Sensor receiver nulls and null steering

A method comprising:

• applying a coordinate rotation to a first set of signal values, wherein each signal value of the first set of signal values is based on an output of a corresponding component of a three-component particle motion sensor at a sensor position, the applying generating a rotated set of signal values, wherein the coordinate rotation comprises a coordinate rotation transforming a first set of coordinate axes to a second set of coordinate axes, and wherein:
• the first set of coordinate axes having each coordinate axis aligned with a corresponding component of the three-component particle motion sensor at the sensor position;
• and
• the second set of coordinate axes comprises a first axis pointed in a direction opposite a direction from the sensor position to a noise source emitting an acoustic noise signal;
• and
• summing a signal value corresponding to the axis in the second coordinate system in the direction opposite the direction of the sensor position to the noise source with an output signal from a co-located hydrophone at the sensor position to generate a directivity null in the direction of the noise source, the summing generating a sum output signal;
• differencing the signal value corresponding to the axis in the second coordinate system in the direction opposite the direction of the sensor position to the noise source with an output signal from the co-located hydrophone at the sensor position to generate a directivity null opposite the direction of the noise source, the differencing generating a difference output signal;
• and
• applying a signal processing operation on the sum signal and the difference signal to remove the attributes of the noise source from the sum output signal.

A method comprising:

• determining a propagation direction of a surface-reflected seismic acoustic signal;
• applying a coordinate rotation to a first set of signal values, wherein each signal value of the first set of signal values is based on an output of a corresponding component of a three-component particle motion sensor at the sensor position, the applying generating a rotated set of signal values, wherein the coordinate rotation comprises a coordinate rotation transforming a first set of coordinate axes to a second set of coordinate axes, and wherein:
• the first set of coordinate axes has each coordinate axis aligned with a corresponding component of the three-component particle motion sensor;
• and
• the second set of coordinate axes comprises a first axis pointed in a direction opposite the propagation direction of the surface-reflected seismic acoustic signal;
• and
• summing a signal value in the rotated set of signal values corresponding to the first axis of the second set of coordinate axes with an output signal from a hydrophone co-located with the three-component particle motion sensor, the summing generating a sum output signal.

A method comprising:

• determining a direction from a first three-component particle motion sensor to a noise source, comprising:
• generating a set of directivity patterns of the first three-component sensor wherein each sensitivity pattern has a null;
• selecting a directivity pattern from the set of directivity patterns having a smallest noise source signal value, the directivity pattern having the smallest noise source signal value defining a first null;
• steering a direction of the first null if the smallest noise source signal value is greater than a preselected noise signal value;
• and
• terminating the first null direction steering if the smallest noise source signal value is less than the preselected noise signal value, wherein a last direction of the first null comprises a direction of the first three-component particle motion sensor to the noise source.