Fitting linear decay to a semilogarithmic line

Question

I am trying to fit this set of data,I tried a simple linear model but it didn't yield successful results, I also tried curve_fit on Python but also no luck - here they are normalized to match peaks:

Is there a function where I can just fit to the peak without it turning into an exponential growth function?

        data1 = {{947.57, 37.8841}, {947.65, 32.8244}, {947.729, 25.9307}, {947.809, 
  29.0297}, {947.889, 36.9354}, {947.968, 34.7851}, {948.048, 
  29.4724}, {948.127, 29.3459}, {948.207, 30.3579}, {948.286, 
  35.9867}, {948.365, 31.7493}, {948.445, 34.5321}, {948.524, 
  33.8364}, {948.604, 37.6311}, {948.683, 35.6072}, {948.762, 
  32.7612}, {948.842, 32.3817}, {948.921, 38.5798}, {949., 
  37.9473}, {949.079, 31.4963}, {949.158, 31.8758}, {949.238, 
  36.8722}, {949.317, 35.1645}, {949.396, 37.3781}, {949.475, 
  36.1765}, {949.554, 34.9748}, {949.633, 33.7731}, {949.712, 
  37.7576}, {949.791, 32.6347}, {949.87, 33.9629}, {949.949, 
  34.8483}, {950.028, 42.1215}, {950.107, 35.8602}, {950.185, 
  33.0774}, {950.264, 34.5953}, {950.343, 39.2122}, {950.422, 
  45.5368}, {950.501, 35.9235}, {950.579, 35.291}, {950.658, 
  36.9354}, {950.737, 48.2564}, {950.815, 43.4497}, {950.894, 
  33.5834}, {950.973, 38.0738}, {951.051, 44.9676}, {951.13, 
  44.6514}, {951.208, 34.0261}, {951.287, 41.7421}, {951.365, 
  46.8017}, {951.444, 50.3435}, {951.522, 40.2242}, {951.601, 
  39.8447}, {951.679, 39.402}, {951.757, 46.9914}, {951.836, 
  45.9795}, {951.914, 45.6}, {951.992, 40.2242}, {952.071, 
  44.6514}, {952.149, 49.711}, {952.227, 45.4103}, {952.305, 
  36.8722}, {952.383, 39.5285}, {952.462, 52.7468}, {952.54, 
  47.5607}, {952.618, 38.8328}, {952.696, 41.4891}, {952.774, 
  45.853}, {952.852, 47.3077}, {952.93, 49.1418}, {953.008, 
  45.9163}, {953.086, 42.4378}, {953.164, 48.0034}, {953.242, 
  52.1776}, {953.32, 50.5332}, {953.397, 41.3626}, {953.475, 
  48.4461}, {953.553, 46.5487}, {953.631, 50.7862}, {953.708, 
  44.9043}, {953.786, 44.5249}, {953.864, 50.217}, {953.942, 
  56.0988}, {954.019, 50.8494}, {954.097, 50.9759}, {954.174, 
  49.3948}, {954.252, 56.0356}, {954.33, 63.372}, {954.407, 
  53.316}, {954.485, 48.8256}, {954.562, 56.0988}, {954.639, 
  67.0403}, {954.717, 60.5892}, {954.794, 53.2528}, {954.872, 
  53.569}, {954.949, 62.3601}, {955.026, 66.3446}, {955.104, 
  64.7634}, {955.181, 61.3482}, {955.258, 63.625}, {955.335, 
  75.3887}, {955.413, 74.693}, {955.49, 66.3446}, {955.567, 
  64.2575}, {955.644, 72.8589}, {955.721, 76.4639}, {955.798, 
  73.9341}, {955.875, 75.5784}, {955.952, 70.7718}, {956.029, 
  79.2467}, {956.106, 82.9149}, {956.183, 74.8195}, {956.26, 
  75.8947}, {956.337, 76.2741}, {956.414, 75.8314}, {956.491, 
  84.2431}, {956.567, 82.5987}, {956.644, 84.3063}, {956.721, 
  87.4054}, {956.798, 92.971}, {956.874, 100.497}, {956.951, 
  98.7896}, {957.028, 104.292}, {957.104, 106.379}, {957.181, 
  107.391}, {957.258, 117.447}, {957.334, 121.937}, {957.411, 
  124.783}, {957.487, 131.551}, {957.564, 138.002}, {957.64, 
  146.919}, {957.717, 145.781}, {957.793, 149.07}, {957.87, 
  149.07}, {957.946, 157.861}, {958.022, 169.751}, {958.099, 
  172.597}, {958.175, 179.175}, {958.251, 175.633}, {958.327, 
  186.638}, {958.404, 210.165}, {958.48, 203.967}, {958.556, 
  201.69}, {958.632, 182.716}, {958.708, 188.345}, {958.784, 
  214.402}, {958.86, 209.533}, {958.936, 173.609}, {959.012, 
  145.149}, {959.088, 149.386}, {959.164, 168.992}, {959.24, 
  145.907}, {959.316, 98.8528}}
    
    

Ideally the fit should look like this:

another image for clarity:

Answer 1

It would be helpful if there is a model to fit taken from some considerations that come from the core of the problem. If this is not available, try this:

Manipulate[data2 = data1 /. {x_, y_} -> {x, y - 34};
 model = a + b*Exp[-c*((x - x0)^2)^z];
 ff = FindFit[data2, model, {{a, 30}, b, c, {x0, 959}}, x];
 Row[{Show[{
     ListPlot[data2, PlotRange -> All],
     Plot[model /. ff, {x, 948, 960}, PlotStyle -> Red]
     }, ImageSize -> 250],
   Show[{
     ListLogPlot[data2, PlotRange -> All],
     LogPlot[model /. ff, {x, 948, 960}, PlotStyle -> Red]
     }, ImageSize -> 250]
   }], {{z, 0.424}, 0.2, 0.9, Appearance -> "Labeled"}]

It returns this:

I hope I understood you right, and it is something you are looking for.

Have fun!

Answer 2

You could try a truncated Fourier series:

poly = LinearModelFit[data1, 
  Join[Table[Sin[i 0.1 x  i], {i, 4}], Table[Cos[0.1 x i ], {i, 4}]], 
  x]
Plot[poly[x], {x, 947.5, 960}, Epilog -> Point[data1]]