# Thread: Cross Correlation analysis with two series of wavelets Thanks: 0 Likes: 0

1. ## Cross Correlation analysis with two series of wavelets

Hey all,

This one will be a tough one to explain...

I essentially have 3 columns of data and 40000+ rows of it. Column A measures seconds from time 0 to say 10. Column B is a series of values creating on a graph wavelets from a source detected by receiver one and Column C is the same series of wavelets detected by receiver two. The two receivers are relatively closely spaced apart and therefore the profiles of these waves will be very similar although NOT identical. The spacing between the wavelets also changes due to the density of the soil/rock they travel throughThe aim is for excel to detect the peaks of each correlating wave and detect the lag time between the two series at each source. An example of a lag between two wavelets is shown

This lag time calculation (column 4!?) allows me to do all the statistical analysis for my job. The traditional way is to manually pick the peaks using ancient software but this simply isn't feasible with the amount of data I have.

My VB ability is marginally better than just recording but only slightly.

Sean

2. ## Re: Cross Correlation analysis with two series of wavelets

show us the raw data that produces a wave - my first thought, if there is enough data, is to detect the max value and take the average of it and say 10 data values either side

3. ## Re: Cross Correlation analysis with two series of wavelets

Seconds x1 x2
 0 -5.87e-05 -0.0001 0.000417 -1.05e-05 -2.16e-05 0.000833 4.64e-07 -1.61e-05 0.00125 -5.53e-06 -2.32e-05 0.001667 -4.74e-06 -2.16e-05 0.002083 -6.32e-06 -2.21e-05 0.0025 2.38e-06 -9.34e-06 0.002917 2.43e-05 2.88e-05 0.003333 2.85e-05 4.73e-05 0.00375 2.64e-05 4.24e-05 0.004167 3.66e-05 5.96e-05 0.004583 3.98e-05 7.17e-05 0.005 4.37e-05 7.63e-05 0.005417 5.28e-05 8.52e-05 0.005833 5.39e-05 8.75e-05 0.00625 5.18e-05 8.56e-05 0.006667 5.28e-05 8.54e-05 0.007083 5.4e-05 9.17e-05 0.0075 5.9e-05 9.97e-05 0.007917 0.000108 0.00016 0.008333 0.000145 0.000199 0.00875 0.000139 0.000199 0.009167 0.000136 0.00018 0.009583 0.00013 0.00018 0.01 0.000116 0.000154 0.010417 6.84e-05 7.92e-05 0.010833 6.07e-05 6.89e-05 0.01125 6.62e-05 8.04e-05 0.011667 6.45e-05 7.6e-05 0.012083 6.16e-05 7.48e-05 0.0125 5.05e-05 5.67e-05 0.012917 2.93e-05 2.13e-05 0.013333 1.75e-05 -2.09e-06 0.01375 2.2e-05 2.43e-06 0.014167 8.96e-06 -1.58e-05 0.014583 1.1e-06 -3.22e-05 0.015 -1.89e-06 -4e-05 0.015417 -1.07e-05 -4.75e-05 0.015833 -1.69e-05 -4.91e-05 0.01625 -1.32e-05 -4.71e-05 0.016667 -1.58e-05 -4.91e-05 0.017083 -2.13e-05 -5.86e-05 0.0175 -2.92e-05 -6.76e-05 0.017917 -8.34e-05 -0.000138 0.018333 -0.000114 -0.000175 0.01875 -0.000112 -0.000126 0.019167 -6.75e-05 -0.000133 0.019583 -9.43e-05 -0.000121 0.02 -7.51e-05 -0.000101 0.020417 -4.83e-05 -4.7e-05 0.020833 -3.14e-05 -2.24e-05 0.02125 -4.12e-05 -3.68e-05 0.021667 -3.43e-05 -3.13e-05 0.022083 -3.65e-05 -3.23e-05 0.0225 -3.42e-05 -2.28e-05 0.022917 -1.72e-05 1.71e-06 0.023333 -1.95e-06 3.21e-05 0.02375 -5.21e-06 2.4e-05 0.024167 7.12e-06 3.62e-05 0.024583 1.91e-05 5.31e-05 0.025 2.52e-05 5.7e-05 0.025417 3.56e-05 6.15e-05 0.025833 3.97e-05 5.74e-05 0.02625 3.76e-05 5.69e-05 0.026667 4.27e-05 5.82e-05 0.027083 5.11e-05 6.8e-05 0.0275 5.87e-05 7.57e-05 0.027917 0.000105 0.000129 0.028333 0.000149 0.000181 0.02875 0.000141 0.00017 0.029167 0.00014 0.00017 0.029583 0.000141 0.000166 0.03 0.000127 0.000143 0.030417 9.39e-05 8.5e-05 0.030833 8.17e-05 7.44e-05 0.03125 8.67e-05 8.38e-05 0.031667 8.48e-05 8.61e-05 0.032083 8.74e-05 8.6e-05 0.0325 8.33e-05 7.9e-05 0.032917 7.5e-05 5.4e-05 0.033333 6.36e-05 2.61e-05 0.03375 6.23e-05 3e-05 0.034167 5.24e-05 1.5e-05 0.034583 4.81e-05 2.19e-06 0.035 3.7e-05 -2.96e-06 0.035417 3.02e-05 -5.15e-06 0.035833 2.32e-05 -3.19e-06 0.03625 2.56e-05 3.55e-07 0.036667 2.18e-05 1.55e-06 0.037083 1.8e-05 -2.66e-06 0.0375 1.01e-05 -1.41e-05 0.037917 -5.43e-05 -9.54e-05 0.038333 -6.99e-05 -0.000113 0.03875 -6.85e-05 -0.000107 0.039167 -6.75e-05 -0.000103 0.039583 -6.48e-05 -9.57e-05 0.04 -5.21e-05 -6.97e-05 0.040417 -1.66e-05 -8.3e-06 0.040833 -7.11e-06 1.1e-06 0.04125 -9.89e-06 -5.37e-06 0.041667 -1.06e-05 -7.34e-06 0.042083 -1.41e-05 -1.01e-05 0.0425 -6.71e-06 4.14e-06 0.042917 6.25e-08 2.92e-05 0.043333 7.3e-06 5.1e-05 0.04375 8.75e-06 4.48e-05 0.044167 1.7e-05 5.52e-05 0.044583 1.98e-05 6.75e-05 0.045 2.63e-05 7.14e-05 0.045417 3.58e-05 7.56e-05 0.045833 3.74e-05 6.91e-05 0.04625 3.74e-05 6.47e-05 0.046667 4.09e-05 6.02e-05 0.047083 5.32e-05 6.52e-05 0.0475 6.87e-05 7.24e-05 0.047917 0.000131 0.000135 0.048333 0.000176 0.000176 0.04875 0.000172 0.000163 0.049167 0.000168 0.000161 0.049583 0.000157 0.000152 0.05 0.000137 0.000133 0.050417 9.06e-05 7.19e-05 0.050833 6.81e-05 6.91e-05 0.05125 6.81e-05 9.16e-05 0.051667 6.27e-05 0.000104 0.052083 5.57e-05 0.00011 0.0525 3.63e-05 8.89e-05 0.052917 1.58e-05 4.87e-05 0.053333 8.46e-06 1.64e-05 0.05375 1.13e-05 1.98e-05 0.054167 1.13e-05 1.71e-06 0.054583 2.28e-05 -1.23e-05 0.055 2.99e-05 -1.81e-05 0.055417 3.27e-05 -2.28e-05 0.055833 3.74e-05 -2.92e-05 0.05625 4.59e-05 -3.58e-05 0.056667 5.21e-05 -3.75e-05 0.057083 5.88e-05 -4.37e-05 0.0575 6.03e-05 -4.56e-05 0.057917 1.3e-05 -9.69e-05 0.058333 -3.01e-05 -0.000125 0.05875 -3.79e-05 -0.000102 0.059167 -6.36e-05 -9.18e-05 0.059583 -8.66e-05 -7.56e-05 0.06 -0.000101 -4.96e-05 0.060417 -8.71e-05 2.29e-05 0.060833 -9.01e-05 4.24e-05 0.06125 -0.000103 3.17e-05 0.061667 -0.000112 2.52e-05 0.062083 -0.000121 8.89e-06 0.0625 -0.000124 -7e-06 0.062917 -0.000111 3.93e-06 0.063333 -0.000107 -4.31e-06 0.06375 -9.72e-05 -2.73e-05 0.064167 -7.35e-05 -2.44e-05 0.064583 -5.09e-05 -1.46e-05 0.065 -2.99e-05 -1.21e-05 0.065417 -1.64e-05 -1.5e-05 0.065833 -1.42e-05 -2.74e-05 0.06625 -1.62e-05 -3.41e-05 0.066667 -1.78e-05 -3.41e-05 0.067083 -9.77e-06 -1.65e-05 0.0675 2.99e-06 6.24e-06 0.067917 5.31e-05 8.11e-05 0.068333 0.000101 0.000145 0.06875 9.3e-05 0.000141 0.069167 9.13e-05 0.000142 0.069583 8.5e-05 0.000126 0.07 7.06e-05 0.000103 0.070417 3.97e-05 3.95e-05 0.070833 3.97e-05 3.43e-05 0.07125 5.8e-05 5.52e-05 0.071667 7.04e-05 5.92e-05 0.072083 7.43e-05 5.59e-05 0.0725 7.38e-05 3.49e-05 0.072917 5.84e-05 -8.99e-06 0.073333 6.91e-05 -2.55e-05 0.07375 8.75e-05 -1.27e-05 0.074167 9.86e-05 -1.9e-05 0.074583 0.000109 -2.13e-05 0.075 0.00012 -1.69e-05 0.075417 0.00012 -1.35e-05 0.075833 0.00012 -5.45e-06 0.07625 0.000127 3.02e-06 0.076667 0.00013 9.92e-06 0.077083 0.00013 1.34e-05 0.0775 0.000127 2.26e-05 0.077917 7.65e-05 -2.46e-05 0.078333 3.2e-05 -5.72e-05 0.07875 2.71e-05 -3.99e-05 0.079167 8.17e-06 -3.56e-05 0.079583 -1.37e-07 -2.47e-05 0.08 5.73e-06 4.25e-06 0.080417 4.17e-05 7.24e-05 0.080833 5.02e-05 8.53e-05 0.08125 3.78e-05 7.21e-05 0.081667 2.81e-05 6.8e-05 0.082083 1.36e-05 6.02e-05 0.0825 5.94e-06 6.35e-05 0.082917 9.02e-06 9.83e-05 0.083333 2.33e-06 0.000113 0.08375 -2.2e-06 9.83e-05 0.084167 3.62e-06 0.000108 0.084583 3.91e-06 0.000111 0.085 3.76e-06 0.000108 0.085417 1.52e-06 9.89e-05 0.085833 -7.79e-06 8.3e-05 0.08625 -2.08e-05 6.92e-05 0.086667 -2.47e-05 5.99e-05 0.087083 -3.02e-05 6.28e-05 0.0875 -2.91e-05 6.58e-05 0.087917 1.53e-05 0.000119 0.088333 5.31e-05 0.00016 0.08875 3.94e-05 0.000131 0.089167 3.74e-05 0.000121 0.089583 3.74e-05 9.89e-05 0.09 3.1e-05 6.9e-05 0.090417 1.12e-06 -6.51e-06 0.090833 7.02e-06 -1.85e-05 0.09125 2.86e-05 -3.42e-06 0.091667 4.07e-05 3.16e-07 0.092083 5.32e-05 7.17e-08 0.0925 5.77e-05 -1.32e-05 0.092917 4.67e-05 -4.77e-05 0.093333 5.19e-05 -5.85e-05 0.09375 6.39e-05 -4.37e-05 0.094167 6.5e-05 -4.44e-05 0.094583 6.47e-05 -4.77e-05 0.095 5.75e-05 -3.81e-05 0.095417 4.84e-05 -3.27e-05 0.095833 4.23e-05 -1.81e-05 0.09625 4.97e-05 -3.87e-06 0.096667 5.77e-05 1.04e-05 0.097083 6.76e-05 1.27e-05 0.0975 7.43e-05 1.14e-05 0.097917 3.52e-05 -4.99e-05 0.098333 1.42e-05 -9.43e-05 0.09875 3.72e-05 -8.13e-05 0.099167 5.16e-05 -8.16e-05 0.099583 6.85e-05 -6.28e-05 0.1 8.66e-05 -3.01e-05

