本文提出微扰与多极展开相结合的方法，近似计算雪人模型近场头相关传输函数（HRTF），并利用此方法定量分析躯干散（反）射声波对HRTF的影响。计算结果表明，躯干散射对HRTF的影响与微扰近似的阶数、频率、声源位置（包括方向和距离）等有关。在一级微扰近似下，躯干散射对HRTF的影响整体上随频率的升高、或声源距离的减小、或仰角的降低、或声源相对受声耳方向的偏离角度的增大而增大。随着微扰级数的增加，高阶微扰项对计算结果的贡献迅速减少。在声源距离不小于0.02 m 以及仰角不小于135°的条件下，对 20 kHz 以下的频率范围，采用三阶微扰近似的计算误差在 ± 1.0dB 以内。 由于 n 阶微扰在物理上是和头部和躯干之间的 n 重散射相对应的，因而本文的结果表明，在雪人模型的条件下， 头部和躯干的前三阶多重散射对 HRTF 是重要的，四阶及以上散射可以忽略。

Proposed in this paper is a combination of the perturbation method and the muhipole expansion method, which is used to approximately calculate the near-field head-related transfer function （HRTF） of the snowman model and to quantitatively analyze the effects of torso scattering and reflection on HRTF. Calculated results indicate that the contribution of torso scattering to HRTF depends on not only the order and frequency of perturbation app- roximation but also the position （including the direction and the distance） of sound source; that, under the first- order perturbation approximation, the contribution of torso scattering increases with the increase in both the frequency and the azimuth of the sound source departing from the ear, and with the decrease in both the distance of the sound source from the head center and the elevation of the sound source ; that the contribution of perturbation terms with higher orders to HRTF greatly decreases with the increase in perturbation orders; and that, when the sound source distance is not less than 0. 02m and the elevation is not less than 135°, the calculation errors of the third-order perturbation approximatation are controlled within ± 1.0 dB below 20 kHz, and the contributions of the fourth-order and the higher-order scatterings are neglectable.