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Bulletin of the Seismological Society of America, Vol. 94, No. 3, pp. 988–1001, June 2004

Modeling the Jiyang Depression, Northern China, Using a Wave-Field

Extrapolation Finite-Difference Method and Waveform Inversion

by Liang Zhao, Tianyu Zheng, and Weiwei Xu

Abstract We study the 2D seismic velocity structure of the south edge of theJiyang depression, in the Bohai Bay Basin, northern China, using recordings from28 broadband seismic stations and a method combining an shear horizontal (SH)forward synthetic calculation and waveform inversion. The forward synthetic cal-culations are performed by a finite-difference (FD) method, with its computationaldomain localized in the basin area and input motions at the base of the model ex-trapolated from the displacement recorded at a nearby hard-rock station. In waveforminversion, the shapes of the strata are varied to search for a best-fitting model basedon the fit of relative timing, amplitude, and phase of the synthetics to the seismicdata. Numerical experiments using synthetic data and test models demonstrate thevalidity, resolution, and sensitivity of our technique. With this technique, we obtaintwo cross sections of the south edge of the Jiyang depression, the Bohai Bay Basin,northern China. The waveform inversions using the seismic data from four teleseis-mic events show consistent results for both cross sections. Those inversion resultsare also in agreement with a geological cross section available in the region. Ourmodels estimate that the south edge of the Jiyang depression is juxtaposed againstthe Luxi uplift and its structures. Our inversion results also reveal a blind fault inthe region and features suggesting major extensions in Paleogene.

Introduction

Basin-edge structure plays a fundamental role in under-standing the formation of sedimentary basins and strongground motions in the basin. In addition, basement and olderstrata become increasingly commercially important becausehydrocarbon production from basement and buried hill hasbeen reported, for example, from a fractured basement innorthern China (Yang et al., 1999). So it is of great impor-tance to investigate the shape of basins resting against largemountains and the configuration of the basin edge.

Many seismic methods, such as reflection methods andrefraction methods, have been proposed to study basin-edgestructures. The reflection and refraction methods using ac-tive sources have extensive applications in the explorationindustry, but it is expensive to apply them. Therefore meth-ods using natural earthquakes (e.g., Scrivner and Helmber-ger, 1994; Hauksson and Hasse, 1997) attract attention fortheir economy of acquiring data, especially with the densedistribution of portable stations inside a basin. The NorthernChina Interior Structure Project (NCISP), which is operatedby the Institute of Geology and Geophysics, Chinese Acad-emy of Science, deployed dense portable stations traversingthe Baohai Bay Basin, northern China, from September 2000to March 2003. The dense seismic coverage provides us witha good opportunity to improve our understanding of the

south edge of the Bohai Bay Basin. However, it is difficultto use seismic data recorded at close distances because ofthe lack of regional earthquakes in our target region. For-tunately, we acquired a large amount of high-quality tele-seismic data sampling across the basin edge. It encouragesus to search for a new way to estimate the basin-edge struc-ture by using these teleseismic data. In this article, we de-velop a technique to estimate the basin-edge structure byusing broadband teleseismic data and to apply this techniqueto study the edge and velocity structure of the Jiyang de-pression, northern China, with additional constraints fromgeology and well-logging data. We discuss the techniqueand modeling results in the next sections.

Seismic Technique Combining Forward WaveformCalculation and Inversion

Our technique consists of forward synthetic FD calcu-lations and waveform and travel-time inversions. The for-ward method consists of extrapolating the wave field to theinterface beneath the FD region and FD calculating in theregion involving the basin. The observed shear horizontal(SH) wave field at a hard-rock site is extrapolated to theexcitation points along the interface between the homoge-

Modeling the Jiyang Depression Using a Wave-Field Extrapolation Finite-Difference Method and Waveform Inversion 989

Figure 1. (a) Locations of portable seismic sta-tions (black triangles) deployed in the Jiyang depres-sion and the southern Bohai Bay Basin, along withtopography in the region. The studied region (blacksquare) is also plotted in the inset. (b) Observedtangential displacement records for event 2001:55:7:23:48. Stations from 21JZZS to 87SZZ were de-ployed at hard-rock sites outside the basin, whereasstations from 95QDZ to 143SLX were inside the ba-sin. Note that the waveforms recorded at the hard-rock sites are very similar, but those recorded insidethe basin are noticeably different.

neous media and the FD region, and synthetics are calculatedby the FD method (e.g., Virieux, 1984). The inversionmethod searches a best-fitting basin model by waveform andtravel-time inversion until the model synthetics fit the databest. The advantages of this approach are that (1) it is ap-plicable with teleseismic data that are very abundant and (2)source parameters and path effects are not necessary in ex-trapolating incident wave field as the excitation of the FDcalculation. The waveform modeling is done for the SH sys-tem because the P-SV waveforms are more complicated toanalyze because of the conversions between P and S energyat basin interfaces.

