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This is the example density depth functions for various sedimentary sections world wide. But someof the sections marked with red, due to their last term, as i increase the value of z(depth) they become negative. But density can never be negative? What could be other possible reason for enter image description here

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    $\begingroup$ What's the source of the table? It could just be a unit problem. For example, if you input the depth in kilometers you'll get more reasonable, positive values until a greater depth. The density seems to be in g/cm3 instead of kg/m3, so you never know... The unit of $z$ is not mentioned in the caption but could be in the main text. $\endgroup$ Oct 30, 2023 at 6:13
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    $\begingroup$ Those a local, second order fits to data. They cannot be valid globally (i.e. for all z). Search in the text what the limitations on the validity of the fit in z is. $\endgroup$ Oct 30, 2023 at 15:30
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    $\begingroup$ Mark, you need to get in the habit of giving additional explanation of where these tables you keep asking about are from. This has been a consistent problem with your questions. Context is important to asking worthwhile questions. Otherwise it's only answering the question for you, and without key information often. -1 $\endgroup$ Oct 31, 2023 at 6:54

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You are looking at low order polynomial approximations of density. Such approximations are only valid over a certain range, typically the range over which the underlying data were collected. Applying the polynomial to a value well outside that range, which is what you are doing, is quite simply invalid. "Garbage in, garbage out."

Do not extrapolate.

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