an

active-source wide-angle reflection/refraction seismic survey deploying Ocean Bottom Seismometers (OBS) is planned for the area in 2020. The goal of this study is to image the subsurface structure including the topography of the subducting plate using synthetic data and to determine the most efficient OBS profile for the upcoming 2020 deployment. The motivations for this project include applying new techniques to existing data to confirm an improvement in resolution, developing a further understanding of the physical properties of the plate interface, and understanding the spatiotemporal relationship between slow slip events and megathrust earthquakes.

2. Data

2.1. OBS Data As mentioned, Ocean Bottom Seismometers (OBS) have been deployed in

various regions off the Japan coast to track the seismic activity occurring between the

oceanic plates (Pacific Plate and Philippine Sea Plate) and the continental plates (Eurasian Plate and North American Plate) of the region. These units contain a variety of equipment to record and store seismic-related data in the area. There are three sizes of OBSs, each of which has a seismometer that can read a specific frequency. The deployment of certain type of OBSs depends on the area in which they are deployed and the purpose of their testing. For the synthetic tests of this study, OBS data from KR08 cruise using R/V Kairei was used to understand the applications of waveform inversion in creating a high-resolution seismic velocity structure.

2.2. Seismic Velocity Structures Seismic velocity structures are used in both of the methodologies discussed in

the next section. Velocity structures are theoretical models based on general knowledge of the subsurface structure of oceanic layers and previously collected active source seismic data results. From current knowledge, the general structure is as follows: Ocean Basin (seawater): 1.50 km/s; Sediments: 1.65 km/s; Basalt: 5.00 km/s; Gabbro (cumulates): 6.80 km/s; and Peridotite (mantle rocks): 8.15km/s.

For the synthetic tests, a velocity structure for a profile in the Bungo channel

area from a previous survey was used (HY03). This data was obtained from a profile with 5 km OBS spacing interval.

Figure 5. Example of layered velocity structure

P-wave velocity (m

/s)

Figure 6 (above). Current velocity structure for the profile to be used in the synthetic tests Figure 7 (right). Geographic locations of existing profiles in Bungo Channel, including HY03

3. Methods 3.1. Travel Time Inversion

Travel time inversion was the first method implemented as it is a conventional method that uses extracted information (travel time), has easy computation methods, and a fast and stable convergence. However, travel time inversion was not specifically applied to the Bungo channel region due to time constraints in the research project time frame. Travel time inversion was applied to a previously collected set of data and the process was examined in order to understand the basic concepts of inversion. The outputs of the travel time inversion were examined and considered in relation to waveform inversion.

For travel time inversion, a general velocity structure is given, and the goal is to refine that velocity structure based on the travel time information between the OBSs and airgun shots collected during an active source seismic survey. The figures on the left side below show the data collected during the survey while the figures on the right show the evolution of the velocity structure as travel times from observed data are applied. Figure 9 is a typical, general representation of the subsurface structure beneath oceanic plates, and the yellow triangles on the surface show the locations of the OBSs in the study site. The OBS data shows the reflections and the first arrival travel times, typically the “pick” used to refine the velocity structure (represented by the red line on Figure 8), while the yellow line shown on Figure 10 and Figure 12 show the calculated travel times based on the initial velocity structure. As shown in Figure 10, the red line (observed travel time) and the yellow line (calculated travel time) do not match. The goal of travel time inversion is to make the calculated data match the observed data by adjusting the velocity structure by small increments. This will give the velocity structure for the observed data, and thus, the subsurface structure of the area. Figure 12 shows the observed and calculated data matching, and Figure 13 shows the updated velocity structure based on the observed data. Again, this was done by incrementally changing the initial velocity structure based on the observed data.

Figure 11. Calculated ray paths, travel times, to be used in inversion process based on initial model

Figure 8. Initial pick from OBS data Figure 9. Initial velocity model

Figure 10. Observed (red) and calculated (yellow) travel times

As travel time inversion only uses extracted information for ease of computation, the resolution of the output velocity structure is not high enough to understand in detail relationships between structure and generation mechanisms of various types of earthquakes. The output velocity structure is a smoothed model, there are no definite definitions of the velocity boundaries between the interfaces, which makes a perfect input velocity structure for waveform inversion. It was essential to understand the step-by-step process of travel time inversion in depth before moving on to waveform inversion since waveform inversion is a more advanced method that provides higher resolution but is computationally much expensive, requires more information including travel time, amplitude, and phase, and, requires a better initial model as input.