Forward Waveform Calculations

Several approaches have been proposed to simulate thewave propagation in the basin or other heterogeneous mediaat large epicentral distances. Both numerical and analyticalmethods have difficulties in handling this type of wave prop-agation (Wen and Helmberger, 1998). The hybrid methods(e.g., Wen, 2002), which combine the advantages of bothnumerical and analytical methods, find broad applicationswherever all-in-one modeling of source, path, and site ef-fects is too expensive (e.g., Ivo et al., 2002). However, withhybrid methods, source parameters and path effects are re-quired to generate generalized ray theory (GRT) solutionsthat are used as the excitation of FD calculation. Conse-quently the accuracy of the modeling results depends on notonly the accuracy of the local model but also on the sourceparameters and path effects used in the calculation. This in-creases the computational time and difficulty of modelingfor teleseismic events. The essence of hybrid methods is thatthey can separate the various effects discussed previouslyinto individual operators (Wen and Helmberger, 1997). Fol-lowing this idea, when we have seismic waveforms observedboth at hard-rock sites and inside the basin, we can reason-ably assume that the path effects from the earthquake sourceto the base of the basin are similar to the path effects to thehard-rock stations. Therefore, the “basin site response” canbe considered as the most significant cause of the waveformdifference between stations outside and inside the basin, andwe can attribute their waveform difference mainly to a basinoperator. The validity of this assumption can be verifiedwith the observations. Figure 1b shows that the tangentialdisplacements recorded at hard-rock stations (21JZZS to88NWZ, Fig. 1a) are in excellent agreement with each other,whereas those recorded inside the basin (stations from95QDZ to 144LJZS) are evidently different. Based on thisunderstanding, we develop a wave-field extrapolation FDmethod using the data at hard-rock sites as input motionsinstead of GRT solutions for FD calculation.

The SH wave-propagation problem is illustrated in Fig-ure 2. We restrict our consideration to in-plane propagationof the SH wave. If the stations are sufficiently far away fromthe source, we can approximate the SH wave as a plane wavewith a near-vertical incidence. For the plane wave, Cartesiancoordinates are chosen as in Figure 2, with x axis taken in

990 L. Zhao, T. Zheng, and W. Xu

Figure 2. Schematic illustration of the principleof the SH wave-field extrapolation FD method. Thebasin is confined inside a rectangle, where the FDmethod is applied. When a hard rock site station P issufficiently far away from the source, the SH waverecorded at P can be extrapolated to the bottom in-terface of the FD region as input motions in the FDcalculations. The solid triangle indicates the positionof hard-rock stations; P�1, P�2, P�3, and so on indicatethe points at the bottom of the FD region; and thedashed lines indicate the grid lines of FD schemati-cally.

Figure 3. Numerical simulations checking the va-lidity of the SH wave-field extrapolation FD method.(a) A simple two-layer homogeneous model; the seis-mic velocity structures in the FD region are the sameas in the surrounding region. The solid triangles rep-resent seismic stations, and the circles indicate thecontrol depth points that parameterize the FD model.(b) Comparisons of tangential displacement records(black solid traces) from event 2001:55:7:23:48 andsynthetic waveform (dashed traces) using the homo-geneous model and extrapolated wave field as inputmotions. The extrapolated data were recorded at ahard-rock station, 21JZZS; the FD model starts at sta-tion 21JZZS (lateral distance � 0 km).

the direction of the horizontal slowness component. Sup-posing that the SH wave travels as a plane wave, its displace-ment Vinc in the frequency domain (Aki and Richards, 1980)is given by

sin j cos jincV � A exp ix x � z � t , (1)� � ��b b

where A is a constant, j is the incidence angle, b is the shear-wave velocity, x is the frequency, and (sin j)/b and (cos j)/b the horizontal and vertical slowness, respectively.

