Characterizing the degree of amplitude‐variation‐with‐offset nonlinearity in seismic physical modelling reflection data. (14th October 2014)

• Record Type: Journal Article
• Authors: Innanen, Kristopher A.; Mahmoudian, Faranak
• Is Part Of: Geophysical prospecting. Volume 63:Number 1(2015:Jan.)
• Page Start: 133
• Page End: 140
• Publication Date: 2014-10-14
• Subjects: Prospecting -- Geophysical methods -- Periodicals; 622.15
• DOI: 10.1111/1365-2478.12169
• Languages: English
• ISSNs: 0016-8025

Abstract

<abstract abstract-type="main"> <title>ABSTRACT</title> <p>The nonlinearity of the seismic amplitude‐variation‐with‐offset response is investigated with physical modelling data. Nonlinearity in amplitude‐variation‐with‐offset becomes important in the presence of large relative changes in acoustic and elastic medium properties. A procedure for pre‐processing physical modelling reflection data is enacted on the reflection from a water‐plexiglas boundary. The resulting picked and processed amplitudes are compared with the exact solutions of the plane‐wave Zoeppritz equations, as well as <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t9fb" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>PP</mml:mtext></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>θ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives></inline-formula> approximations that are first, second, and third order in <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t9hf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi>P</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t9kj" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi>S</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, and <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t9m3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>ρ</mml:mi><mml:mo>/</mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>. In the low angle range of 0°–20°, the third‐order plane‐wave approximation is sufficient to capture the nonlinearity of the amplitude‐variation‐with‐offset response of a liquid‐solid boundary with <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t928" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0005" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>V</mml:mi><mml:mi>P</mml:mi></mml:msub></mml:math></alternatives></inline-formula>, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t91q" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0006" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>V</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>, and ρ contrasts of 1485–2745 m/s, 0–1380 m/s, and 1.00–1.19 gm/cc respectively, to an accuracy value of roughly 1%. This is in contrast to the linear Aki–Richards approximation, which is in error by as much as 25% in the same angle range. Even‐order nonlinear corrective terms are observed to be primarily involved in correcting the angle dependence of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2xq0t94c" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00168025:media:gpr12169:gpr12169-math-0007" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mtext>PP</mml:mtext></mml:msub></mml:math></alternatives></inline-formula>, whereas the odd‐order nonlinear terms are involved in determining the absolute amplitude‐variation‐with‐offset magnitudes.</p> </abstract>