You can try something like this:

Qt Code: 
  1. class MyTransform: public QwtTransform
  2. {
  3. public:
  4.     MyTransform( double threshold ):
  5.         m_threshold( threshold ),
  6.         m_offset( threshold - log( threshold ) )
  7.     {
  8.     }
  9.  
  10.     virtual double transform( double value ) const
  11.     {
  12.         double v = qAbs( value );
  13.         if ( v > m_threshold )
  14.             v = m_offset + log( v );
  15.  
  16.         return value < 0.0 ? -v : v;
  17.     }
  18.  
  19.     virtual double invTransform( double value ) const
  20.     {
  21.         double v = qAbs( value );
  22.         if ( v > m_offset )
  23.             v = qExp( v ) - m_offset;
  24.  
  25.         return value < 0.0 ? -v : v;
  26.     }
  27.  
  28.     virtual double bounded( double value ) const
  29.     {
  30.         return value;
  31.     }
  32.  
  33.     virtual QwtTransform *copy() const
  34.     {
  35.         return new MyTransform( m_threshold );
  36.     }
  37.  
  38. private:
  39.     const double m_threshold;
  40.     const double m_offset;
  41. };
  42.  
  43. ...
  45. scaleEngine->setTransformation( new MyTransform( 10.0 ) );
  46. plot->setAxisScaleEngine( QwtPlot::yLeft, scaleEngine );
  47.  
  48. QwtScaleDiv scaleDiv( -10000.0, 10000.0 );
  49.  
  50. QList<double> majorTicks;
  51. majorTicks << -10000 << -1000 << -100 << -10 << -8 << -6 << -4 << -2 << 0 << 2 << 4 << 6 << 8 << 10 << 100 << 1000 << 10000;
  52. scaleDiv.setTicks( QwtScaleDiv::MajorTick, majorTicks );
  53.  
  54. plot->setAxisScaleDiv( QwtPlot::yLeft, scaleDiv );
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If you can't set the ticks manually ( f.e. your application supports zooming ) you also have to implement your own type of QwtScaleEngine.

Uwe