For the SH wave, the reflection coefficients on the freesurface are equal to 1, and the tangential displacement onthe free surface at position g is two times that of the incidentSH wave. Then, for SH-wave propagating in homogeneousmedium, the tangential component of displacement recordedat hard-rock sites can be extrapolated to the bottom interfaceof the FD region. The extrapolated wave field is given as

V(n, t) � V(g; t � s)/2, (2)

where s is retarded time. The IASP91 global model (Kennettand Engdahl, 1991) is used to calculate the retarded time.

Following these procedures, the record observed at ahard-rock site P is extrapolated to the interface grid pointsP�1, P�2, P�3, and so on of the FD region as the input motionsin FD calculations.

In FD calculation, the basin cross-sectional model vectoris velocity as a function of position m(x) � v(x, z), and it is

parameterized as isovelocity layers with linearly dippingsegments represented with control depth points (for exam-ple, solid circles indicate the depth points in Fig. 3a). Theexplicit numerical FD schemes of fourth order in space andsecond order in time are applied in the interior of the FDregion, whereas those of second order in space and time areused for the grid points at the boundary of the FD region(Wen, 2002). At the left, right, and bottom boundaries, weapply the absorbing conditions of Clayton and Engquist(1977).


Table 1Event List

EventOrigin, Universal Time

(dd/mm/yy) Latitude LongitudeDepth(km) Mw

010102 02/01/01, 0730:04 126.81 6.75 33 6.4010129 29/01/01, 2321:26 133.33 �0.68 33 6.2010224 24/02/01, 0723:49 126.25 1.27 35 7.1010319 19/03/01, 0552:16 128.02 �4.03 33 6.5

Waveform Inversion

To explain the records inside the basin and invert thebasin structure, full waveform inversion methods wereproved to be very effective (e.g., Aoi et al., 1995; Ji et al.,2000), because they have high resolution (Luo and Schuster,1991). We use this method to model the basin structure. Inthe inversion process, the basin model is adjusted until syn-thetic waveform fits the data best.

The waveform inversion problem can be formulated asthe numerical solution of the following operator equation(Mehanee and Zhdanov, 2002)

A(m(x)) � p(t) , (3)obs

where A is the forward modeling operator, p(t)obs are theobserved seismograms, and m(x) � M (M is a Hilbert spaceof model parameters with an L2 norm). This inversion prob-lem is usually an ill-posed problem whose solution can benonunique and unstable. We reduce the nonuniqueness andinstability by minimizing the Tikhonov parametric function(Tikhonov and Arsenin, 1977),

�P [m(x)] � E[m(x)] � �s[m(x)], (4)

where E[m(x)] is a misfit function that includes a matchingdegree of waveform and travel time, s[m(x)] is a stabilizingfunction, and � is a stabilizing coefficient.

We follow Ji et al. (2000) and define waveform misfitas a square norm of the difference between the synthetic andrecorded seismograms.

2�p(t) p(t � s) dtobs synf(s) � 1 � , (5)2 2�[p(t) � p(t � s) ]dtobs syn

where p(t)syn and p(t)obs are the synthetic and recorded seis-mograms, respectively, and s is the time shift between thetwo.

Then misfit function is presented as (Luo and Schuster,1991):

N1 2E(m(x)) � W (ds � ds )t � i l�N � 1 i�2

N1 2� W f (ds ) , (6)f � i i�N i�1

where N is the number of stations, dsl is the retarded timebetween synthetic and record at the point of origin of the FDregion, Wt and Wf are weights for travel-time residual andwaveform fit, respectively. We choose weights based on thedata quality.

The stabilizer can be treated as a tool for including apriori information about the geological structures in the in-version problem solution (Mehanee and Zhdanov, 2002).

We use a minimum norm of difference between the selectedmodel and the drilling core data as stabilizer:

2s (m) � �m(x) � m (x)� � min, (7)L core2

where mcore (x) is the depth vector of the strata interfaces forthe drilling core data.

Following Ji et al. (2000), we use the conjugate gradientalgorithm (Polak, 1971) to seek the minimum of the Tik-honov parametric function defined in equation (4).

Numerical Tests

We carry out several numerical tests on the validity ofthe SH wave-field exploration FD method, resolution ofmodel parameters, and effects of using a stabilizer to incor-porate geological information into inversion.

