| WO/2016/108826 | DUAL CORE LOCKING GEOPHONE |
| US5691893A | 1997-11-25 | |||
| US20060162440A1 | 2006-07-27 | |||
| US20010016020A1 | 2001-08-23 |
| CLAIMS 1. A method for removing noise from a recorded signal dn(t) recorded simultaneously on a plurality of channels by means of N receivers, said noise having different receiver specific signal strength and is embedded in an actual signal sn(t), said method comprising: applying Fourier transform to the time representation of the recorded signal dn(t) resulting in a signal dn(ω) comprising receiver independent noise b(co) with different receiver specific signal strength a„ and the actual signal sn((o), represented as: estimating an and b(co) by minimizing the energy of sn((o) according to: differentiating X2with respect to an and b (ω) and setting derivatives to zero, resulting in representations of an and b (ω) given by: solving said equations for b (ω) and a„ numerically. 2. The method according to claim 1 , where the solutions for b (ω) and an are found by an iterative method. The method according to claim 2, where the iteration are continued until there are no significant changes in the energy χ 2 from one iteration to the next. The method according to claim 2, where 10 iterations are performed. |
Introduction
The present invention generally relates to processing of a data signal with the purpose of removing noise from a signal. More specifically the invention defines a method for removing pick-up noise from signals recorded simultaneously on a plurality of receivers and with different signal strength.
Background
Noise may present a problem when recording a signal. There are several factors that may introduce noise. One factor is insufficient shielding of electric cables that may result in recorded signals embedded in noise (pick-up noise).
Another factor is noise introduced in a transducer used for recording a signal. If a transducer functioning as a pressure sensitive device has insufficient acoustic isolation it may be exposed to noise that is recoded together with a signal of interest. An example where this may occur is in a fiber-optical acoustic
accelerometer. The refraction index of an optical fiber is sensitive to the strain of the fiber. Where subjected to an acoustic wave field, the refractive index of the optical fiber will change. These local changes will generate reflections of the laser light travelling through the fiber. This effect is the basis for the use of optical fibers as Distributed Acoustic Sensors (DAS). A fiber-optical acoustic accelerometer, on the other hand is using devices which are extra-sensitive to strain at discrete locations along the fiber, such as a Bragg grating or an interferometric arrangement comparing the perturbed optical fiber to an unperturbed optical fiber. As these accelerometers are based on transmission of analog laser light through the entire fiber, the measurements may become sensitive to variations in the refraction index of the fiber associated acoustic signal picked up along the length of the fiber, as these variations will reflect part of the laser signal (the DAS effect), and therefore disturb the properties of the reference laser light. This may happen if the fiber has insufficient acoustic isolation protecting against acoustic pick-up of noise. This type of noise may render recorded data unusable.
Frequency filtering for removing the noise will not work as the pick-up noise may have the same bandwidth as the signal one wants to preserve. If the pick-up noise is the same on each channel, removing the median or mean trace would take out the noise. However, when the "pick-up" coefficient varies from one channel to the next, the solution according to the invention will remove the noise. The present invention defines a method for estimating noise in a recorded signal contaminated with pick-up noise. After the noise is estimated it can be removed from the recorded signal leaving only the signal of interest.
According to the inventive method, a least-squares estimation and removal of noise that is picked up coherently is performed, but at different strength on a plurality of channels. The method can be applied to signals embedded in strong noise.
Description of the method
The method for removing noise from a recorded signal will now be described with reference to Figure 1 showing three different representations of data from same recorded signal.
A signal s n (t) is recorded simultaneously on a plurality of channels represented by N receivers at different spatial locations. In addition to the signal s n (t), the actual recorded data d n (t) will contain noise of different origins. Whereas the signal will arrive at different times on each of the receivers, the time on channel n being dependent on the relative location of the receiver n to the source of the signal, pickup noise is assumed to be simultaneous and coherent on all receivers. The noise will have different receiver specific signal strength and will be embedded in an actual signal s n (t) of interest.
Figure 1 a) shows an example of a representation of the raw data d n (t) of a signal recorded simultaneously on a plurality of receivers N. The signal recorded is from propagating acoustic waves which are heavily contaminated by noise. This is a typical example of a signal embedded in pick-up noise. The figure shows time (the vertical axis) versus depth (the horizontal axis) of a recorded seismic signal recorded with a fiber-optical acoustic accelerometer.
Another example of such pick-up noise is well known from analog electrical signals being transmitted on a bundle of insufficiently insolated conducting wires. The bundle of wires may then be subjected to electromagnetic fields that will generate additional currents on the conductors. This noise will be recorded together with the desired signal s n (t). Depending on the sensitivity of each conducting wire to this external field, the additional noise will have the form a n b(t), where a channel- specific constants a n depend on the sensitivity of conductor n to the external source of noise. The time dependency b(t) of the noise would be the same on each channel, as the external electromagnetic field affects each conducting wire simultaneously. The method for isolating and removing the noise part of the signal comprises several steps.
The first step is to apply Fourier transform to the time representation of the recorded signal d n (t) resulting in a signal d n (ω) comprising receiver independent noise b(ω) with different receiver specific signal strength a„ and the actual signal s n (ω) , represented as:
The next step is to estimate specific signal strength a„ and the receiver independent noise b(co) by minimizing the energy χ 2 of s n ((o) according to:
Energy χ 2 is then differentiated with respect to signal strength a n and the independent noise b (ω) and by setting derivatives to zero, resulting in
representations of a n and b (ω) given by:
Equation (2) can be solved for the receiver independent noise b(ω) and the specific signal strength a n either explicitly, using an equation solver to numerically invert the equation - or it can be solved iteratively, starting with inserting starting values for a n for all n in the expression for b (ω), then inserting the values for b(ω) into the expression for a„, etc. If no other information is available, the starting values for a„ could typically all be 1. The iterations would continue until there are no significant changes in the energy χ 2 from one iteration to the next. Typically, convergence is achieved after less than 10 iterations.
Figure 1 b) shows the actual data of the desired signal s n (t) resulting from subtracting a„ times b(t) from s n (t), i.e. the noise is removed.
Figure 1 c) shows a representation of estimated noise b (ω) resulting from iterating 10 times through equation (3). The present invention solves the problem of isolating a signal that is heavily contaminated by noise.