General introduction

Understanding of tomographic image in terms of dynamics of the Earth's interior requires knowledge of what causes lateral variation of seismic wave velocities. One way of distinguishing origins of heterogeneity is to compare observed tomographic velocity anomalies to those predicted by mineral physics. The purpose of this study is to model three-dimensional VP/VS ratio variation which is suitable to be measured for laboratory experiments but rarely derived seismologically.We focus on using broadband S-P differential travel times, since P and S information corresponds originally. The VP/VS tomography model so derived can be undergone direct comparison of those from laboratory measurements. In this paper, we show the measurement procedure of S-P differential travel times,inversion technique for modeling VP/VS ratio, and the resultant VP/VS tomographic model. We also show the P to S velocity anomaly ratio R tomography as an application of this inversion technique.

Measurement of S-P travel times

Picking an arrival time of S wave is in general difficult, and waveform correlation is a method to solve this problem. We take into account the physical dispersion which is characterized by two parameters t* and f0 to synthesize S waveform from observed P waveform by correcting attenuation effect. S-P differential travel time is measured by cross-correlating synthetic and observed S waves for the first half cycle. The reference frequency f0 is conventionally set to 1 Hz. We, however, found a systematic discrepancy of about 0.5 s between cross-correlated and handpicked S-P times. This indicates a higher value for the reference frequency that is consistent with the onset frequency of short-period body waves. The 0.5 s discrepancy disappears when the reference frequency is taken to be 2 Hz. We, therefore, used 2 Hz as the reference frequency of teleseismic body waves.

Inverse problem for Vp/Vs ratio

Observed and reference S-P times can be written as follows by using Vp/Vs ratio

observation time :

reference time :

We handpicked P onsets among those 13,500 S-P times, and prepared 13,000 of them. They are compared to the predicted time from P tomographic model of Fukao et. al., [2001] to be found that they are in good agreement. This indicates the equivalence of Vp and Vpref in the above equations. Setting （Vp/Vs）-（Vp/Vs）ref to the unknown parameter to be modeled, the subtraction of （1） and （2）, can be solved as a linear inversion problem.

VP/VS tomographic model

Using Vp/Vs and P tomographic models, three-dimensional Vs distribution can be derived as Vs=Vp/（Vp/Vs）. These models are shown in Fig.1. The old Indian plate which closed Tethys sea can be seen beneath India where smaller Vp/Vs values are detected. Note also that slow anomalies beneath Solomon and Samoa islands in S model （circled by solid lines） have significant difference in Vp/Vs model, indicating the cause of velocity anomalies of the two regions may be originated from different factors.

R tomography

The tomographic technique of $V P/V S$ ratio can be applied to model three-dimensional distribution of R. Suppose SP,s is the slowness of P and S waves which consists one-dimensional and fractional slowness of SO and δS. Let R be defined as,

the observed and reference times can then be written as

observed equation:

reference equation:

Assuming SP=SPref as we confirmed previously, we again obtain a linear equation for inversion with model parameter of δR;

The resultant model is shown in Fig.2. R will take a laterally uniform value provided that seismic velocities are perturbed only by lateral temperature heterogeneity through the anharmonicity effect,not through the anelasticity effect. Derived tomographic R model shows comprehensive increase with respect to depths, but varies about +/-0.3 in terms of standard deviation. Taking into account the over all correspondence between low R regions and slab regions, or high R regions and slow VS regions, the lateral variation of R may indicates the lateral patterns of Q. This implication may suggest that most of the velocity anomalies in the lower mantle can be explained as the thermal effects and the heterogeneity between seismological observations and temperature dependent laboratory measurements are localized such as in Solomon islands region at depth 2000 km having anomalous VP/VS ratio. These features could not be inferred by comparing only one-dimensional R plots of mineral physics predictions and seismological observations （Fig.3）. We emphasize the importance of preparing three-dimensional distributions of VP/VS ratio or R values in interpreting seismic tomography into mantle dynamics by the use of mineral physics measurements.