The first test is to check the validity of the SH wave-field extrapolation of the FD calculation by using the datafrom hard-rock stations deployed at the Luxi uplift. In thewave-field extrapolation, we take the record of station21JZZS for event 010224 (Table 1) as input motion; in theFD calculation we use a 2D homogeneous model in whichstations from 21JZZS to 87SZZ are aligned according totheir epicenter distances. Comparison of synthetics (dashedlines in Fig. 3b) and records (solid lines in Fig. 3b) showsgood agreement in both timing and waveform. Similar re-sults are obtained when we use data from other events listedin Table 1. Despite the fact that the hard-rock stations arenot deployed in a line to the epicenter but rather within arectangle with a width of 100 km (Fig. 1a), the 2D wave-field FD method is still valid. This implies that it can beextended to 3D problems.

Compared with regional event data, the teleseismic datahave lower frequency content from 0.05 to 1 Hz. It is veryimportant to investigate to what detail our teleseismic datacan constrain the basin structure. To illustrate it, we performa second test using synthetic data. The test model involvesa simple single-layer (solid line in Fig. 4a), and it is param-eterized by depth control points with a 5-km horizontal in-terval. The test data are generated by using the record atstation 87SZZ for event 010102 (listed in Table 1) as theinput motion. Then we add a local rise of basement beneatha location 30 km from the model point of origin and calculatesynthetics (dashed line in Fig. 4a). The comparison betweentest data (solid lines) and synthetic motions (dashed lines) isshown in Figure 4b. The result shows an average of a 0.2-


Figure 4. Waveform-sensitive and inversion re-sults with respect to a localized variation of modelparameter. (a) Test model (solid line) and a modelwith a local 1-km-high rise (dashed line). Solid tri-angles indicate the positions of receivers. (b) Com-parison between test data (solid traces) calculated us-ing the test model and synthetic motions (dashedtraces) calculated using the model with a local 1-kmrise. (c) Average time residual (solid line) and averagewaveform misfit (dashed line) versus the height of therise. The unit of time residual is second. (d) Invertedresults using shear velocities 10% higher (dashedline) and lower (long dashed line) than the assumedvalue, respectively. The solid line indicates the targetmodel.

sec time difference and an average of 0.07 waveform misfitdefined in equation (6). For the receiver located above therise, the time residual increases to 0.625 sec and the maxi-mum waveform misfit reaches 0.12. We gradually decreasethe height of the rise from 2 to 0.1 km and calculate theaverage timing residual and waveform misfit. Figure 4c

shows the timing difference and waveform misfit as theheight of rise decreases from 2 to 0.1 km, and the travel-time residual provides a more important constraint thanwaveform misfit. For this particular numerical test, the in-version continues in a correct conjugate direction when alocal rise of 0.2-km height occurs, which indicates that thefrequency content of our teleseismic data would allow us torecover a local rise of 0.2-km height and 10-km width. How-ever, this resolution depends on the frequency content of thedata (see Modeling Results section), the frequency contentof our teleseismic data would allow detection of a local riseof 1.0-km height and 10-km width. In general, such a localrise would increase 5%–20% waveform misfit and producea 0.2–0.5-sec time residual.

Other parameters, such as velocity variation, 3D undu-lation of the bottom topography of basin, and sign-to-noiseratio, would also affect the resolution of the inversion. Be-cause of the nonlinearity of the inversion, it is difficult todefine the relationship between inversion resolution andthese parameters. However, we can determine them quali-tatively by numerical tests. To examine the effect of theuncertainties of the assumed velocity, we perform a numer-ical test using a model with a local rise of 2-km height. Theinversed results are shown in Figure 4d for the cases inwhich the shear wave velocities are 10% higher and lowerthan the assumed value, respectively. The resultant depth inthe inversion increases (decreases) about 15% for the caseswith the higher (lower) assumed velocity. However, an un-certainty of 10% in the assumed velocity does not affect theability to recover the major characters of the model. High-frequency noise does not change the inverse result (Ji et al.,2000), whereas a strong 3D undulation of the bottom topog-raphy of the basin would have a strong effect on the reso-lution of the inversions based on a 2D assumption. Conse-quently, it is important to restrict our consideration toin-plane propagation of the wave in selecting the events toreduce the 3D effect.

