Temporal aliasing occurs when a waveform is sampled with less than two points per time period for a signal at a given frequency. This insufficiently sampled frequency will be incorrectly mapped into a lower (aliased) frequency. Analogous to this, spatial aliasing is said to occur when a propagating waveform is measured at spatial intervals larger than half the wavelength of any given signal in that waveform. Temporally aliased frequencies cannot be recovered with standard methods. On the other hand, we argue that “spatial aliasing” can be viewed as an expression of a nonuniqueness for estimating the direction of the propagation for signal at a given frequency, and that spatial aliasing may be overcome when 3C seismic sensors are used. Realizing this allows for using higher frequencies, and it therefore enables the generation of higher resolution images from the data. This is particularly useful for borehole-seismic data, which tend to contain higher frequencies than surface-seismic data, but does require that an array of 3C sensors is used or that an array of less expensive 1C sensors is supplemented by 3C sensors.

中文翻译：

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空间混叠和 3C 地震传感器

当对给定频率的信号以每个时间段少于两个点对波形进行采样时，就会发生时间混叠。这个采样不足的频率将被错误地映射到较低的（混叠）频率。与此类似，当以大于该波形中任何给定信号波长一半的空间间隔测量传播波形时，就会发生空间混叠。使用标准方法无法恢复时间混叠频率。另一方面，我们认为“空间混叠”可以被视为估计给定频率下信号传播方向的非唯一性的表达，并且当使用 3C 地震传感器时可以克服空间混叠。意识到这一点可以使用更高的频率，因此，它可以从数据中生成更高分辨率的图像。这对于钻孔地震数据特别有用，这些数据往往包含比地表地震数据更高的频率，但确实需要使用 3C 传感器阵列，或者需要使用 3C 传感器补充一组较便宜的 1C 传感器。