4. ## Re: Cross Correlation analysis with two series of wavelets

I plotted the data and the peak from the last column is higher, but both peak widths are the same. What info would you like. I do not think it is possible to detect any lag between the peaks hitting a maximum because there are very few data points maybe 5 that define the peak

5. ## Re: Cross Correlation analysis with two series of wavelets

Sorry my apologies, I pasted the top of the data then went home after work. The top of the data doesn't show anything really. This shows a bit more. Peak or trough is required. So in this data set the troughs would be appropriate

 3.495 0.003115 0.001985 3.49542 0.003294 0.001946 3.49583 0.003429 0.001883 3.49625 0.003548 0.001806 3.49667 0.003639 0.00173 3.49708 0.003709 0.001679 3.4975 0.00374 0.001686 3.49792 0.003703 0.001711 3.49833 0.003556 0.001727 3.49875 0.003412 0.00184 3.49917 0.003209 0.00191 3.49958 0.002988 0.00197 3.5 0.002736 0.002007 3.50042 0.002539 0.002056 3.50083 0.00238 0.002056 3.50125 0.002244 0.001977 3.50167 0.002132 0.001892 3.50208 0.002012 0.001765 3.5025 0.001865 0.001573 3.50292 0.001694 0.001352 3.50333 0.001466 0.00108 3.50375 0.001204 0.000792 3.50417 0.000926 0.000546 3.50458 0.000611 0.000363 3.505 0.000216 0.000193 3.50542 -0.00027 1.13e-05 3.50583 -0.00083 -0.0002 3.50625 -0.00146 -0.00044 3.50667 -0.0021 -0.0007 3.50708 -0.00272 -0.00093 3.5075 -0.0033 -0.00116 3.50792 -0.00379 -0.00136 3.50833 -0.00414 -0.00153 3.50875 -0.00447 -0.00182 3.50917 -0.0047 -0.00212 3.50958 -0.00487 -0.00245 3.51 -0.005 -0.00281 3.51042 -0.00507 -0.00321 3.51083 -0.00503 -0.00353 3.51125 -0.0049 -0.00374 3.51167 -0.00471 -0.00392 3.51208 -0.00446 -0.00408 3.5125 -0.00413 -0.00423 3.51292 -0.00377 -0.00436 3.51333 -0.00335 -0.00441 3.51375 -0.00291 -0.00437 3.51417 -0.00247 -0.00429 3.51458 -0.00203 -0.00419 3.515 -0.00159 -0.00403 3.51542 -0.00119 -0.00382 3.51583 -0.00081 -0.00354 3.51625 -0.00046 -0.00321 3.51667 -0.00015 -0.00284 3.51708 0.000113 -0.00245 3.5175 0.000305 -0.00205 3.51792 0.000438 -0.00168 3.51833 0.000519 -0.00134 3.51875 0.000652 -0.00089 3.51917 0.000708 -0.00047 3.51958 0.000729 -3.4e-05 3.52 0.000687 0.000389 3.52042 0.000608 0.000794 3.52083 0.000495 0.001104 3.52125 0.000324 0.001285 3.52167 9.63e-05 0.001408 3.52208 -0.00016 0.001494 3.5225 -0.00041 0.00155 3.52292 -0.00059 0.001613 3.52333 -0.00074 0.001605 3.52375 -0.0009 0.001497 3.52417 -0.00104 0.001325 3.52458 -0.00112 0.001144 3.525 -0.00117 0.000966 3.52542 -0.00117 0.000823 3.52583 -0.00108 0.000694 3.52625 -0.00091 0.000594 3.52667 -0.0007 0.000532 3.52708 -0.00048 0.000521 3.5275 -0.00025 0.000531 3.52792 7.3e-06 0.000578 3.52833 0.000349 0.000716 3.52875 0.00063 0.000816 3.52917 0.000928 