When additional information from geology or well logdata is available, we can incorporate the information as ad-ditional constraints to the model. This is done by introducing


Figure 5. Numerical simulations showing the effects of stabilizer in waveform in-version. (a) Test model, starting model, and comparisons between the synthetic dis-placements calculated based on the test model (solid traces) and the starting model(dashed traces). Note the difference between synthetics calculated based on these twomodels. (b and c) Basin models obtained based on waveform inversion without (b) andwith (c) a stabilizer, and comparisons of their synthetics with the synthetic data cal-culated from the test model. The synthetics calculated based on both these resultantbasin models show good agreement with the synthetic data, whereas the one that usesa stabilizer recovers the starting model much better.

a stabilizer in the inversion. We show an example to illus-trate the effects of using a stabilizer in the inversion on thefinal inverted model using synthetic data. The test modelinvolves a two-layer steplike structure. The position of87SZZ is set as the origin of the FD region, and the test dataare generated using the record at station 87SZZ for event010224 as input motion. We use a sloping layered model asour starting model in inversion. In Figure 5a, comparisonshows large discrepancies between the test data (solid lines)and synthetics (dashed lines) calculated based on the startingmodel. In the inversion, the weights of waveform fit andarrival-time residual are both 0.5. If we assume that we knowthe depths of the first layer beneath locations 20 and 55 kmaway from the model point of origin from the drilling coredata, we can substitute these depths in equation (7) as astabilizer. We obtain two inverted models in which one usesstabilizer and the other does not. Figure 5b and c shows thatboth these models generate synthetics that match the test dataequally well, which means that we cannot judge which isthe optimal result without other a priori information. Al-though the pseudo model (dashed line with black circles in

Fig. 5b) is similar to the test model (solid line in Fig. 5b)overall, local differences exist. In Figure 5b, it is obviousthat “thickness trade-off effect” exists. Beneath the locations20 and 55 km away from the model point of origin, thethickening of the first layer compensates for the thinning ofthe second layer. This kind of trade-off is very common inthe multilayered inversion model. However, if we have somea priori information, such as borehole or well-logging data,we can use it as a stabilizer and obtain a better-constrainedresult (Fig. 5c). Thus, using a stabilizer can incorporate apriori geological information and well log data in the inver-sions, reduce the “thickness trade-off effect,” and better con-strain the basin model.

Modeling of the Southern Edge of the JiyangDepression

Geological Settings

The Jiyang depression is a Mesozoic Cenozoic sedi-mentary depression with abundant oil and gas (Liu and


Figure 6. (a) Locations of seismic stations andcross sections AA�, BB�, and RR�. (b) Locations ofseismic events and great circle paths. (c) The startingmodel estimated from a rough geology cross sectionsimilar to our cross sections.

Yang, 1995). It is one of six main subbasins of the BohaiBay Basin Province, lying in the southeast of the BaohaiBay Basin Province that developed during Cenozoic exten-sional tectonics of the North China Plate. Published reports(e.g., Allen et al., 1997) suggested that the Bohai Bay Basinformed after the early Cenozoic extension and late Cenozoicthermal subsidence. To the south of the Jiyang depressionare the mountains of the Luxi uplift with Precambrian crys-talline basement that is the southern boundary of the BohaiBay Basin Province. To the north, are the Chengning rift andthe Huanghua depression (Lu et al., 1997). Tertiary strataform the major reservoir rocks of the basin, resting uncon-formably on a variety of older prerift strata, and are coveredconformably or unconformably by Quaternary sediments.Lithologies are dominated by terrestrial clastic rocks (Allenet al., 1997).

Seismic Data Set

As a part of NCISP, between November 2000 and July2001, 65 portable broadband stations were deployed tra-versing the eastern part of the Bohai Bay Basin Province(Fig. 1a, which shows only those stations used in the presentstudy). The stations traversing the southern boundary of theBohai Bay Basin were deployed in two nearly straight linesextending from south (the Luxi Uplift) to north (the Jiyangdepression) using CMG-3ESP sensors and REFTEK-72Adata-acquisition systems. The average spacing between sta-tions is �10 km. The data are used to constrain models alongtwo cross sections (Fig. 6a, AA� and BB�). Unfortunately,the instrument malfunctions of several stations resulted in adata gap in some places along cross section BB�.

We select four seismic events whose locations are atalmost the same azimuths along these two profiles AA� andBB�. Their magnitudes (Mw) are � 6.0. Table 1 lists theevent parameters, and Figure 6b shows the location map.Event locations and origin times are taken from the UnitedStates Geological Survey (USGS) website catalog.