Fig.1 P, S, Vp/Vs tomography models

The old Indian plate which closed Tethys sea can be seen beneath India where smaller Vp/Vs values are detected. Slow anomalies beneath Solomon and Samoa islands in S model have significant difference in Vp/Vs model.

Fig.2 R tomographic model

Smaller values of R are dominated in slab regions such as the Western Pacific, North and South America, or Tonga at depths about 1000 km. These regions are expected to be less attenuative（high-Q） so that anelastic effect contributes little to R so that smaller values of R are expected from the mineral physics view point. Large values of R are dominated in regions of VS slow anomalies. Large negative anomaly in S velocity perturbation makes R significantly large （2000 km）.It is easily inferred that attenuative （low-Q） media increases R both through the anhamonic and anelastic effects.

Fig.3 spherically averaged R with other studies

Spherically averaged R is plotted in black solid line with standard deviation. Our data is between predicted R values with and without anelastic effect by Karato and Karki, [2001] which may vary depending on attenuation factor.

本論文は2部構成となっており，それぞれが7章からなる．はじめに論文全体へのイントロダクションとして，地球内部の地震波速度異常の成因が温度異常によるものなのか，物質組成異常によるものなのかを明らかにするために，Vp/Vs比のトモグラフィー解析をおこなう必要があることが説かれている．

第1部ではそのための基礎データ解析の手法と，そこから得られた副産物である地球内部の非弾性構造について新たな知見・発見が記されている．第1章は，イントロダクションであり，地球の非弾性の効果がどのように地球構造モデルの研究で扱われてきたかが簡潔に記してある．第2章は，解析に用いたデータの説明である．第3章には著者らが開発した，波形相関法による広帯域地震波形からP波，S波の相対走時及び非弾性効果を読み取る手法が提出されている．精密な解析手続きを踏むことが，以下の重要な成果のもとになったと考えられるので，高く評価される．第4章には，第一の副産物である，下部マントルの非弾性構造モデルが提出されている．マントル深部にいくにつれ非弾性が小さくなっている結果が得られており，今までにない結果であり注目に値する．続く5，6章は，P波−S波の相対走時の統計的な解析から，遠地地震波の立ち上がりの情報は，平均して2Hzの走時に対応していることを明らかにしている．地震波の伝播速度は，非弾性効果により観測可能な周波数依存性があることがわかっている．既存の研究では，短周期地震波から読み取られる遠地地震波の到着時間は1Hzに対応すると暗に仮定していたが，それが実際の観測事実を説明しないことを明らかにした極めて重要な成果である．7章には第1部のまとめが記されている．

第2部では，Vp/Vsトモグラフィーの手法の提出と得られた結果に基づく地球内部構造に関するあらたな知見が記されている．第1章は，イントロダクションであり，近年のトモグラフィー研究の流れがまとめられている．第2章はトモグラフィーに使う走時データの説明で，第1部のものを使うことが記されている．第3章では，トモグラフィーに使うデータの統計的性質が検討されている．既存の多くの研究はこの章に記されているような解析をもとにしており，この章以後が本部の重要な学問的貢献となる．第4章では，P波−S波の相対走時を使った，Vp/Vs比のトモグラフィーという新しいトモグラフィーの概念，手法の導入，仮定の妥当性の検討が記されいる．Vp/Vs比は地球内部の物性に関する情報をもっている可能性があることを考えあわせると，極めて重要な成果である．第5章では，Vp/Vs比のトモグラフィーの結果が示されている．マントル内の地震波速度不均質の多くのが温度不均質に依るものらしいこと，しかしながら一部の下部マントルには物質組成がことなる領域があるらしいことなどが明らかにされている．第6章では，さらに拡張したトモグラフィーの手法の提案をしており，予備的な結果とともに，将来への発展性を期待させるものとなっている．

なお，本論文第1部は，深尾良夫・大林政行との共同研究であるが，論文提出者が主体となって解析を行ったもので，論文提出者の寄与が十分であると判断する．

したがって，博士（理学）の学位を授与できると認める．