0.001012 3.52958 0.0012 0.001246 3.53 0.001466 0.001472 3.53042 0.00167 0.001611 3.53083 0.001849 0.001731 3.53125 0.002003 0.001878 3.53167 0.002096 0.001979 3.53208 0.002182 0.002091 3.5325 0.002285 0.002206 3.53292 0.002406 0.002279 3.53333 0.002551 0.002348 3.53375 0.002706 0.002393 3.53417 0.002852 0.002379 3.53458 0.002982 0.002315 3.535 0.003103 0.002254 3.53542 0.003205 0.002189 3.53583 0.003291 0.002122 3.53625 0.003371 0.002048 3.53667 0.003442 0.00195 3.53708 0.003479 0.001838 3.5375 0.003489 0.001761 3.53792 0.003459 0.001702 3.53833 0.003374 0.001643 3.53875 0.003342 0.00171 3.53917 0.003263 0.001756 3.53958 0.003165 0.001798 3.54 0.003017 0.001825 3.54042 0.002874 0.001881 3.54083 0.002682 0.001888 3.54125 0.002449 0.001827 3.54167 0.00222 0.00178 3.54208 0.001999 0.001719 3.5425 0.001765 0.001628 3.54292 0.001566 0.001529 3.54333 0.00135 0.001367 3.54375 0.001121 0.001136 3.54417 0.00086 0.000885 3.54458 0.000536 0.000623 3.545 0.000138 0.000342 3.54542 -0.00029 6.72e-05 3.54583 -0.00077 -0.00019 3.54625 -0.00132 -0.00044 3.54667 -0.00191 -0.00068 3.54708 -0.00251 -0.00091 3.5475 -0.00311 -0.00115 3.54792 -0.00366 -0.00138 3.54833 -0.00412 -0.00158 3.54875 -0.00458 -0.00188 3.54917 -0.00492 -0.00215 3.54958 -0.00515 -0.00243 3.55 -0.00526 -0.00272 3.55042 -0.00531 -0.00307 3.55083 -0.00526 -0.00339 3.55125 -0.00508 -0.00366 3.55167 -0.00483 -0.00394 3.55208 -0.00451 -0.00418 3.5525 -0.00415 -0.00438 3.55292 -0.00378 -0.00454 3.55333 -0.00335 -0.00461 3.55375 -0.0029 -0.00459 3.55417 -0.00247 -0.00451 3.55458 -0.00208 -0.0044 3.555 -0.00173 -0.00422 3.55542 -0.00141 -0.004 3.55583 -0.00108 -0.00372 3.55625 -0.00077 -0.00338 3.55667 -0.00047 -0.00298 3.55708 -0.00019 -0.00257 3.5575 8.75e-05 -0.00215 3.55792 0.000319 -0.00176 3.55833 0.000493 -0.00143 3.55875 0.000688 -0.00102 3.55917 0.000791 -0.00064 3.55958 0.000846 -0.00024 3.56 0.000862 0.000145 3.56042 0.000833 0.000543 3.56083 0.000738 0.000879 3.56125 0.00056 0.001115 3.56167 0.000355 0.001324 3.56208 0.000147 0.001476 3.5625 -7.3e-05 0.001586 3.56292 -0.00027 0.001671 3.56333 -0.00046 0.001679 3.56375 -0.00065 0.0016 3.56417 -0.00079 0.001485 3.56458 -0.00087 0.00136 3.565 -0.00092 0.001206 3.56542 -0.00092 0.001057 3.56583 -0.00089 0.000903 3.56625 -0.00085 0.000769 3.56667 -0.00079 0.000657 3.56708 -0.00072 0.000595 3.5675 -0.00064 0.000576 3.56792 -0.00049 0.000638 3.56833 -0.00021 0.000808 3.56875 4.79e-05 0.000932 3.56917 0.000385 0.001122 3.56958 0.00077 0.001288 3.57 0.001197 0.001422 3.57042 0.001565 0.001463 3.57083 0.001884 0.001503 3.57125 0.002141 0.001604 3.57167 0.002322 0.001716 3.57208 0.002467 0.001869 3.5725 0.002583 0.002053 3.57292 0.00265 0.002205 3.57333 0.002726 0.002355 3.57375 0.002815 0.002467