Only the data recorded at the stations deployed at theedge of the basin or inside it are selected for modeling. Theseismic data are bandpass filtered between 0.005 and 4 Hz,and the instrument responses are removed. The basin effectsin these data are obvious. For example, Figure 1b shows thatthe basin stations exhibit weak direct arrivals but strong re-flected phases. The reflected phases become stronger for thestations in the deeper basin.

We take stations 87SZZ and 88NWZ (Fig. 6a), de-ployed at the Luxi uplift, as the hard-rock site stations alongthe AA� and BB�, respectively. We extrapolate the obser-vations at these two stations to the FD grids at the bottom ofthe FD regions. In the FD calculations, we choose the loca-tions of 87SZZ and 88NWZ as the left boundaries of the FDregions, respectively. The epicentral distance and azimuthfrom the events to reference stations 87SZZ and 88NWZ areshown in Table 2.

Modeling Results

Using the technique developed in this article, we modelthe observed waveforms and invert the basin models alongcross sections AA� and BB�, respectively. We first constructour preliminary basin geometry (shown in Fig. 6c) based on


Table 2Epicentral Distance and Azimuth from the Events to the Stations

at Point of Origin

Epicentral distance, km Azimuth, degree

Event To 87SZZ To 88NWZ To 87SZZ To 88NWZ

010102 3430.5 3433.6 346.7 346.5010129 4418.5 4423.0 341.2 341.0010224 3990.8 3993.3 349.1 348.9010319 4609.9 4612.6 348.3 348.1

Table 3Average Velocity Assigned for the Stratified Sediments

StrataAverage VP

(km/sec)Average VS

(km/sec)

Quaternary (Q) 1.32 0.60Neogene (N) 2.20 1.25Paleogene (E) 2.90 1.70Pre-Tertiary (P-T) 3.80 2.20

a rough geology cross section (Lu et al., 1997) similar toours and assign average compressional wave velocities ofthe sedimentary layers inside the basin based on drilling coreand sonic log data. The drilling core and sonic log data arefrom the Eastern China Oil Company, and we are not per-mitted to present the details of the data. We then use forwardwaveform calculation and inversion to constrain the basinmodels. Seismic exploration experiments suggested eightmajor seismic reflectors in the basin (Wang and Qian, 1992).Because our seismic data have a lower vertical resolutionthan the seismic reflection data, we divide our basin modelinto four major velocity layers, corresponding to the Qua-ternary, Neogene, Paleogene, and Pre-Tertiary strata, re-spectively. The average shear velocities (Table 3) are ob-tained from the compressive wave velocities and the VP/VS

ratios of the four strata averaged from the drilling core andsonic data. The shear velocity of the basement rock is as-signed to be 3.18 km/sec calculated based on an averagecompressional velocity of 5.5 km/sec and a VP/VS ratio of1.73 (Lu, 1993). We adopt a grid size of 0.05 km in FDcalculations and a horizontal spacing of 5 km between con-trol points of the basin models.

The best-fitting models for the two cross sections AA�and BB� are shown in Figures 7 and 8, respectively, and thesynthetic waveforms (dashed lines) from our best-fittingmodels are compared with the records (solid lines). The rela-tive timing and waveform match the data well. Although theinput motions at the hard-rock site stations are quite differentfor four events, the models inverted from the seismic datafor these four earthquakes are very similar, which proves therobustness and reliability of this technique. The small dif-ferences between the models estimated from four events maybe attributed to data noise, azimuth differences, and the in-

fluence of 3D undulation of the bottom topography of thebasin.

We present several forward synthetic calculations to il-lustrate the relationship between the model features and theobserved motions. It is very difficult to determine their non-linear relationship quantitatively, so we display it qualita-tively by several tests. We take the inverted model alongAA� as an example. We start with a simple structure andadd complexity at each step. The comparison between syn-thetic waveforms (dashed lines) and observed data for event010102 (listed in Table 1) are shown in Figure 9. The resultsshow that changes of the shapes of interfaces affect syn-thetics differently. From Figure 9a to b, changing the thinsurface layer has less effect on timing and waveform thanunderlying layers. However, allowing the depth of the base-ment interface to vary (from Fig. 9b to c) significantly im-proves the fit to both the timing and waveform, and espe-cially it makes the reflected phases match well. On the otherhand, adjustment of intermediate layers (from Fig. 9c to d)has a strong effect on timing and waveform, but it has lesseffect on the reflected phases.

