Finally, the phase delay tells the depth of an interface that caused P- ... analysis is a method based on ray-theory for a horizontally stratified earth ... the method of receiver function can be extended as a general ... objectives, extensive refraction or reflection wave ... phase delay of P-S converted waves arriving after the direct.
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Imaging underground structure using receiver function for P-S converted waves Subaru Tsujjimoto, Hitoshi Mikada*, and Kyosuke Onishi, Kyoto University, and Eiichi Asakawa, JGI,Inc. phase delay of P-S converted waves arriving after the direct P waves. Once the phase information of the receiver function is obtained, then one can estimate the depth of the velocity interface. This analysis has advantage in the estimation of the depth of velocity interface using a simple deconvolution procedure for two components of seismograms when P-to-S converted waves are generated at the interface. However, in the analysis of earthquake it is difficult to keep high S/N ratio and to collect data sufficiently from earthquakes that occur without human control. We tried to expand the existing receiver function analysis to a wave-theoretical imaging tool for buried interfaces that cause P-SV conversion. The introduction of receiver-arrays and migration techniques that are in practice in the industry has turned out an indispensable procedure in this modification. Finally, we succeeded to apply the receiver function to P-SV mode converted from refracted compressional waves. After these modifications, the method has become an imaging tool that utilizes not only earthquakes but also artificially generated seismic waves in reflection and refraction surveys.
Summary Receiver function analysis is known as a method frequently practiced to utilize both vertical and horizontal components of seismic records to reveal subsurface structure using earthquake signals in natural seismology. In the receiver function analysis, a receiver function is estimated by the deconvolution of P-SV horizontal record with the vertical component. This receiver function is used to measure the phase delay of P-SV converted against P-P waves. Finally, the phase delay tells the depth of an interface that caused PSV conversion. It is obvious that the receiver function analysis is a method based on ray-theory for a horizontally stratified earth model. We tried to expand the methodology to an imaging tool to utilize the advantage of the receiver function analysis to use both P and SV waves recorded by tri-component geophones. Also, our modification makes it possible to use not only earthquake records but also artificial signals generated by active sources. We found that the method of receiver function can be extended as a general exploration method for imaging underground geological or geophysical interfaces that causing P-SV mode conversion in traveling seismic waves.
Receiver Function Analysis Introduction Teleseimic waves generated from far or deep earthquakes propagate through an interface before we observe them on seismometers (Figure 1).
The estimation of macroscale sub-seafloor crustal structure is required to reveal the tectonic development history of lithosphere. In the case of places of active-tectonics, estimating oceanic crustal structure is an effective means for clarifying the regional-scale tectonics and for disaster mitigation from earthquakes and tsunamis. For these objectives, extensive refraction or reflection wave explorations using artificial sources and traveltime tomography have been applied (Tsujimoto and Mikada, 2008) using OBS (Ocean Bottom Seismometer). The exploration use multi-component (x,y,z components and pressure) seismometers, but existing refraction data processing method tends to analyze only compressional wave or vertical component of seismometers for the estimation of crustal structure. Shear wave or horizontal component of seismograms is analyzed only for determine the Vp-Vs ratio or other values after structure analysis. Hence, there is a possibility to use shear wave or horizontal component of seismograms to estimate more precisely the thickness of oceanic crust. Receiver function is frequently used to analyze the upper structure of mantle as a method estimating the thickness of oceanic crust (Langston, 1979). This analysis uses both vertical and horizontal components of seismograms from far earthquakes (teleseismic events) and deconvolves the horizontal with the vertical component to estimate the
The received data contain P-to-S (P-S) and S-to-P (S-P) converted waves at the surface. The first arrival is the direct
Figure 1: Direct P wave and P-S converted waves. Due to the difference in phase velocity, converted-S is generated at the difference location from P-P conversion point. Receiver function locates the P-S conversion point as shown in Figure 2.
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Imaging underground structure using receiver function
Figure 2: Receiver function: Direct P wave and later S waves include P-S converted wave can be observed. Small p’s indicate refracted P at the interface in Figure 1. Ph and Sh denote P and S waves reflected at the surface (Tsujimoto and Mikada, 2008). The phase delay between Direct P and Ps is used to estimate the depth of the interface.
Figure 4: Horizontal component of Seismogram from sea surface shot: parabolic direct water wave in near field and refracted wave through Moho as first arrival in far field can be observed
P. P-SV waves converted at an underground interface arrive following the first arrival. Receiver function analysis is a method of estimating the depth of velocity interfaces (velocity discontinuity) from the delay time of Ps wave to the direct P wave (Langston, 1979; Figure 2). after deconvolving the horizontal with the vertical component data. An example of the deconvolution applied to seismic records is shown in Figure 2.