Is the kind of thing I'm looking for possible? Cheers for your reply

6. ## Re: Cross Correlation analysis with two series of wavelets

I used conditional formatting to find all the minima in cols B and C using =and(b2
are you interested in the time difference between each pair of minima or the minimum value itself

PM me if you want to continue off line as I think there is nothing fundamental of interest to the general forum readers

7. ## Re: Cross Correlation analysis with two series of wavelets

Uisng formulas, you can see that the correlation of the first 150 samples of W1 peaks with a 5-sample delay to W2:

 Row\Col A B C D E F G 1 T W1 W2 Offset 2 3.4950 0.0031 0.0020 0 0.825 F2: =CORREL(\$B\$2:\$B\$151, INDEX(\$C\$2:\$C\$191, E2 + 1):INDEX(\$C\$2:\$C\$191, E2 + 150)) 3 3.4954 0.0033 0.0019 1 0.856 4 3.4958 0.0034 0.0019 2 0.882 5 3.4963 0.0035 0.0018 3 0.902 6 3.4967 0.0036 0.0017 4 0.916 7 3.4971 0.0037 0.0017 5 0.923 8 3.4975 0.0037 0.0017 6 0.921 9 3.4979 0.0037 0.0017 7 0.910 10 3.4983 0.0036 0.0017 8 0.890 11 3.4988 0.0034 0.0018 9 0.859 12 3.4992 0.0032 0.0019 10 0.819 13 3.4996 0.0030 0.0020 11 0.769 14 3.5000 0.0027 0.0020 12 0.710 15 3.5004 0.0025 0.0021 13 0.644 16 3.5008 0.0024 0.0021 14 0.570 17 3.5013 0.0022 0.0020 15 0.490 18 3.5017 0.0021 0.0019 16 0.405 19 3.5021 0.0020 0.0018 17 0.317 20 3.5025 0.0019 0.0016 18 0.226 21 3.5029 0.0017 0.0014 19 0.135 22 3.5033 0.0015 0.0011 20 0.044 23 3.5038 0.0012 0.0008 21 -0.045 24 3.5042 0.0009 0.0005 22 -0.130 25 3.5046 0.0006 0.0004 26 3.5050 0.0002 0.0002 27 3.5054 -0.0003 0.0000 28 3.5058 -0.0008 -0.0002 29 3.5063 -0.0015 -0.0004 30 3.5067 -0.0021 -0.0007 31 3.5071 -0.0027 -0.0009 32 3.5075 -0.0033 -0.0012 33 3.5079 -0.0038 -0.0014

8. ## Re: Cross Correlation analysis with two series of wavelets

EDIT: For the first set of data, which has smaller time values, the correlation peak is at 0 offset. Maybe a better test is to see what time dilation of W1 is a best fit for W2. Does that make sense?

9. ## Re: Cross Correlation analysis with two series of wavelets

shg, I've not tried this yet but this is EXACTLY what I'm looking for!! Makes perfect sense I'll get back to you

10. ## Re: Cross Correlation analysis with two series of wavelets

Works perfectly! Thank you, you've no idea how much time I've spent trying to figure this out.

What do you mean by time dilation? Do you mean the amount of time change between the two waves as if one was stretched? If so how would I go about this?

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