Waveform inversion also reveals a blind fault beneatha location 30–50 km away from the model point of origin.We show that the blind fault is a robust feature. We performinversions by forcing the local basin geometry near the faultregion to be smooth (shown in Fig. 10). Inversion resultsshow that with a smooth basement, the time residual of sta-tion 125XFX increases from 0.09 to 0.32 sec and the averagewaveform misfit increases by about 60% from 0.18 to 0.28.Figure 10b shows a large discrepancy between synthetics(dashed line) and data (dashed line) for station 125XFX.This is in great contrast with the excellent waveform andtravel-time fits for the optimal model with fault (Fig. 7c).When we invert basin models without smoothing the basinstructure near the fault, the inversions converge quickly tothe optimal model after nine iterations. In contrast, if weforced the structure beneath the location 30–50 km awayfrom the model point of origin to be a smooth shape in in-versions, we are not able to obtain a convergent result. Dur-ing 100 iterations, the average time residual and averagewaveform misfit fluctuate but decrease only slightly (Fig.10c). The time residual for station 125XFX is still 0.32 secand large discrepancies between synthetics and observedwaveforms remain for stations 125XFX, 131LJZS, and137HJZ (Fig. 10d). The constraints on the existence of thefault are mainly from the observations recorded at stations125XFX, 131LJZS, and 137HJZ, especially that at the sta-tion directly above the fault, 125XFX.

We obtain our preferred models along cross sectionsAA� (Fig. 11a) and BB� (Fig. 11c) by averaging the depthsof control points of four models obtained from four events.In general, the models obtained for these two cross sectionsare similar. However, some difference exists between thetwo models along AA� and BB�. Most noticeably, cross sec-tion AA� has a thicker Paleogene formation and a thinnerPre-Tertiary formation than cross section BB�.


Figure 7. Best-fitting models for cross section AA� obtained based on waveforminversion of four teleseismic events and comparisons of synthetic displacements(dashed traces) and seismic data (solid traces), while the waveform is normalized toits maximum amplitude. Solid triangles indicate the positions of receivers projected tothe line AA� according to their epicenter distances. The input motions to the FD cal-culations are extrapolated based on the seismic data observed at a hard rock site station87SZZ (located at distance 0 km in the model). (a) Event 010102. (b) Event 010129.(c) Event 010224. (d) Event 010319.


Figure 8. Same as in Figure 7, except for cross section BB� and the hard rockstation 88NWZ. Only models with a length of 85 km are shown.


Figure 9. Waveform sensitivity to different features in the inverted basin model forcross section AA�. Model complexity increases from (a) to (d). The lower panels showcomparisons between the data (thick lines) and synthetic waveforms (dashed lines)generated from the models in the upper panels. The solid triangles indicate receivers.


Figure 10. Numerical tests for basin models without a fault beneath the location30–50 km away from the point of origin. (a) The fault beneath the location 30–50 kmaway from the point of origin is smoothed based on model c in Figure 8, that is, thestructure beneath the location 30–50 km away from the model point of origin is forcedto be smooth during inversions. (b) Comparison between synthetics (dashed lines) anddata (solid line) for the smoothed model. (c) Change of the average time residual (solidline) and waveform misfit (dashed line) after 100 iterations. (d) Comparison betweensynthetics calculated from the smoothed model after 100 iterations (dashed lines) anddata (solid line). Note the waveform misfits at stations 125XFX, 131LJZS, and 137HJZ.

Discussion

To evaluate our results, we compare our final invertedmodels with a geological cross section (Fig. 11) from Zhaiet al. (1988). The location of their cross section line RR� isshown in Figure 6a. It is noted that line RR� locates betweenlines AA� and BB�, but the cross section RR� is somewhatprolonged in the North and somewhat shortened in theSouth. Our models (Fig. 11a and c) are similar to the geo-logical cross section (Fig. 11b) overall: (1) they all extendto a depth of �6.5 km and the Tertiary formations are theirmajor reservoirs; (2) distinct faults exist beneath the posi-tions �50 km and �75 km distant from the point of origin;

and (3) the basin starts thinning toward the Chengjia-Zhuangrise at about �85 km from the model point of origin.

The fault geometries suggest arrays of half-grabens aredeveloped on planar faults of the basement, and these displaya typical style of extension. This suggests that extensionplayed an important role in the evolution of the Jiyang de-pression. Based on geometry configuration of faults andstrata, we infer that a major Cenozoic extension occurredthrough Paleogene (Allen et al., 1997), and continuedthrough Neogene and Quaternary with a decreasing rate ofextension. As a result, the Neogene stratum has a greatersedimentary extent than the Paleogene stratum.