Model and Results We applied the receiver function analysis to a realistic model that has water, sediment, crust and upper mantle layers (Figure 3). An hundred and twenty receivers spaced every 1km are aligned on the seafloor. Earthquake signals are realized as arrays of point sources that generate plane waves, while active sources are located along the sea surface as shown in Figure 3. Seismograms of each component are obtained with FDM. Time grid interval is 0.0005s, grid width is 10m and source type is a 10Hz Ricker wavelet. Figure 4 shows horizontal component of seismogram calculated from a shot at a distance of 20km from the left end of the model. We observe direct water arrivals of a chevron pattern centered at the shot location. Refracted wave arrivals are seen outside of the chevron pattern for large offset. We applied the receiver function analysis to the refraction waves. Receiver function for every location of receiver is then calculated using both vertical and horizontal components of the simulated wavefields. Conventional receiver function analysis estimates the phase delay of P-S converted waves against the first arrivals, but we aligned receiver functions side by side to find underground velocity interfaces that cause P-S conversions in our new processing method. Figure 5 depicts such receiver function panel for the structure shown in Figure 3 using a surface shot record. Figure 6 demonstrates a similar receiver functions to upcoming place wave incidence (earthquake source). As easily observed, underground interface of P-S conversions are imaged for both source locations. Here, it is
Figure 3: A realistic oceanic crust model used in the simulation. OBS’es are aligned on the seafloor. The crust is composed of two horizontal layers. Upper mantle is expressed by a half-space. A constant water depth of 4 km is assumed. Total 120 receivers are aligned on the seafloor spaced every 1km. Every deep sourced seismic signal is simulated by a linearly aligned set of point sources while each artificial source is expressed by a surface point source on the sea surface.
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Imaging underground structure using receiver function
Figure 7: Schematic relationship between true and apparent and true converting point for shear converted waves from refracted P waves.
Figure 5: Receiver functions obtained for a shot located at the sea surface. Both sedimentary and deep interfaces are imaged. Red line indicates a true time section for the structure shown in Figure 3. demonstrated that the receiver function analysis has become an imaging tool using P-S converted waves. Time migration of refraction wave Both figures 5 and 6 indicate that the locations of underground velocity interfaces are imaged at slightly different locations from the true locations. As shown in Figure 7, the misfit of refraction locations takes place due to imaging the conversion points to apparent locations located just beneath the receiver locations as for slanted reflectors in reflection surveys. Therefore, apparent P-S
Figure 8: Iterative two-step procedure for the migration of events for each step of time. Apparent or false location of each P-S conversion of receiver functions moves to the true conversion point.
Figure 9: Result of time migration to receiver functions for data obtained for a surface shot shown in Figure 5. Red lines indicate the true locations of P-S conversion for refracted P waves.
Figure 6. Receiver functions obtained for an upcoming place wave incidence to the structure. Red line indicates a true time section for the structure shown in Figure 3.
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Imaging underground structure using receiver function
converting interfaces need to be migrated to the true locations using seismic migration techniques. In this section the time migration is conducted to the receiver function data of refraction wave. For the migration of P-S conversion interfaces, we employed F-K migration using a floating datum. This processing is composed of the iteration of two-step procedure; (1) datum shift and (2) back propagation as for seismic migration to reflection seismic data (Figure 8). Figure 9 depicts the result of time migration for data shown in Figure 5. The receiver functions for refracted compressional P waves are now converted to a migrated image. Depth Imaging using F-K migration Figure 10: Final image after the summation for receiver functions for 10 different seismic signals incident to the structure shown in Figure 3. The number and the location of surface shots or the incident angle of upcoming plane waves are indicated in the text.
The final step of the processing is the depth migration to get a subsurface structure image from receiver functions. We employed a method using phase-shift operator proposed by Gazdag (1978) and time-to-depth conversion method proposed by Stolt (1978) to accommodate shear wave velocity since this study deals the seismic migration of data to image P-S converted waves.
seismic data. Receiver function analysis is surely one of the methods to combine both active and passive seismic surveys.
After the application of depth imaging for each shot and for each earthquake, we sum up all depth-imaged receiver functions. The result of the summation for 10 surface shots (5 each for both side spaced every 5 km), and for 10 upcoming plane waves (incident angles of -18.5, -14.0, -9.5, -4.8, -2.4, 2.4, 4.8, 9.5, 14.0, 18.4 degrees to the vertical direction) is shown in Figure 10. We expect that the summation enhance the signal-to-noise ratio of the migrated image. Stacking enables the imaging to decrease noises and increase the accuracy of inversion.
Acknowledgement This work was supported by Japan Oil, Gas and Metals National Corporation.
Conclusion We succeeded to image the velocity discontinuity of the simulation model using time migration of receiver functions for both refracted and transmitted waves into target structure through wave-theoretical depth imaging. The receiver function analysis has been used as a tool to explore target subsurface structure using ray-theoretical estimation of the locations of deep velocity interface causing P-S conversion. This study tried to apply receiver function analysis to active refraction survey data and to passive seismic imaging data at the same time. Our study proved that the receiver function analysis could be extended to an imaging tool using a wave-theoretical approach as for reflection seismic data. The introduction of the present approach would lead one to the utilization of not only active source seismic methods such as reflection or refraction surveys but also passive
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EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2009 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Ammon, C. J., G. E. Randall, and G. Zandt, 1990, On the nonuniqueness of receiver function inversions: Journal of Geophysical Research, 95, 15303–15318. Gazdag, J., 1978, Wave-equation migration by phase shift: Geophysics, 43, doi:10.1190/1.1440899. Langston, C.A., 1979, Structure under Mount Rainier, Washington, inferred from teleseismic body waves: Journal of Geophysical Research, 84, 4749–4762. Stolt, R. H., 1978, Migration by Fourier transform: Geophysics, 43, doi:10.1190/1.1440826. Tsujimoto, S., and H. Mikada, 2008, Estimation of oceanic crustal structure using receiver function: OCEANS 2008 - MTS/IEEE Kobe Techno-Ocean, doi:10.1109/OCEANSKOBE.2008.4531068.
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