3.2. Waveform Inversion Waveform inversion uses a similar process: taking an initial model and using

collected data to refine the structure and improve the overall resolution. However, as mentioned, the input model for waveform inversion must be slightly more refined than the model used as input for travel time inversion. Therefore, the output for travel time inversion is an ideal input for waveform inversion. For the synthetic test, a theoretical output from a travel time inversion process (a smoothed model) will be used as input and refined to show the definition in the boundaries between each velocity layer, which represents the difference in physical properties of the layers in the structure.

The mathematical calculations behind waveform inversion are related to forward modeling and inversion. For this project, the main focus was inversion as this is only a synthetic test and a velocity structure for the region already exists from previous active seismic survey imaging. Through these calculations, the residuals between the initial model and the true model will be calculated with each iteration of waveform inversion. With each iteration, the residuals will be reduced by a calculated gradient update in an effort to match the initial model to the synthetic true model that has been provided. The gradient update will be determined based on the values of the initial model, true model, and the differences between the two in an effort to update in small increments to increase accuracy.

For the calculations, Madagascar Seismic was used. In addition, various pre-processing methods were involved to set up the model space, generate the synthetic source and receiver locations for the testing, selecting frequency parameters, and application of refining tasks such as masks and wave number filters. The model space for the velocity structure was a grid with two types of padding to absorb the reflections and reduce interference that could appear in the output structure. These

Figure 12. OBS data after inversion Figure 13. Output model from travel time inversion

buffers used extrapolation of the outer values. The buffer dimension was set at 25 grid spaces, and the origin (ox,oz) was set at a value that would allow an additional buffer between the first source/receiver location. The next step was to generate the source and receiver locations for the synthetic tests based on parameters that could be ideal in creating the best resolutions in the output model. In actuality, the OBSs are the receivers while the airgun shots are the sources, but in this study, reciprocity was used to decrease computational costs since the calculations run from source to receiver, and there will always be more airgun shots (sources) than OBSs (receivers). This means the sources were the receivers and vice versa, so the OBS locations were stored in “source” files, while the airgun shots were stored in “receiver” files. To generate the locations of each of these, a script was written to automate the process of initially placing an OBS or shot at the beginning of the profile, and then an iteration process was executed to add the desired spacing interval until the maximum x-value (horizontal length of profile) was reached. This process was used to generate the x-value for both the sources (OBSs) and receivers (airgun shots). As for the z-value (depth), the OBS locations are theoretically supposed to be located on the seafloor, so previously collected bathymetric data was used to determine the z-value for each previously calculated x-value. Airgun shots are typically executed at 10m below the seawater’s surface, so this was set as the z-value for each x-value.

In addition, to clarify the resolution, masks and wave number filters were applied to the final output of the velocity structure. The mask targeted artifacts in the water that create noise and reflections. By applying the mask, the noise and reflections from the interaction of the airgun shot with the seawater were reduced enough to clarify the boundary between seawater and the first subsurface layer. The wave number filter targeted the vertical oscillations at the boundary between seawater and the first subsurface layer. These oscillations obscured the definite boundary between the two layers and causes further noise within the model. By applying the mask and the filter, the noise from seawater reflections and other distractions was reduced significantly to clarify the overall image of the subsurface structure.

Figure 14 and 15. Figure 14 (left) shows the update (change between true and start) before the mask and filter. Figure 15 (right) shows after the mask and filter.

As this was a synthetic test and a velocity structure with definite boundaries

between layers already exists, the existing model was smoothed, and waveform inversion was used to refine the smoothed model (initial) to obtain the true model (output). The update to reach the true model from the starting model can be represented by the following:

Vp.difference = Vp.true – Vp.start

4. Results 4.1. Waveform Inversion for equivalent 1-km spacing

After running waveform inversion for 5 iterations, the following represents the calculated update that should be applied to the starting model to reach the true model. The true update that needs to be applied, represented by the manually calculated difference between the true model and the starting model, is also displayed so that a comparison can be made between the two. The following are the results of 5 iterations:

Inversion after 5 iterations: True:

Figure 16. True (existing) model Figure 17. Starting (smoothed) model

Figure 18. Difference between true and starting model

Figure 19. Figure 20

The following show the results of the update after running 10 iterations of the waveform inversion process. Again, the true update is displayed for comparison purposes:

The following show the results of the update after running 15 iterations of the

waveform inversion process:

5. Discussion

5.1. Other Possible Configurations Other configurations for the upcoming profile can be tested in a similar way.

The next test in the future includes using a 2-km spacing interval of OBSs, which will use half the number of the OBSs for one profile. As mentioned, OBSs are limited in supply, so the less that are used, while still obtaining accurate results, the better. In addition, if half of the allocated OBSs are only used for one profile, there is the possibility of an additional second profile in the study area. Depending on the existing profiles in the area, this could be a profile placed parallel to the initial one or it could be a profile placed perpendicularly to create a cross section in that area to understand the geometry of the plate interface.

There is also the possibility of varying the spacing interval based on areas of interest. Say there is a subducting seamount that researchers would like better resolutions of in order to determine its effect on the subduction zone. For this, the OBSs could be spaced at 2-km for the majority of the profile but placed in a denser distribution in the area of interest. This is one theoretical example to explain the possibility of variation in interval spacing.

Figure 24.Figure 23.

Figure 21.

Inversion after 15 iterations:

Inversion after 10 iterations: True:

True:

Figure 22.

6. Conclusion

The application of both travel time inversion and waveform inversion were essential to this study. As travel time inversion is a conventional method, it was fundamental to understand the details and extent of this method before exploring newer methods such as waveform inversion. It was also important to understand the differences between the two and how one can help the other. As an initial step in the synthetic test, we generated a synthetic dataset with 1-km interval spacing along the length of the HY03 profile (Nakanishi et al. 2018, KR08 cruise using R/V Kairei) and confirmed that waveform inversion can successfully reproduce the original 2D heterogeneous velocity model even when starting from a smoothly varying velocity model.

Due to the limited ship-time and OBSs available for the survey, it is important to optimize the placement of the OBSs and airgun shots. The most efficient design should allow the highest accuracy and resolution in the waveform-inversion images of the subsurface structure, including the subducting plate’s topography, while using the least amount of acquisition resources. As mentioned in the previous section, coarser OBS interval are being explored and examined in terms of output velocity structure resolution. Other acquisition geometries will be examined in the search for those that best resolves the plate interface. These synthetic tests will contribute to determining the wide-angle-survey profiles using 100 OBSs planned in 2020, so that the detailed subsurface structure of the new profile can be obtained by waveform inversion.

The new profile/profiles to be deployed will serve as tools to further understand the effect of slow earthquakes on megathrust earthquakes. It will provide more knowledge in the sense of whether slow earthquakes are a cause or predecessor of megathrust earthquakes, which could aid the field of megathrust earthquakes and increase efforts of disaster mitigation in the future.

Acknowledgements I would like to express my gratitude to Prof. Kimihiro Mochizuki for providing me

with the opportunity to learn so much about the field of seismology and experience research at the Earthquake Research Institute at the University of Tokyo. Almost every day, Prof. Mochizuki would take time out of his own busy schedule to teach me about the general science of earthquakes and the science of slow earthquakes and to ensure I was happy with the project. He was always patient with me, as I was new to the field and had much to learn, and for that I am truly grateful because I had the opportunity to discover my own excitement for slow earthquakes.

I really enjoyed my time at the Earthquake Research Institute because it was such a welcoming environment, and I truly enjoyed my time at work, which was why I was there so often. My supporter, Lina Yamaya, always made me feel welcome, asked if I needed help frequently, invited me to social gatherings with other graduate students, and overall supported me throughout the program.

I would also like to thank Dr. Rie Nakata for teaching me about waveform inversion and spending time with me to explain a wonderful code that she has written. She was a great source for advice through every step of the project and greatly contributed to my success during the UTRIP program.

I would like to extend thanks to the International Office at the Earthquake Research Institute for organizing and including the UTRIP students in fun activities for all

internship programs, including an unforgettable trip to Mt. Fuji. It was really nice to be involved and meet other international and graduate students at ERI.

Last but not least, I would like to thank the International Liaison Office, the Graduate School of Science at the University of Tokyo, and everyone involved in planning the UTRIP program for making this opportunity possible. The research portion of this program was extremely valuable, but the meaningful cultural activities and field trips that were planned made it even more valuable to my future and overall insight into the world. I am extremely grateful for being selected for this program and everything it has brought into my life. References Hirose and Obara, 2005. “Repeating short- and long-term slow slip events with deep

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