The shape of the basement is characterized by steplike


Figure 11. Comparison of our preferred models for cross sections AA� (a) and BB�(c) and a geological cross section from Zhai et al. (1988) (b). The dashed lines in panelb indicate major faults. Note that the Quaternary formation and the Neogene formationare merged as “Q�N” in the geological cross section in panel b. For comparison, wemerge their three formations of Paleogene as one stratum.

structures, and its fractures are attributed to the effect of theextensions (Fig. 11). The unconformable of basement im-plies that rocks have undergone weathering, erosion, andsolution. Beneath the Tertiary strata, the Pre-Tertiary sedi-ments appear to have been deposited on basement. It is re-ported that the Pre-Tertiary depositions mainly belong toUpper Jurassic and Lower Cretaceous (Li and Lu, 1988).However, the Pre-Tertiary rocks appear to have also under-gone strong weathering, erosion, and solution, because theyare present as a very thin and unconformable stratum. Ter-tiary strata form the major reservoirs resting unconformablyon the Pre-Tertiary rocks. Our models also indicate that theTertiary deposition, which is a major reservoir for oil (Allenet al., 1997), has its largest thickness (up to 4 km) beneaththe Dongying sag (Fig. 11).

Waveforms recorded in sedimentary basins are affectedby the 3D structure of the basin (Scrivner and Helmberger,1994; Aoi et al., 1995) indicated that 2D inversion wouldbecome insufficient when the 3D effects are strong. The factthat we obtain consistent basin models for four events withslightly different azimuths suggests to us that our 2D ap-proximations are reasonable. Our numerical tests have

prompted the feasibility of 3D wave-field extrapolation, soit is possible to extend our method to 3D modeling of basinthrough 3D forward calculations and inversion. The advan-tages of 3D modeling would be that we can exploit the SHwaves propagating through an interesting region from tele-seismic events with arbitrary azimuth, and the 3D effects ofwave propagation can be fully taken into account. The keyto implementing 3D modeling is to generate syntheticswithin a reasonable calculation time and to deploy manymore stations within the target areas.

Conclusions

We develop an SH wave-field extrapolation the FDmethod to estimate the configuration of basin edge by usingteleseismic data. This method consists of wave-field extrap-olation, FD calculation, and waveform inversion. A numer-ical test using the data from hard-rock stations checks thevalidity of forward synthetic calculations and reveals a pos-sibility of extension to 3D problems. Other numerical ex-periments are performed to test its resolution, its sensitivity,and the validity of stabilizer in inversion.


With data for four teleseimic events, this method is usedto estimate two cross sections of the southern edge structureof the Jiyang depression, the Bohai Bay Basin, northernChina. Similar models are obtained from inversions of seis-mic data recorded for four events. Results show good agree-ment between the observed seismograms and the syntheticsand the overall agreement between our model and the geo-logical structure of the basin. Several forward synthetic cal-culations illustrate the relationship between the model fea-tures and the observed motions. Our inversion results reveala blind fault beneath station 125XFX. Numerical tests alsoindicate the robustness of the existence of faults beneath thestation 125XFX.

Our results reveal that the southern edge of the Jiyangdepression extends from shallow depth down to about 6.5km, and it is characterized by a steplike configuration. Itsshape seems to be defined by a series of distinct faults thatprovide some evidence for the extension of the basin alongits south edge. The faults’ geometry suggests that major ex-tensions occurred and ended at the end of Paleogene. TheTertiary strata form the major reservoir rocks of the depres-sion.

Acknowledgments

We thank Lianxing Wen for his help in using FD calculations and hismost helpful reviews, and we acknowledge the participants of the Broad-band Seismic Array Laboratory, IGGCAS. This research is supported byNKHRSF Project of China (G19990433) and the Chinese Academy of Sci-ence (No. KZCX 1-07). We appreciate the careful and thoughtful reviewsby Dr. Fred F. Pollitz, Jean Virieux, and an anonymous reviewer.

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Qijiahuozi, Deshengmenwai, Chaoyang DistrictInstitute of Geology and GeophysicsChinese Academy of ScienceP.O. Box 9825, Beijing, 100029, [email protected].

(L.Z.)

[email protected](T.Z.)

[email protected](W.X.)

Manuscript received 14 August 2003.

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